SEARCH · Search NASA

Results for “Diffusion model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,045 records · Page 58

All sources NASA NTRS DOE OSTI

NASA NTRS1991

A study of hydrogen diffusion flames using PDF turbulence model

The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

Hsu, Andrew T.↗

DOE OSTI2025

An Investigation of Thermal Properties of 2D Materials [Dissertation]

Studying the thermal conductivity of 2D materials is important due to the applications of 2D materials in fields such as thermal management, thermoelectricity, renewable energy, and sensors. As such, measurements of the thermal conductivity of these 2D materials become important to measure. Thermal conductivity is often difficult to measure for 2D materials due to their atomically thin nature and many experimental methods for doing so requiring contact with the sample, which can alter the thermal properties. A non-contact method for calculating the thermal conductivity of 2D materials supported on substrates in order to model the thermal conductivity of 2D materials for devices, is proposed and experimentally performed in this dissertation. The optothermal Raman technique is a useful non-contact diagnostic technique useful in determining the thermal conductivity of 2D materials. The optothermal Raman typically does not account for heat losses due to convection or radiation or substrate resistance, which are shown to be important factors to consider when developing an optothermal Raman model. Additionally, the calculation of the interfacial thermal conductance between the bottom surface of the sample and the top surface of the substrate, plays an important role in determining the final value of the thermal conductivity of a supported sample, and will yield differing results based on whether or not the conductance is calculated using an approach such as the Diffuse Mismatch Model (DMM) or calculated directly by varying the laser heating profile (usually done by changing the laser objective). This is shown to be the case for both graphene on Ni, graphene on Cu, and SnSe 2 on Cu. In addition to experimentally calculating the thermal conductivity of a 2D material with the optothermal Raman technique, the thermal conductivity of 2D materials can also be calculated using computational methods. The three-phonon method is a method which can be used to simulate phonon scattering processes and determine the thermal conductivity of semiconductors, wherein phonon scattering is the dominant mechanism which determines the thermal conductivity. The three-phonon method uses relaxation times for phonon scattering with other phonons, electrons, and other material system elements, such as isotopes or material defects, in order to create a single-mode relaxation time approximation (SMRTA), which is used to calculate the final value of the thermal conductivity. An important consideration when determining the thermal conductivity of a 2D material using this method is the device geometry, which is reflected in this work as the phonon-boundary scattering relaxation time. This inclusion is important along with the inclusion of phonon-electron scattering in accurately determining the thermal conductivity of a 2D material. In both the optothermal Raman experiments and the three-phonon method computations, strain is shown to have a demonstrable effect on the thermal conductivity of 2D materials. When a 1.1% strain was applied to the mechanical properties of SnSe, the three-phonon processes yielded a lower thermal conductivity than the no-strain case. For the optothermal Raman experiments, the strain induced in the Cu substrate and transferred to a single-layer graphene (SLG) sample yields a trend where the thermal conductivity of the SLG decreases with respect to strain applied. In the case where the interfacial thermal conductance was calculated directly, the conductance increased with respect to strain applied. This presents strain as a reliable and viable method for tuning the thermal properties of 2D materials for device applications.

36 MATERIALS SCIENCE↗

NASA NTRS2016

ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES) - Merging Observations and Laboratory Data

The Diffuse Interstellar Bands (DIBs) are a set of ~500 absorption bands that are detected in the spectra of stars with interstellar clouds in the line of sight. DIBs are found from the NUV to the NIR in the spectra of reddened stars spanning different interstellar environments in our local, and in other galaxies. DIB carriers are a significant part of the interstellar chemical inventory. They are stable and ubiquitous in a broad variety of environments and play a unique role in interstellar physics/chemistry. It has long been realized that the solving of the DIB problem requires a strong synergy between astronomical observations, laboratory astrophysics, and astrophysical modeling of line-of-sights. PAHs are among the molecular species that have been proposed as DIB carriers. We will present an assessment of the PAH-DIB model in view of the progress and the advances that have been achieved over the past years through a series of studies involving astronomical observations of DIBs, laboratory simulation of interstellar analogs for neutrals and ionized PAHs, theoretical calculations of PAH spectra and the modelization of diffuse and translucent interstellar clouds. We will present a summary of what has been learned from these complementary studies, the constraints that can now be derived for the PAHs as DIB carriers in the context of the PAH-DIB model and how these constraints can be applied to the EDIBLES project. The spectra of several neutral and ionized PAHs isolated in the gas phase at low temperature have been measured in the laboratory under experimental conditions that mimic interstellar conditions and are compared with an extensive set of astronomical spectra of reddened, early type stars. The comparisons of astronomical and laboratory data provide upper limits for the abundances of specific neutral PAH molecules and ions along specific lines-of-sight. Something that is not attainable from infrared observations alone. We present the characteristics of the laboratory facilities, MIS and COSmIC, that have been developed for this study and discuss the findings resulting from the comparison of the laboratory data with high resolution, high S/N ratio astronomical observations. MIS stands for Matrix Isolation Spectroscopy, a well-proven technique for isolating cold molecular species in inert solid environments. COSmIC stands for Cosmic Simulation Chamber. It combines a supersonic free jet expansion with discharge plasma and high-sensitivity cavity ringdown spectroscopy and time-of-flight mass spectrometry detection tools for the generation and the detection of cold, isolated gas-phase molecules and ions under experimental conditions that closely mimic interstellar conditions. The column densities of the individual neutral PAH molecules and ions probed in these surveys are derived from the comparison of these unique laboratory data with high resolution, high S/N ratio astronomical observations. The comparisons of astronomical and laboratory data lead to clear and unambiguous conclusions regarding the expected abundances for PAHs of various sizes and charge states in the interstellar environments probed in the surveys. Band profile comparisons between laboratory and astronomical spectra lead to information regarding the molecular structures and characteristics associated with the DIB carriers in the corresponding lines-of-sight. These quantitative surveys of neutral and ionized PAHs in the optical range open the way for unambiguous quantitative searches of PAHs and complex organics in a variety of interstellar and circumstellar environments.

astrophysics↗

DOE OSTI2020

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.

42 ENGINEERING↗

NASA NTRS1990

Evaluation of a hybrid kinetics/mixing-controlled combustion model for turbulent premixed and diffusion combustion using KIVA-2

Two dimensional calculations were made of spark ignited premixed-charge combustion and direct injection stratified-charge combustion in gasoline fueled piston engines. Results are obtained using kinetic-controlled combustion submodel governed by a four-step global chemical reaction or a hybrid laminar kinetics/mixing-controlled combustion submodel that accounts for laminar kinetics and turbulent mixing effects. The numerical solutions are obtained by using KIVA-2 computer code which uses a kinetic-controlled combustion submodel governed by a four-step global chemical reaction (i.e., it assumes that the mixing time is smaller than the chemistry). A hybrid laminar/mixing-controlled combustion submodel was implemented into KIVA-2. In this model, chemical species approach their thermodynamics equilibrium with a rate that is a combination of the turbulent-mixing time and the chemical-kinetics time. The combination is formed in such a way that the longer of the two times has more influence on the conversion rate and the energy release. An additional element of the model is that the laminar-flame kinetics strongly influence the early flame development following ignition.

Nguyen, H. Lee↗

NASA NTRS1990

Evaluation of a hybrid kinetics/mixing-controlled combustion model for turbulent premixed and diffusion combustion using KIVA-II

Two-dimensional calculations were made of spark ignited premixed-charge combustion and direct injection stratified-charge combustion in gasoline fueled piston engines. Results are obtained using kinetic-controlled combustion submodel governed by a four-step global chemical reaction or a hybrid laminar kinetics/mixing-controlled combustion submodel that accounts for laminar kinetics and turbulent mixing effects. The numerical solutions are obtained by using KIVA-2 computer code which uses a kinetic-controlled combustion submodel governed by a four-step global chemical reaction (i.e., it assumes that the mixing time is smaller than the chemistry). A hybrid laminar/mixing-controlled combustion submodel was implemented into KIVA-2. In this model, chemical species approach their thermodynamics equilibrium with a rate that is a combination of the turbulent-mixing time and the chemical-kinetics time. The combination is formed in such a way that the longer of the two times has more influence on the conversion rate and the energy release. An additional element of the model is that the laminar-flame kinetics strongly influence the early flame development following ignition.

Nguyen, H. Lee↗

NASA NTRS1982

Diffusion instability in a bimodal disc

A simplified model of radial diffusion in a planetary disk with a bimodal size distribution is presented. The large particle component excites the small particles' dispersion velocity via gravitational scattering. The resulting small particle viscous stress goes through a maximum near optical depth = sq root 3. Such a stress profile promotes the development of high and low optical depth zones. The resulting ringlet appearance is due primarily to the distribution of small particles, which produce most of the optical depth but may constitute only a minor portion of system mass.

Ward, W. R.↗

NASA NTRS2000

Formation of Leading-Edge Pinholes in the Space Shuttle Wings Investigated

The space shuttle wing leading edge and nose cap are composed of a carbon/carbon composite that is protected by silicon carbide. The coefficient of thermal expansion mismatch leads to cracks in the silicon carbide. The outer coating of the silicon carbide is a sodium-silicate-based glass that becomes fluid at the shuttles high reentry temperatures and fills these cracks. Small pinholes roughly 0.1 mm in diameter have been observed on these materials after 12 or more flights. These pinholes have been investigated by researchers at the NASA Johnson Space Center, Rockwell International, the Boeing Company, Lockheed Martin Corporation, and the NASA Glenn Research Center at Lewis Field to determine the possible sources and the extent of damage. A typical pinhole is illustrated in the photomicrographs. These pinholes are found primarily on the wing leading edges and not on the nose cap, which is covered when the orbiter is on the launch pad. The pinholes are generally associated with a bead of zincrich glass. Examination of the orbiter and launch structure indicates that weathering paint on the launch structure leads to deposits of zinc-containing paint flakes on the wing leading edge. These may become embedded in the crevices of the wing leading edge and form the observed zinc-rich glass. Laboratory experiments indicate that zinc oxide reacts vigorously with the glass coating on the silicon carbide. Thus, it is likely that this is the reaction that leads to pinhole formation (Christensen, S.V.: Reinforced Carbon/Carbon Pin Hole Formation Through Zinc Oxide Attack. Rockwell International Internal Letter, RDW 96 057, May 1996). Cross-sectional examination of pinholes suggests that they are enlarged thermal expansion mismatch cracks. This is illustrated in the photomicrographs. A careful microstructural analysis indicates that the pinhole walls consist of layers of zinc-containing glass. Thus, pinholes are likely formed by zinc oxide particles lodging in crevices and forming a corrosive zinc-rich glass that enlarges existing cracks. Having established the likely source of the pinholes, we next needed to model the damage. Our concern was that if a pinhole went through the silicon carbide to the carbon/carbon substrate, oxygen would have a clear path to oxidize the carbon at high temperatures. This possibility was examined with studies in a laboratory furnace. An ultrasonic drill was used to make artificial pinholes in a sample of protected carbon/carbon. After exposure, the specimens were weighed and cross-sectioned to quantify the extent of oxidation below the pinhole. The results at higher temperatures showed good agreement with a simple diffusion-control model. This model is based on the two-step oxidation of carbon to carbon monoxide and carbon dioxide. The fluxes are illustrated in the final figure. The model indicates a strong dependence on pinhole diameter. For smaller diameters and short times, the oxidation of carbon is very limited.

Jacobson, Nathan S.↗

NASA NTRS1994

Evaluation of turbulence models in the PARC code for transonic diffuser flows

Flows through a transonic diffuser were investigated with the PARC code using five turbulence models to determine the effects of turbulence model selection on flow prediction. Three of the turbulence models were algebraic models: Thomas (the standard algebraic turbulence model in PARC), Baldwin-Lomax, and Modified Mixing Length-Thomas (MMLT). The other two models were the low Reynolds number k-epsilon models of Chien and Speziale. Three diffuser flows, referred to as the no-shock, weak-shock, and strong-shock cases, were calculated with each model to conduct the evaluation. Pressure distributions, velocity profiles, locations of shocks, and maximum Mach numbers in the duct were the flow quantities compared. Overall, the Chien k-epsilon model was the most accurate of the five models when considering results obtained for all three cases. However, the MMLT model provided solutions as accurate as the Chien model for the no-shock and the weak-shock cases, at a substantially lower computational cost (measured in CPU time required to obtain converged solutions). The strong shock flow, which included a region of shock-induced flow separation, was only predicted well by the two k-epsilon models.

Georgiadis, N. J.↗

NASA NTRS1999

Mechanism for Surface Warming in the Equatorial Pacific during 1994-95

Mechanisms controlling the variation in sea surface temperature warm event in the equatorial Pacific were investigated through ocean model simulations. In addition, the mechanisms of the climatological SST cycle were investigated. The dominant mechanisms governing the seasonal cycle of SST vary significantly across the basin. In the western Pacific the annual cycle of SST is primarily in response to external heat flux. In the central basin the magnitude of zonal advection is comparable to that of the external heat flux. In the eastern basin the role of zonal advection is reduced and the vertical mixing is more important. In the easternmost equatorial Pacific the vertical entrainment contribution is as large as that of vertical diffusion. The model estimate of the vertical mixing contribution to the mixed layer heat budget compared well with estimates obtained by analysis of observations using the same diagnostic vertical mixing scheme. During 1994- 1995 the largest positive SST anomaly was observed in the mid-basin and was related to reduced latent heat flux due to weak surface winds. In the western basin the initial warming was related to enhanced external heating and reduced cooling effects of both vertical mixing and horizontal advection associated with weaker than usual wind stress. In the eastern Pacific where winds were not significantly anomalous throughout 1994-1995, only a moderate warm surface anomaly was detected. This is in contrast to strong El Nino events where the SST anomaly is largest in the eastern basin and, as shown by previous studies, the anomaly is due to zonal advection rather than anomalous surface heat flux. The end of the warm event was marked by cooling in July 1995 everywhere across the equatorial Pacific.

Rienecker, Michele M.↗

DOE OSTI2018

Effects of Electric and Magnetic Fields on the Spin Current in Organic Spintronic Devices

Organic semiconductors are suitable for spin transport because of the extremely long spin-diffusion length, which stems from the weak spin-orbit coupling. In this article, the drift-diffusion transport model to evaluate the spin current in a ferromagnetic/organic semiconductor structure is studied. Effects of the spin-dependent interfacial conductance, temperature and the polarization of the FM bulk on the spin current are discussed in the existence of the electric and magnetic fields. It is obtained that the electric and magnetic fields increase the spin current significantly.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗

NASA NTRS1984

A generalized behavioral model for rotating short period comets with spectral orbital elements and axial orientation

A generalized model for short period comets is developed which integrates in a fairly rigorous manner the isolation history of regions on rotating comets with specified axial orientation and the complex feedback processes involving heat, gas and dust transport, dust mantle development and coma opacity. Attention is focused on development, reconfiguration and partial or complete launching of dust mantles and the reciprocal effects of these three processes on ice surface temperature and gas and dust production. The dust mantle controls the H2O flux not only by its effect on the temperature at the ice interface but (dominantly) by its dynamic stability which strongly influences vapor diffusivity. The model includes the effects of latitude, rotation and spin axis orientation are included and applied to an initially homogeneous sphere of H2O ice and silicate using the orbital parameters of comet Encke. Numerous variations of the model, using combinations of grain size distribution, dust-to-ice ratio, latitude and spin axis orientation, are presented and discussed. Resulted for a similar nonrotating, constant Sun orientation models are also included.

Fanale, F. P.↗

DOE OSTI2019

A Finite-Element Approach for the Partitioning of Carbon in Q&P Steel

This paper reports a Galerkin finite-element analysis of carbon partitioning from martensite into austenite during the quenching and partitioning (Q&P) processes in steels. In contrast to classical or sophisticated diffusion field models, an alternative nonlinear governing equation based on chemical potential and composition is considered. The model is applied to simulate the carbon partitioning of modified 22MnB5 alloys assuming an immobile austenite–martensite phase boundary and, in turn, is compared with experimental measurements of the volume fraction and carbon content of retained austenite. The simulations show outstanding results on the influence of Si and C content on the partitioning parameters.

36 MATERIALS SCIENCE↗

NASA NTRS2000

Landscape Evolution, A Comparison of Form and Process

This project's goals were to collect, analyze and interpret 3-dimensional physiographic data for understanding the processes responsible for landscape modification. The primary landforms to be studied were Neogene cinder cones in Arizona (San Francisco Volcanic Field (SFVF), Coconino and Kaibab National Forests, Arizona). We also obtained and are still analyzing digital topographic data for the Long Valley-White Mountains area of California, which display Quaternary normal fault scarps, as well as extensive evidence of degradation. The work resulted in a large database of measured rates of downslope transport of slope debris. It was hypothesized that the work would increase our understanding of process-response models of hillslope degradation, and of the effects of climate change and other parameters on degradation rates. In greater detail, our primary goal was to compare evolutionary sequences of hillslopes, as exemplified by the topography of landforms of the same type but of different ages, with measurements of the surficial processes active on the landforms. Assuming that other parameters, such as hillslope materials and vegetation are held constant, and that the effects of changing climate are negligible, then the sediment transport rates measured today on the landforms should be the same as those calculated from the inversion of landform topography by use of a diffusion-type model. However, if the effects of changing climate or other factors are not negligible, then the observed transport rates would differ from those which must be invoked to explain the current topography. We hypothesized in fact that because degradation on the event scale is highly transient and localized, we would find a wide divergence between modern, measured transport rates, and rates calculated by global landform inversion or modeling. Because of the length of time involved in collection of sufficient data on current degradation rates, we are still continuing to analyse and interpret the data. Completion of the work will increase our understanding of the potential effects of anthropogenic climate and surficial change on the Earth's solid surface, and possibly allow us to constrain paths of hill-slope evolution following anthropogenic modifications, as well as compare the short-term with the long-term rates of hillslope degradation.

Bursik, Marcus I.↗

NASA NTRS2003

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Bentz, Daniel N.↗

DOE OSTI2022

The role of geographical spreaders in infectious pattern formation and front propagation speeds

The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible–Infectious–Recovered (SIR) model applicable across a wide range of basic reproduction numbers R O . The goal is to examine the role of geographical spreaders on transient spatial pattern formation of infectious populations and the associated maximum invasive front speeds c max . In the simulations conducted here, geographical spreaders are defined as a portion of the infected population Φ experiencing high mobility between identical communities. The spatial organization of the infected population and c max are determined when the infections are randomly initiated in space within multiple communities. For small but finite , scaling analysis and numerical simulations in 1-dimension suggest that when the spreading kernel is Gaussian-shaped, where is the inverse of the infectious duration. This finding for agrees with a diffusion-based representation of mobility in 1-D. Numerical simulations in 2-D across wide-ranging suggest that , the variance of the spatial kernel describing mobility of long-distance geographical spreaders across communities, determines the spatial organization of infections across communities. When (long-distance mobility, where is the minimum spatial extent defining adjacent communities), the infectious population will experience a transient but spatially coherent pattern with a wavelength that can be derived from the spreading kernel properties. Moreover, the 2-D simulations for the bounded kernel suggest that attainment of is also dictated by but the magnitude is not sensitive to unlike diffusion-based models.

60 APPLIED LIFE SCIENCES↗