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Quasi-linear pitch angle and energy diffusion of pickup ions near Comet Halley

The process of ion pickup in the environment of Halley's comet is studied in order to see if velocity diffusion driven by the observed level of turbulence can explain the observed development of the implanted ion distribution. The theoretical description used is based on a quasi-linear approach and considers the implantation and transport of cometary ions along solar wind flow lines. To make such a study requires some way of extrapolating the measurements on the Giotto trajectory into the upstream region; models for mass loading and turbulence are used. A simplified kinetic equation describing the source, convection, and quasi-linear velocity diffusion of the heavy cometary ions is solved numerically along flow lines parallel to the sun-comet line. Full two-dimensional (pitch angle and velocity) distributions are obtained at positions along the Giotto trajectory, which are compared with measurements. This study finds that quasi-linear theory, with the empirical model for the observed turbulence level, produces the right order of pitch angle diffusion.

Huddleston, D. E.↗

Turbulent transport of a passive-scalar field by using a renormalization-group method

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Hossain, Murshed↗

Agglomeration multigrid for viscous turbulent flows

Agglomeration multigrid, which has been demonstrated as an efficient and automatic technique for the solution of the Euler equations on unstructured meshes, is extended to viscous turbulent flows. For diffusion terms, coarse grid discretizations are not possible, and more accurate grid transfer operators are required as well. A Galerkin coarse grid operator construction and an implicit prolongation operator are proposed. Their suitability is evaluated by examining their effect on the solution of Laplace's equation. The resulting strategy is employed to solve the Reynolds-averaged Navier-Stokes equations for aerodynamic flows. Convergence rates comparable to those obtained by a previously developed non-nested mesh multigrid approach are demonstrated, and suggestions for further improvements are given.

Mavriplis, D. J.↗

THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT

We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.

79 ASTRONOMY AND ASTROPHYSICS↗

Static and dynamic properties of atomic nuclei with high-resolution potentials

Here, we compute ground-state and dynamical properties of 4 He and 16 O nuclei using as input high-resolution, phenomenological nucleon-nucleon and three-nucleon forces that are local in coordinate space. The nuclear Schrodinger equation for both nuclei is accurately solved employing the auxiliary-field diffusion Monte Carlo approach. For the 4 He nucleus, detailed benchmarks are carried out with the hyperspherical harmonics method. In addition to presenting results for the binding energies and radii, we also analyze the momentum distributions of these nuclei and their Euclidean response function corresponding to the isoscalar density transition. The latter quantity is particularly relevant for lepton-nucleus scattering experiments, as it paves the way to quantum Monte Carlo calculations of electroweak response functions of 16 O.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

GRAVITATIONAL ENCOUNTERS AND THE EVOLUTION OF GALACTIC NUCLEI. III. ANOMALOUS RELAXATION

This paper is the third in a series presenting the results of direct numerical integrations of the Fokker–Planck equation for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper II included diffusion coefficients that described the effects of random (“classical”) and correlated (“resonant”) relaxation. In this paper, the diffusion coefficients of Paper II have been generalized to account for the effects of “anomalous relaxation,” the qualitatively different way in which eccentric orbits evolve in the regime of rapid relativistic precession. Two functional forms for the anomalous diffusion coefficients are investigated, based on power-law or exponential modifications of the resonant diffusion coefficients. The parameters defining the modified coefficients are first constrained by comparing the results of Fokker–Planck integrations with previously published N-body integrations. Steady-state solutions are then obtained via the Fokker–Planck equation for models with properties similar to those of the Milky Way nucleus. Inclusion of anomalous relaxation leads to the formation of less prominent cores than in the case of resonant relaxation alone, due to the lengthening of diffusion timescales for eccentric orbits. Steady-state capture rates of stars by the SBH are found to always be less than capture rates in the presence of resonant relaxation alone.

79 ASTRONOMY AND ASTROPHYSICS↗

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models

An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.

Schneider, Hans R.↗

Towards an Enhanced Droplet Activation Scheme for Multi-Moment Bulk Microphysics Schemes

Initial droplet spectra produced upon activation impact the ensuing chain of microphysical processes andtherefore play a crucial role in cloud evolution. This work re-examines dependencies of newly formed clouddroplet size distribution (CDSD) characteristics on environmental and aerosol properties via parcel model simulationsthat serve as the basis for a multi-moment bulk microphysics droplet activation scheme suitable for acloud-resolving model (CRM). It is found that applying a fixed size threshold to define activated droplets versusemploying physical considerations can lead to erroneous activation and overly broad CDSDs for high aerosolconcentration and weak updraft conditions. Aerosol distributions characterized by larger median sizes and/orincreased solubility can result in greater activated droplet numbers, whereas impacts of these parameters onCDSD spectral width depend on both aerosol number concentration and updraft velocity. An expansion of theactivation scheme to include CDSD spectral width is proposed to aid efforts to extend high-order momentprediction to cloud droplet categories in CRMs as well as better represent variability in the activation process onthe cloud scale.simulations to investigate the regime dependence of the relative dispersion(d)1 of newly activated CDSDs, where d is the ratio of dropletradius standard deviation (σ) to the mean radius (r ). C16 demonstratedthat increasing Na resulted in increasing (decreasing) d values via reducedcondensational narrowing (spectral broadening) rates within theAL (UL) regime, with d values peaking in the TR regime. Their findingssuggest a similar regime dependence for d as R09 noted for Nc and helpexplain reportedly conflicting relationships between Na and CDSDspectral characteristics (cf. Hudson and Noble, 2014; Liu et al., 2014),although the applicability of these results within bulk microphysicalschemes was not addressed.Simulating aerosol-cloud interactions with CRMs employing bulkmicrophysics requires that the scheme minimally predict two CDSDparameters, namely mass and number concentrations, and represent thedroplet activation process. Various activation schemes aim to determineNc from aerosol and environmental properties and include analyticalexpressions (e.g., Abdul-Razzak et al., 1998; Morrison et al., 2005) aswell as lookup tables (LUTs) based on detailed parcel model calculations(e.g., Saleeby and Cotton, 2004, hereafter SC04; Segal and Khain,2006; Thompson and Eidhammer, 2014). Expressions to diagnose CDSDspectral width from Nc (Grabowski, 1998; Liu et al., 2006; Morrison andGrabowski, 2007) or cloud water content (Geoffroy et al., 2010) havealso been developed, although more robust methods to obtain CDSDspectral width upon activation are presently lacking. This latter point isrelevant for triple-moment (3 M) bulk microphysics that aim to predictdistribution spectral width alongside number and mass concentrations(e.g., Loftus et al., 2014; Milbrandt and Yau, 2005).The current work extends the findings of C16 to the current LUTbasedaerosol activation scheme used in the Regional AtmosphericModeling System (RAMS) (Cotton et al., 2003; SC04; Saleeby and vanden Heever, 2013, hereafter SvdH13) and additionally examinesaerosol size and solubility impacts on newly activated CDSD properties.Because early cloud development processes such as condensationalgrowth, evaporation, and droplet self-collection depend on and impactCDSD spectral width (Hudson and Yum, 1997; Seifert and Beheng 2001;Lu and Seinfeld, 2006; Igel and van den Heever, 2017), an expansion ofthe activation LUTs to include CDSD spectral width is proposed as apreliminary step for extending 3M prediction to CDSDs in CRMs forimproved simulations of aerosol-cloud interactions.2. MethodologyThe current RAMS two-moment microphysics module determinesthe fractional number of aerosol particles that activate to cloud dropletsfrom five-dimensional LUTs based on model predicted air temperature(T), w, Na, and the geometric median radius (rg) and soluble fraction (ε)of the aerosol size distribution (SvdH13). These LUTs are created offlineusing a one-dimensional Lagrangian adiabatic parcel model (Feingoldand Heymsfield, 1992; Heymsfield and Sabin, 1989; SC04) to simulateexplicit droplet activation and initial CDSD growth for a range of ambientatmospheric conditions [T, w] and binned lognormal aerosol sizedistributions given by= ⎡⎣ ⎢− ⎤⎦ ⎥N r Nr π σr rσ( )2 lnexp[ln( / )]2(ln )aggg22 (1)where r is the dry aerosol particle bin radius and σg is the geometricstandard deviation of the distribution. As the parcel model simulationsfocus on the activation process, other processes such as coalescence,sedimentation, and mixing are not considered. Details of the parcelmodel can be found in SC04 and SvdH13, and only a brief description isprovided here. At the onset of parcel model calculations, the initiallydry aerosol particles in all bins first deliquesce and reach theirequilibrium diameters in a sub-saturated environment based on theKöhler equation for solution droplets. The parcel is then lifted at a fixedupward velocity w, and particle growth by vapor diffusion, along withconcurrent changes in the ambient environment, are iteratively computedusing the Variable-coefficient Ordinary Differential Equation(VODE) solver (Brown et al., 1989). The time resolution of these calculationsis determined within the VODE solver, and the frequency atwhich the solver is called is controlled by a longer model time stepbased on fixed upward parcel displacement increments (Δz) at thespecified w (Δt=Δz/w). Model calculations proceed until the parcelreaches a height 50m beyond the level of maximum saturation ratio(Smax) or total parcel displacement exceeds 2 km. Upon model termination,Smax and the fractional number of aerosols (factv) resulting innewly formed cloud droplets, defined as particles having diameters of atleast 2 μm, are cataloged in the LUTs according to the specified T, w, Na,rg, and ε parameter values.A critical point regarding the creation of these LUTs is the use of afixed minimum diameter (Dmin) to define cloud droplets in the parcelmodel, which can produce erroneous CDSD characteristics, particularlywithin the UL regime. For aerosol distributions with large rg valuesunder low SS conditions, for example, deliquesced aerosols within thelarge tail of the distribution can exceed 2 μm in diameter yet remainunactivated as ‘haze’ particles (Levin and Cotton, 2009; McFigganset al., 2006). For this study, aerosol particles activate to cloud dropletsbased on the critical diameter Dcrit as a function of parcel supersaturationratio (Sr) as in R09:D = σ MS RTρ83 ln( ) critsol wr w (2)where σsol is the surface tension of a solution droplet, Mw and ρw are themolar mass and density of liquid water, respectively, and R is theuniversal gas constant. Additionally, at relatively large w values withinthe AL regime, Nc stabilizes shortly after reaching supersaturation.However, parcel ascent and condensational growth continue beyondthe level of Smax, potentially causing additional narrowing of the CDSD.In the current work, model calculations terminate upon reaching Smaxas changes in Nc are negligible with continued ascent (Peng et al., 2007;R09).Parcel model simulations are performed to examine the sensitivitiesof CDSD characteristics to w, Na, rg, and ε, with the ranges for theseparameters listed in Table 1. Aerosols are assumed to be a mix of solubleand insoluble material of equal density, specified by ε, where fullysoluble aerosols correspond to ammonium sulfate with hygroscopicityparameter κ=0.61 (Petters and Kreidenweis, 2007). FollowingSvdH13, aerosol geometric standard deviation is fixed at σg=1.8, andaerosol distributions (Eq. 1) are partitioned into 100 logarithmicallyspacedbins spanning a size range specific to each rg value. For all simulations,Δz=1 m, and initial values of relative humidity, air temperatureand pressure are set to RH=0.99, T=10 °C and p=900 hPa,respectively.

Loftus, Adrian M.↗

A comparison between implicit and hybrid methods for the calculation of steady and unsteady inlet flows

Numerical simulation of steady and unsteady transonic diffuser flows using two different computer codes are discussed and compared with experimental data. The codes solve the Reynolds-averaged, compressible, Navier-Stokes equations using various turbulence models. One of the codes has been applied extensively to diffuser flows and uses the hybrid method of MacCormack. This code is relatively inefficient numerically. The second code, which was developed more recently, is fully implicit and is relatively efficient numerically. Simulations of steady flows using the implicit code are shown to be in good agreement with simulations using the hybrid code. Both simulations are in good agreement with experimental results. Simulations of unsteady flows using the two codes are in good qualitative agreement with each other, although the quantitative agreement is not as good as in the steady flow cases. The implicit code is shown to be eight times faster than the hybrid code for unsteady flow calculations and up to 32 times faster for steady flow calculations. Results of calculations using alternative turbulence models are also discussed.

Coakley, T. J.↗

A reduced order model to analytically infer atmospheric CO 2 concentration from stomatal and climate data

To address questions related to the acceleration or deceleration of the global hydrological cycle or links between the carbon and water cycles over land, reliable data for past climatic conditions based on proxies are required. In particular, the reconstruction of palaeoatmospheric CO 2 content (C a ) is needed to assist the separation of natural from anthropogenic C a variability and to explore phase relations between C a and air temperature T a time series. Both T a and C a are needed to fingerprint anthropogenic signatures in vapor pressure deficit, a major driver used to explain acceleration or deceleration phases in the global hydrological cycle. Current approaches to C a reconstruction rely on a robust inverse correlation between measured stomatal density in leaves (ν) of many plant taxa and C a . There are two methods that exploit this correlation: The first uses calibration curves obtained from extant species assumed to represent the fossil taxa, thereby restricting the suitable taxa to those existing today. The second is a hybrid eco-hydrological/physiological approach that determines C a with the aid of systems of equations based on quasi-instantaneous leaf-gas exchange theories and fossil stomatal data collected along with other measured leaf anatomical traits and parameters. In this contribution, a reduced order model (ROM) is proposed that derives C a from a single equation incorporating the aforementioned stomatal data, basic climate (e.g. temperature), estimated biochemical parameters of assimilation and isotope data. The usage of the ROM is then illustrated by applying it to isotopic and anatomical measurements from three extant species. The ROM derivation is based on a balance between the biochemical demand and atmospheric supply of CO 2 that leads to an explicit expression linking stomatal conductance to internal CO 2 concentration (C i ) and C a . The resulting expression of stomatal conductance from the carbon economy of the leaf is then equated to another expression derived from water vapor gas diffusion that includes anatomical traits. When combined with isotopic measurements for long-term C i /C a , C a can be analytically determined and is interpreted as the time-averaged C a that existed over the life-span of the leaf. Key advantages of the proposed ROM are: 1) the usage of isotopic data provides constraints on the reconstructed atmospheric CO 2 concentration from ν, 2) the analytical form of this approach permits direct links between parameter uncertainties and reconstructed C a , and 3) the time-scale mismatch between the application of instantaneous leaf-gas exchange expressions constrained with longer-term isotopic data is reconciled through averaging rules and sensitivity analysis. The latter point was rarely considered in prior reconstruction studies that combined models of leaf-gas exchange and isotopic data to reconstruct C a from ν. The proposed ROM is not without its limitations given the need to a priori assume a parameter related to the control on photosynthetic rate. Our work here further explores immanent constraints for the aforementioned photosynthetic parameter.

54 ENVIRONMENTAL SCIENCES↗

Model-based optimization strategies for direct hydrogenation of carbon dioxide to dimethyl ether

Here, this study discusses model-based optimization strategies for CO 2 hydrogenation to dimethyl ether (DME) over aCuZnZr (CZZ) and ferrite (FER) mixed catalyst system in a packed-bed reactor configuration. A two-dimensional axisymmetric, nonisothermal packed-bed reactor model was developed using COMSOL Multiphysics 6.2 software. The model solves two-dimensional (radial and axial) heat and mass transport equations in the packed-bed and integrates intraparticle diffusion and heat transfer in a 1D approach. This powerful feature differs from a traditional porous media approach and takes into account any heat and mass transfer limitations that may exist. Analysis shows that the heat transfer limitations are negligible, but strong internal mass transfer limitations were observed at 10 ≤ WHSV ≤ 90 h -1 on the FER catalyst and at 240 °C. The optimum catalyst composition (i.e., mixing ratio) varies depending on the operating regime. The FER catalyst weight in the mixture can be as low as 5 wt.%, but the ideal composition de-pends on the internal mass transfer limitation and its relationship with the operating regime (i.e., weight hourly space velocity, temperature). A catalyst composition of 80 wt.% CZZ and 20 wt.% FER was suggested; this composition can provide high CO 2 conversion and DME production rates at a wide range of temperatures and flow rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Expanding the capability of reaction-diffusion codes using pseudo traps and temperature partitioning: Applied to hydrogen uptake and release from tungsten

Simulating the implantation and thermal desorption evolution in a reaction-diffusion model requires solving a set of coupled differential equations that describe the trapping and release of atomic species in Plasma Facing Materials (PFMs). These fundamental equations are well outlined by the Tritium Migration Analysis Program (TMAP) which can model systems with no more than three active traps per atomic species. To overcome this limitation, we have developed a Pseudo Trap and Temperature Partition (PTTP) scheme allowing us to lump multiple inactive traps into one pseudo trap, simplifying the system of equations to be solved. For all temperatures, we show the trapping of atoms from solute is exactly accounted for when using a pseudo trap. However, a single effective pseudo trap energy can not well replicate the release from multiple traps, each with its own detrapping energy. However, atoms held in a high energy trap will remain trapped at relatively low temperatures, and thus there is a temperature range in which release from high energy traps is effectively inactive. By partitioning the temperature range into segments, a pseudo trap can be defined for each segment to account for multiple high energy traps that are actively trapping but are effectively not releasing atoms. With increasing temperature, as in controlled thermal desorption, the lowest energy trap is nearly emptied and can be removed from the set of coupled equations, while the next higher energy trap becomes an actively releasing trap. Each segment is thus calculated sequentially, with the last time step of a given segment solution being used as an initial input for the next segment as only the pseudo and actively releasing traps are modeled. This PTTP scheme is then applied to experimental thermal desorption data for tungsten (W) samples damaged with heavy ions, which display six distinct release peaks during thermal desorption. Without modifying the TMAP7 source code the PTTP scheme is shown to successfully model the D retention in all six traps. In conclusion, we demonstrate the full reconstruction from the plasma implantation phase through the controlled thermal desorption phase with detrapping energies near 0.9, 1.1, 1.4, 1.7, 1.9 and 2.1 eV for a W sample damaged at room temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Polyethylene in Dead-End Silica Nanopores: Forces and Mobility from Non-Equilibrium Statistical Mechanics and Exchange Spectroscopy Nuclear Magnetic Resonance

Billions of tons of plastic have been produced, and only a small fraction of this has been recycled. Tennakoon et al. [Nature Catalysis 3, 893 (2020)] developed a catalyst that repeatedly cleaves C 10 –C 30 hydrocarbons from the end of a polyethylene chain. The reaction occurs at a Pt nanoparticle at the base of a cylindrical silica mesopore with a diameter of 2 nm and a length of 110 nm. Portions of the polymer situated inside the pore can be differentiated from those outside using 13 C nuclear magnetic resonance (NMR), allowing the dynamics and extent of polymer threading to be monitored using two-dimensional (2D) exchange spectroscopy NMR. Here we construct a Fokker–Planck equation for the polymer dynamics by assuming a reptation diffusivity and a graduated adsorption free energy that depends linearly on the depth of polymer penetration in the pore. The solutions allow us to predict the intensities of the 2D NMR resonances as a function of time. We use the solutions to extract a polymer diffusivity at each temperature and estimate the per-segment desorption free energy, enthalpy, and entropy. Random and systematic errors are examined to test key assumptions in the theory and interpretation of the experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reduced Sediment Settling in Turbulent Flows Due To Basset History and Virtual Mass Effects

The behavior of suspended particles in turbulent flows is a recalcitrant problem spanning wide-ranging fields including geomorphology, hydrology, and dispersion of particulate matter in the atmosphere. One key mechanism underlying particle suspension is the difference between particle settling velocity (w s ) in turbulence and its still water counterpart (w so ). This difference is explored here for a range of particle-to-fluid densities (1 – 10) and particle diameter to Kolmogorov micro-eddy sizes (0.1 – 10). Conventional models of particle fluxes that equate w s to w so result in eddy diffusivities and turbulent Schmidt numbers contradictory to laboratory experiments. Incorporating virtual mass and Basset history forces resolves these inconsistencies, providing clarity as to why w s /w so is sub-unity for the aforementioned conditions. The proposed formulation can be imminently used to model particle settling in turbulence, especially when sediment distribution outcomes over extended time scales far surpassing turbulence time scales are sought.

Geology↗

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

97 MATHEMATICS AND COMPUTING↗

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/$\mathrm{cm^3}$ to 16 g/$\mathrm{cm^3}$ and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. Here, we find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗