Snapshot Simulations Research Articles

CO2-driven and orbitally driven oxygen isotope variability in the Early Eocene

Abstract. Paleoclimate reconstructions of the Early Eocene provide important data constraints on the climate and hydrologic cycle under extreme warm conditions. Available terrestrial water isotope records have been primarily interpreted to signal an enhanced hydrologic cycle in the Early Eocene associated with large-scale warming induced by high atmospheric CO2. However, orbital-scale variations in these isotope records have been difficult to quantify and largely overlooked, even though orbitally driven changes in solar irradiance can impact temperature and the hydrologic cycle. In this study, we fill this gap using water isotope–climate simulations to investigate the orbital sensitivity of Earth's hydrologic cycle under different CO2 background states. We analyze the relative difference between climatic changes resulting from CO2 and orbital changes and find that the seasonal climate responses to orbital changes are larger than CO2-driven changes in several regions. Using terrestrial δ18O and δ2H records from the Paleocene–Eocene Thermal Maximum (PETM), we compare our modeled isotopic seasonal range to fossil evidence and find approximate agreement between empirical and simulated isotopic compositions. The limitations surrounding the equilibrated snapshot simulations of this transient event and empirical data include timing and time interval discrepancies between model and data, the preservation state of the proxy, analytical uncertainty, the relationship between δ18O or δ2H and environmental context, and vegetation uncertainties within the simulations. In spite of the limitations, this study illustrates the utility of fully coupled, isotope-enabled climate models when comparing climatic changes and interpreting proxy records in times of extreme warmth.

MmWave Channel Stationarity Analysis of V2X Communications in an Urban Environment

Vehicular communication channels are subject to high non-stationarity mainly characterized by the scatterers' and/or transceivers' high mobility. In this sense, this work presents a characterization of the channel quasi-stationarity regions (QSR) in a V2X generic high-dense urban environment at millimeter wave (mmWave) frequencies (28 GHz). Results are extracted from multiple snapshot simulations by means of a three-dimensional ray-launching (3D-RL) algorithm inducing the continuous mobility of the vehicles on the scene and validated with an experimental campaign of measurements in the real scenario. The average power delay profile (APDP) correlation matrix is used as a descriptor of the channel non-stationarity and the mean correlation is outlined for several thresholds. The obtained QSR results are consistent with the related works reported in the literature. Finally, the effects of these QSR in small- and large-scale parameters are assessed as per threshold considerations.

The spatial-temporal patterns of East Asian climate in response to insolation, CO2 and ice sheets during MIS-5

Marine Isotope Stage (MIS) 5, between about 130 and 70 ka BP, is characterized by climate oscillations consisting of three interstadials and two stadials. Many climate simulations have been performed for the warmest MIS-5e period, but few has been made to cover the entire MIS-5 to investigate the climate variability during this long period. In this study, two sets of snapshot simulations by a step of 2 ka covering the whole MIS-5 period are performed with the model HadCM3 to investigate the relative impacts of insolation, CO2 and Northern Hemisphere ice sheets on the East Asian climate variability. Our results show that precipitation and temperature in different subregions in East Asia have different sensitivity to astronomical forcing, CO2 and ice sheets, in particular when seasonal and mean annual changes are concerned. The variability of temperature and precipitation within MIS-5 is mainly controlled by precession but their magnitudes are modulated by CO2 and ice sheets. The impact of ice sheets on summer precipitation vary between subregions and is sensitive to ice sheet configurations and background insolation. The summer precipitation in southern China is more sensitive to ice sheets than in northern China. Moisture budget analysis show that insolation and CO2 affect the summer precipitation by the dynamic and thermodynamic processes, respectively, and the impact of ice sheets is mainly through the vertical dynamic processes which is strongly associated with the ice sheet-induced wave train at the hemisphere scale.

A high-resolution climate simulation dataset for the past 540 million years

The Phanerozoic Eon has witnessed considerable changes in the climate system as well as abundant animals and plant life. Therefore, the evolution of the climate system in this Eon is worthy of extensive research. Only by studying climate changes in the past can we understand the driving mechanisms for climate changes in the future and make reliable climate projections. Apart from observational paleoclimate proxy datasets, climate simulations provide an alternative approach to investigate past climate conditions of the Earth, especially for long time span in the deep past. Here we perform 55 snapshot simulations for the past 540 million years, with a 10-million-year interval, using the Community Earth System Model version 1.2.2 (CESM1.2.2). The climate simulation dataset includes global distributions of monthly surface temperatures and precipitation, with a 1° horizontal resolution of 0.9° × 1.25° in latitude and longitude. This open access climate dataset is useful for multidisciplinary research, such as paleoclimate, geology, geochemistry, and paleontology.

A Holocene Perspective of Vegetation Controls on Seasonal Boreal Wildfire Sizes Using Numerical Paleo-Ecology

Wildland fire is the most important disturbance in boreal forests of eastern North America, shaping composition, structure and spatial arrangement of the flora. Although the long-term evolution of frequency and quantity of biomass burnt in these forest are known relatively well from paleoecological studies, we know little about the evolution of fire sizes. Here, we developed a modelling framework that provides insights into processes and changes involved through time in the historical fire-vegetation-climate environment of the coniferous and mixedwood forests of eastern boreal North America, with a particular attention on the metric of fire size. On the one hand, lacustrine charcoal particles sequestered in sediments from mixedwood forest and coniferous forest regions (MF and CF, respectively) were analyzed with the most advanced statistical treatments to reconstruct changes in biomass burning, fire frequency, and their ratio, the fire size (FS index), over the last 7000 BP. On the other hand, a fire propagation model was used to simulate fire sizes in the past using both a reference landscape, whose MF and CF compositions through time were prescribed using pollen reconstructions, and climate inputs provided by the HadCM3BL-M1 snapshot simulations. Lacustrine charcoals showed that Holocene FS indices have not differed significantly between MF and CF due to high variability in fire frequencies. However, biomass burning from MF has always been lower than from CF, such differences being significant since 5000 BP. Beyond the variability, MF’s mean FS index was lower than CF’s one throughout the Holocene, with slight changes in both forests from 7000 to 1000 BP, and simultaneous increases over the last millennium. The fire model showed that MF fires were systematically smaller than CF ones throughout the Holocene, with larger differences in the past than today. The fire model also highlighted that spring fires in both forest types have always been larger than summer fires over the last 7000 years, such results being in agreement with present-day fire statistics. This study illustrates how fire models, built and used for forecast and firefighting today, can be used under past conditions to enhance our understanding in the fire-vegetation-climate nexus.

Timing and magnitude of Southern Ocean sea ice/carbon cycle feedbacks

The Southern Ocean (SO) played a prominent role in the exchange of carbon between ocean and atmosphere on glacial timescales through its regulation of deep ocean ventilation. Previous studies indicated that SO sea ice could dynamically link several processes of carbon sequestration, but these studies relied on models with simplified ocean and sea ice dynamics or snapshot simulations with general circulation models. Here, we use a transient run of an intermediate complexity climate model, covering the past eight glacial cycles, to investigate the orbital-scale dynamics of deep ocean ventilation changes due to SO sea ice. Cold climates increase sea ice cover, sea ice export, and Antarctic Bottom Water formation, which are accompanied by increased SO upwelling, stronger poleward export of Circumpolar Deep Water, and a reduction of the atmospheric exposure time of surface waters by a factor of 10. Moreover, increased brine formation around Antarctica enhances deep ocean stratification, which could act to decrease vertical mixing by a factor of four compared with the current climate. Sensitivity tests with a steady-state carbon cycle model indicate that the two mechanisms combined can reduce atmospheric carbon by 40 ppm, with ocean stratification acting early within a glacial cycle to amplify the carbon cycle response.

A simulated Northern Hemisphere terrestrial climate dataset for the past 60,000 years

We present a continuous land-based climate reconstruction dataset extending back 60 kyr from 0 BP (1950) at 0.5° resolution on a monthly timestep for 0°N to 90°N. It has been generated from 42 discrete snapshot simulations using the HadCM3B-M2.1 coupled general circulation model. We incorporate Dansgaard-Oeschger (DO) and Heinrich events to represent millennial scale variability, based on a temperature reconstruction from Greenland ice-cores, with a spatial fingerprint based on a freshwater hosing simulation with HadCM3B-M2.1. Interannual variability is also added and derived from the initial snapshot simulations. Model output has been downscaled to 0.5° resolution (using simple bilinear interpolation) and bias corrected. Here we present surface air temperature, precipitation, incoming shortwave energy, minimum monthly temperature, snow depth, wind chill and number of rainy days per month. This is one of the first open access climate datasets of this kind and can be used to study the impact of millennial to orbital-scale climate change on terrestrial greenhouse gas cycling, northern extra-tropical vegetation, and megaflora and megafauna population dynamics.

Empirical Run‐Time Bias Correction for Antarctic Regional Climate Projections With a Stretched‐Grid AGCM

AbstractThis work presents snapshot simulations of the late 20th and late 21st century Antarctic climate under the RCP8.5 scenario carried out with an empirically bias‐corrected global atmospheric general circulation model (AGCM), forced with bias‐corrected sea‐surface temperatures and sea ice and run with about 100‐km resolution over Antarctica. The bias correction substantially improves the simulated mean late 20th century climate. The simulated atmospheric circulation of the bias‐corrected model compares very favorably to the best available AMIP (Atmospheric Model Intercomparison Project)‐type climate models. The simulated interannual circulation variability is improved by the bias correction. Depending on the metric, a slight improvement or degradation is found in the simulated variability on synoptic timescales. The simulated climate change over the 21st century is broadly similar in the corrected and uncorrected versions of the atmospheric model, and atmospheric circulation patterns are not geographically “pinned” by the applied bias correction. These results suggest that the method presented here can be used for bias‐corrected climate projections. Finally, the authors discuss different possible choices in terms of the place of bias corrections and other intermediate steps in the modeling chain leading from global coupled climate simulations to impact assessment.

Dependence on the environment of the abundance function of light-cone simulation dark matter haloes

Aims. We study the dependence of the halo abundance function (AF) on different environments in a whole-sky ΛCDM light-cone halo catalogue extending to z ~ 0.65, using a simple and well-defined halo isolation criterion. Methods. The isolation status of each individual dark matter halo is determined by the distance to its nearest neighbour, which defines the maximum spherical region devoid of halos above a threshold mass around it (although the true size of such region may be much larger since it is not necessarily spherical). A versatile double power-law Schechter function is used to fit the dark matter halo AF, and its derived parameters are studied as a function of halo isolation status. Results. (a) Our function fits the halo abundances for all halo isolation statuses extremely well, while the well-established theoretical mass functions, integrated over the volume of the light-cone, provide an adequate but poorer fit than our phenomenological model. (b) As expected, and in agreement with other studies based on snap-shot simulations, we find significant differences of the halo abundance function as a function of halo isolation, indicating different rates of halo formation. The slope of the power law and the characteristic mass of the Schechter-like fitting function decrease with isolation, a result consistent with the formation of less massive haloes in lower density regions. (c) We find an unexpected upturn of the characteristic mass of the most isolated haloes of our sample. This upturn originates and characterises only the higher redshift regime (z ≳ 0.45), which probably implies a significant and recent evolution of the isolation status of the most isolated and most massive haloes.

A New Non-iterative Method for Pressure-driven Snapshot Simulations with EPANET

This study compares different recently proposed methods for Pressure-Driven snapshot simulations of water distribution networks using the EPANET software interface and proposes a new one. The proposed method is based on the insertion of a sequence of devices consisting of a General Purpose Valve (GPV), a fictitious junction, a reach with a check valve and a reservoir at each water demand node. The proposed method differs from other methods previously proposed in the literature – and similarly based on the insertion of sequences of devices consisting of a valve and a reservoir or emitter – in that it uses a GPV. In fact the GPV allows the user to define the relationship between the flow (i.e. supplied demand) and available pressure, making the proposed sequence of devices capable of representing different relationships among these variables, unlike the other non-iterative methods already proposed in the scientific literature, in which the relationship is implicitly fixed by the structure of the sequence of devices used. Applications to two case studies and comparison with the results of the non-iterative methods already proposed in the scientific literature highlight the accuracy and flexibility of the proposed method and show, by contrast, the unreliability and limits, in terms of precision, of some of the methods previously proposed in the literature.

Abrupt reorganization of North Pacific and western North American climate during the last deglaciation

AbstractDramatic hydroclimate shifts occurred in western North America during the last deglaciation, but the timing and mechanisms driving these changes are uncertain and debated, and previous modeling has largely relied on linear interpolations between equilibrium snapshot simulations. Using a published transient climate simulation and a range of proxy records, we analyze the region's climate evolution in order to identify the mechanisms governing hydroclimate shifts. A rapid loss of ice around 14,000 years ago causes an abrupt reorganization of the circulation, which precipitates drying and moistening of southwestern and northwestern North America, respectively. The atmospheric circulation transitions between two states on a timescale of decades to centuries, during which time the westerly jet shifts north by about 7°. In contrast to previous studies, we find that changes in the water budget of western North America prior to this event are not attributable to variations in the position of the jet, but rather to the intensity of moisture transport into the continent.

Analysis of Non-Iterative Methods and Proposal of a New One for Pressure-Driven Snapshot Simulations with EPANET

This paper compares different recently proposed methods for pressure-driven snapshot simulations of water distribution networks using the EPANET software interface and proposes a new one. The proposed method is based on the insertion of a sequence of devices consisting of a General Purpose Valve (GPV), a fictitious junction, a reach with a check valve and a reservoir at each water demand node. The proposed method differs from other methods previously proposed in the literature – and similarly based on the insertion of sequences of devices consisting of a valve and a reservoir or emitter – in that it uses a GPV; more specifically, for this valve the user can fix the relationship between outflow discharge (or the flow delivered to users) and the available pressure head at the node, thus allowing for a flexible representation of the relationship between these two parameters, whereas with the other methods this relationship remains fixed, based on the structure of the sequence of devices used. Practical applications to three different real-life cases show the unreliability and limits, in terms of accuracy, of some of the methods previously proposed in the literature. They also show, by contrast, the validity of the new method, which has proven to be reliable and accurate, as well as flexible, since it enables any relationship to be defined between the delivered flow and available head.

Understanding the temporal slope of the temperature‐water isotope relation during the deglaciation using isoCAM3: The slope equation

The temporal and spatial slopes of water isotope-temperature relations are studied for the last 21,000 years over the middle and high latitudes using a series of snapshot simulations of global climate and water isotopes in the isotope-enabled atmospheric model isoCAM3. Our model simulation suggests that both the temporal slope and spatial slope remain largely stable throughout the last deglaciation. Furthermore, the temporal slope can vary substantially across regions. Nevertheless, on average, and most likely, the temporal slope is about 0.3‰ °C−1 and is about half of the spatial slope. Finally, the relation between temporal and spatial slopes is understood using a semiempirical equation that is derived based on both the Rayleigh distillation and a fixed spatial slope. The slope equation quantifies the Boyle's mechanism and suggests that the temporal slope is usually smaller than the spatial slope in the extratropics mainly because of the polar amplification feature in global climate change, such that the response in local temperature at middle and high latitudes is usually greater than that in the total equivalent source temperature.

The biogeophysical climatic impacts of anthropogenic land use change during the Holocene

Abstract. The first agricultural societies were established around 10 ka BP and had spread across much of Europe and southern Asia by 5.5 ka BP with resultant anthropogenic deforestation for crop and pasture land. Various studies (e.g. Joos et al., 2004; Kaplan et al., 2011; Mitchell et al., 2013) have attempted to assess the biogeochemical implications for Holocene climate in terms of increased carbon dioxide and methane emissions. However, less work has been done to examine the biogeophysical impacts of this early land use change. In this study, global climate model simulations with Hadley Centre Coupled Model version 3 (HadCM3) were used to examine the biogeophysical effects of Holocene land cover change on climate, both globally and regionally, from the early Holocene (8 ka BP) to the early industrial era (1850 CE). Two experiments were performed with alternative descriptions of past vegetation: (i) one in which potential natural vegetation was simulated by Top-down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) but without land use changes and (ii) one where the anthropogenic land use model Kaplan and Krumhardt 2010 (KK10; Kaplan et al., 2009, 2011) was used to set the HadCM3 crop regions. Snapshot simulations were run at 1000-year intervals to examine when the first signature of anthropogenic climate change can be detected both regionally, in the areas of land use change, and globally. Results from our model simulations indicate that in regions of early land disturbance such as Europe and south-east Asia detectable temperature changes, outside the normal range of variability, are encountered in the model as early as 7 ka BP in the June–July–August (JJA) season and throughout the entire annual cycle by 2–3 ka BP. Areas outside the regions of land disturbance are also affected, with virtually the whole globe experiencing significant temperature changes (predominantly cooling) by the early industrial period. The global annual mean temperature anomalies found in our single model simulations were −0.22 at 1850 CE, −0.11 at 2 ka BP, and −0.03 °C at 7 ka BP. Regionally, the largest temperature changes were in Europe with anomalies of −0.83 at 1850 CE, −0.58 at 2 ka BP, and −0.24 °C at 7 ka BP. Large-scale precipitation features such as the Indian monsoon, the Intertropical Convergence Zone (ITCZ), and the North Atlantic storm track are also impacted by local land use and remote teleconnections. We investigated how advection by surface winds, mean sea level pressure (MSLP) anomalies, and tropospheric stationary wave train disturbances in the mid- to high latitudes led to remote teleconnections.

Using Single-Forcing GCM Simulations to Reconstruct and Interpret Quaternary Climate Change

Abstract The long-term climate variations of the Quaternary were primarily influenced by concurrent changes in Earth’s orbit, greenhouse gases, and ice sheets. However, because climate changes over the coming century will largely be driven by changes in greenhouse gases alone, it is important to better understand the separate contributions of each of these forcings in the past. To investigate this, idealized equilibrium simulations are conducted in which the climate is driven by separate changes in obliquity, precession, CO2, and ice sheets. To test the linearity of past climate change, anomalies from these single-forcing experiments are scaled and summed to compute linear reconstructions of past climate, which are then compared to mid-Holocene and last glacial maximum (LGM) snapshot simulations, where all forcings are applied together, as well as proxy climate records. This comparison shows that much of the climate response may be approximated as a linear response to forcings, while some features, such as modeled changes in sea ice and Atlantic meridional overturning circulation (AMOC), appear to be heavily influenced by nonlinearities. In regions where the linear reconstructions replicate the full-forcing experiments well, this analysis can help identify how each forcing contributes to the climate response. Monsoons at the mid-Holocene respond strongly to precession, while LGM monsoons are heavily influenced by the altered greenhouse gases and ice sheets. Contrary to previous studies, ice sheets produce pronounced tropical cooling at the LGM. Compared to proxy temperature records, the linear reconstructions replicate long-term changes well and also show which climate variations are not easily explained as direct responses to long-term forcings.

A global model simulation of present and future nitrate aerosols and their direct radiative forcing of climate

Abstract. The ammonia cycle and nitrate particle formation are introduced into the LMDz-INCA (Laboratoire de Météorologie Dynamique, version 4 – INteraction with Chemistry and Aerosols, version 3) global model. An important aspect of this new model is that both fine nitrate particle formation in the accumulation mode and coarse nitrate forming on existing dust and sea-salt particles are considered. The model simulates distributions of nitrates and related species in agreement with previous studies and observations. The calculated present-day total nitrate direct radiative forcing since the pre-industrial is −0.056 W m−2. This forcing corresponds to 18% of the sulfate forcing. Fine particles largely dominate the nitrate forcing, representing close to 90% of this value. The model has been used to investigate the future changes in nitrates and direct radiative forcing of climate based on snapshot simulations for the four representative concentration pathway (RCP) scenarios and for the 2030, 2050, and 2100 time horizons. Due to a decrease in fossil fuel emissions in the future, the concentration of most of the species involved in the nitrate–ammonium–sulfate system drop by 2100 except for ammonia, which originates from agricultural practices and for which emissions significantly increase in the future. Despite the decrease of nitrate surface levels in Europe and North America, the global burden of accumulation mode nitrates increases by up to a factor of 2.6 in 2100. This increase in ammonium nitrate in the future arises despite decreasing NOx emissions due to increased availability of ammonia to form ammonium nitrate. The total aerosol direct forcing decreases from its present-day value of −0.234 W m−2 to a range of −0.070 to −0.130 W m−2 in 2100 based on the considered scenario. The direct forcing decreases for all aerosols except for nitrates, for which the direct negative forcing increases to a range of −0.060 to −0.115 W m−2 in 2100. Including nitrates in the radiative forcing calculations increases the total direct forcing of aerosols by a factor of 1.3 in 2000, by a factor of 1.7–2.6 in 2030, by 1.9–4.8 in 2050, and by 6.4–8.6 in 2100. These results show that the agricultural emissions of ammonia will play a key role in the future mitigation of climate change, with nitrates becoming the dominant contributor to the anthropogenic aerosol optical depth during the second half of the 21st century and significantly increasing the calculated aerosol direct forcing. This significant increase in the influence that nitrate exerts on climate in the future will at the same time affect regional air quality and nitrogen deposition to the ecosystem.

Comparing transient, accelerated, and equilibrium simulations of the last 30 000 years with the GENIE-1 model

Abstract. We examine several aspects of the ocean-atmosphere system over the last 30 000 years, by carrying out simulations with prescribed ice sheets, atmospheric CO2 concentration, and orbital parameters. We use the GENIE-1 model with a frictional geostrophic ocean, dynamic sea ice, an energy balance atmosphere, and a land-surface scheme with fixed vegetation. A transient simulation, with boundary conditions derived from ice-core records and ice sheet reconstructions, is compared with equilibrium snapshot simulations, including the Last Glacial Maximum (21 000 years before present; 21 kyrBP), mid-Holocene (6 kyrBP) and pre-industrial. The equilibrium snapshot simulations are all very similar to their corresponding time period in the transient simulation, indicating that over the last 30 000 years, the model's ocean-atmosphere system is close to equilibrium with its boundary conditions. However, our simulations neglect the transfer of fresh water from and to the ocean, resulting from the growth and decay of ice sheets, which would, in reality, lead to greater disequilibrium. Additionally, the GENIE-1 model exhibits a rather limited response in terms of its Atlantic Meridional Overturning Circulation (AMOC) over the 30 000 years; a more sensitive AMOC would also be likely to lead to greater disequilibrium. We investigate the method of accelerating the boundary conditions of a transient simulation and find that the Southern Ocean is the region most affected by the acceleration. The Northern Hemisphere, even with a factor of 10 acceleration, is relatively unaffected. The results are robust to changes to several tunable parameters in the model. They also hold when a higher vertical resolution is used in the ocean.

About the location of base stations for a UMTS system: Analytical study and simulations

One of the first decisions that a radio network designer must take is the location of base stations and the distance between them in order to give the best coverage to a region and, possibly, to reduce deployment costs. In this paper, the authors give an insight to this matter by presenting a possible solution to a real problem: Planning the base stations layout for a universal mobile telecommunications system (UMTS) in the city of Barcelona. At the basis of this problem, there is the interdependence between coverage and capacity in a wideband-code division multiple access (W-CDMA) system, which is a new element in the planning of BS layout for mobile communications. This aspect has been first treated with an analytical study of the cell coverage range for a specific environment and service. The achieved results have been checked with the help of snapshot simulations together with a geographical information system (GIS) tool incorporated in the simulator that allows to perform analysis and to visualize results in a useful way. By using the simulator, it is also possible to study a more complex environment, that of a set of base stations providing multiple services to a large number of users.

Statistical simulations of diffusional coarsening in finite clusters

The problem of diffusional interactions in a finite-sized cluster of spherical particles is studied. Simulations of diffusional interactions with size distribution and volume fraction ${V}_{v},$ as input parameters, referred to as snapshot (static) simulations, are compared with dynamic (time-dependent) simulation results. The precise size distribution information in the snapshot simulations is obtained on the basis of a perturbation technique proposed recently by Fradkov et al. [Phys. Rev. E 53, 3925 (1996)]. Robust iterative solution schemes for the quasistatic diffusion equation facilitate investigations of coarsening systems comprised of one million particles at ultralow ${(10}^{\ensuremath{-}13})$ to moderate (0.25) volume fractions. The objective of carrying out simulations at such low volume fractions is to analyze the first-order volume-fraction-dependent correction to the effective coarsening rate predicted by the Todes, Lifshitz, and Slyozov (TLS) theory at infinite dilution. When volume fraction is considered as an input parameter, the deviation of coarsening rates from that of the infinite dilution limit of TLS varies as $\sqrt[\mathrm{A}\mathrm{P}\mathrm{S}::\mathrm{X}\mathrm{M}\mathrm{L}::\mathrm{G}\mathrm{e}\mathrm{n}\mathrm{P}\mathrm{h}\mathrm{r}\mathrm{a}\mathrm{s}\mathrm{e}=\mathrm{H}\mathrm{A}\mathrm{S}\mathrm{H}(0\mathrm{x}512990)]{{V}_{v}}$ for a finite cluster and $\sqrt{{V}_{v}}$ (Debye screening) for an infinite system. Accurate numerical investigations of the rollover volume fraction ${(V}_{v}^{*})$ above which the $\sqrt[\mathrm{A}\mathrm{P}\mathrm{S}::\mathrm{X}\mathrm{M}\mathrm{L}::\mathrm{G}\mathrm{e}\mathrm{n}\mathrm{P}\mathrm{h}\mathrm{r}\mathrm{a}\mathrm{s}\mathrm{e}=\mathrm{H}\mathrm{A}\mathrm{S}\mathrm{H}(0\mathrm{x}514\mathrm{c}44)]{{V}_{v}}$ behavior changes to $\sqrt{{V}_{v}}$ showed that ${V}_{v}^{*}$ varies as ${n}^{\ensuremath{-}2},$ where $n$ is the number of particles in the spherical cluster. The deviation of coarsening rates from TLS observed from dynamic simulations agrees with that predicted by snapshot simulations for ${V}_{v}<0.01.$ The dynamic results are higher than the snapshot results for ${V}_{v}>0.01.$ The coarsening rate of the average particle can be calculated directly from dynamic simulations and indirectly from snapshot simulations by a perturbation relation. A different type of snapshot-ensemble averaging is suggested on the basis of the functional nature of the individual particle monopole source or sink strengths. Dynamic and snapshot simulations with dipoles were carried out up to a volume fraction of 0.25, and departure from Debye screening behavior was observed. The inclusion of dipole terms affects the deviations noticeably only above a volume fraction of 0.1.

Late-stage coarsening dynamics in phase separating systems: simulation results

Simulations of diffusional interactions among precipitate particles with a given instantaneous size distribution and volume fraction are referred to as snapshot simulations. Dynamic (time-dependent) and snapshot simulations of large ensembles of coarsening particles with monopolar and dipolar interactions are presented. The snapshot simulations show that the deviation of coarsening rates from that of the infinite dilution limit of TLS varies as 3√V v or √V v (Debye screening) depending on the range of volume fraction and number of particles in the system. Dynamic simulation results of the same system confirm the cubic growth law of particles showing that they are in the asymptotic regime. The deviation of coarsening rates from TLS from dynamic simulations is larger than that predicted by the snapshot simulations at V v = 0.10 and higher. The results of the snapshot and dynamic simulations however agree at volume fractions ≤0.01. Structure factor calculations indicate that the scaled structure factor S(q) ~ q −4 (Porod's law) at large values of wave number q, consistent with the presence of sharp interfaces between the droplet and matrix phases.