Molecular Mixing Model Research Articles

Warming Leads to Changes in Soil Organic Carbon Molecules Due to Decreased Mineral Protection.

Climate change affects the content and composition of soil organic carbon (SOC). However, warming-induced changes in the SOC compounds remain unknown. Using nuclear magnetic resonance spectroscopy, molecular mixing models, and Fourier transform ion cyclotron resonance mass spectrometry, we analyzed the variations and relationships in molecular compounds in Mollisol with 10-56 g C kg-1 soil-1 by translocating soils under six climate regimes. We found that increased temperature and precipitation were negatively correlated with carbohydrate versus lipid and lignin versus protein. The former was consistent across soils with varying SOC contents, but the latter decreased as the SOC content increased. The carbohydrate-lipid correlations were related to dithionite-citrate-extractable Fe, while the lignin-protein correlations were linked to changes in moisture and pyrophosphate-extractable Fe/Al. Our findings indicate that the reduction in the mineral protection of SOC is associated with molecular alterations in SOC under warming conditions.

A DNS evaluation of three MMC-like mixing models for transported PDF modelling of turbulent nonpremixed flames

Transported probability density function (TPDF) methods are suitable for modelling turbulent reactive flows. One of the main challenges is to accurately model the molecular mixing terms. In TPDF mixing models, it is desired that the principle of localness is satisfied so that the molecular mixing is performed locally in both physical and composition spaces. The multiple mapping conditioning (MMC) mixing model can ensure mixing localness without violating other desired principles. The present study examines three MMC-like mixing models, including the original MMC (OMMC) mixing model, shadow-position mixing model (SPMM) and a conceptually simplified multiple mapping conditioning (SMMC) mixing model. Three direct numerical simulation (DNS) datasets modelling turbulent nonpremixed ethylene flames with increasing levels of extinction are used for model evaluation. The DNS datasets are also used to provide both initial conditions and inputs needed over the course of TPDF runs to remove the uncertainties caused by turbulence closure, allowing the study to focus on the molecular mixing model. The mixing model coefficients are specified analytically by reference to a canonical mean scalar gradient (MSG) flow in order to achieve specifiable dissipation rate and user-controllable localness. The results show that the MMC-like mixing models yield similar prediction of flame extinction and reignition if the coefficients are properly specified. The MMC-like mixing models can also be tuned to achieve a desired level of localness. For conditional statistics, the MMC-like mixing models can yield correct level of conditional variances. By changing localness, the MMC-like models can yield solutions resembling the interaction by exchange with the mean (IEM) or Euclidean minimum spanning tree (EMST) mixing model for extreme parameter choices. The models differ in their abilities to specify unconditional dissipation rates, at least in the flow considered, and in their ease of implementation.

Investigation of the mixing inside the confined impinging jet mixer using the Fokker–Planck mixing model

Confined Impinging Jet Mixers (CIJMs) are widely used due to their small-scale-mixing efficiency. This property makes them especially useful for nanoprecipitation. The CIJM process parameters are computationally expensive to predict when using direct-numerical simulation (DNS) and large-eddy simulation (LES). In this work, binary nonreactive mixing of a CIJM is studied using a CFD approach with less computational cost than DNS and LES. The flow field is modelled using Reynolds-averaged Navier–Stokes (RANS) equations and molecular mixing is studied using the Fokker–Planck (FP) molecular-mixing model. The extended quadrature method of moments and generalized quadrature method of moments approaches with β kernel density functions are used to approximate the solution to the evolution of the univariate composition. The results of the flow simulation are compared to experimental and DNS data reported in the literature at various inlet flow rates. Multiple closure models for RANS simulation were investigated in this study. The model that produced the most favorable results was the Launder–Reece–Rodi (LRR) turbulence model due to its ability to handle flow separation and complex vortical structures. The FP mixing model was then employed to resolve the probability density function of a univariate composition to determine the efficacy of mixing at the molecular level for different inlet flow rates. The model used in this study is less computationally expensive than DNS and LES and is shown to be sufficient to accurately capture nanoparticle mixing. Thus, the present work provides a framework for industrial improvement to nanoparticle mixing processes using numerical analysis.

Molecular trade-offs in soil organic carbon composition at continental scale

The molecular composition of soil organic carbon remains contentious. Microbial-, plant- and fire-derived compounds may each contribute, but whether they vary predictably among ecosystems remains unclear. Here we present carbon functional groups and molecules from a diverse spectrum of North American surface mineral soils, collected primarily from the National Ecological Observatory Network and quantified by nuclear magnetic resonance spectroscopy and a molecular mixing model. We find that soils vary widely in relative contributions of carbohydrate, lipid, protein, lignin and char-like carbon, but each compound class has similar overall abundance. Ninety percent of the variance in carbon composition can be explained by three principal component axes representing a trade-off between lignin and protein, a trade-off between carbohydrate and char, and lipids. Reactive aluminium, crystalline iron oxides and pH plus overlying organic horizon thickness—predictors that are all related to climate—best explain variation along each respective axis. Together, our data point to continental-scale trade-offs in soil carbon molecular composition that are linked to environmental and geochemical variables known to predict carbon mass concentrations. Controversies regarding the genesis of soil carbon and its potential responses to global change can be partially reconciled by considering diverse ecosystem properties that drive complementary persistence mechanisms.

Evidence for the Existence of Humic Acids in Peat Soils Based on Solid‐State 13C NMR

Humic extracts, in particular humic acids, of organic‐rich peat soils were examined by solid‐state 13C nuclear magnetic resonance (NMR) and shown to be integral components of the peat, contrary to recent suggestions that humic materials are artifacts of alkali extraction. The authenticity of humic substances is demonstrated by recombining the various humic fractions and comparing the NMR spectrum of the recombined peat with the original untreated peat sample. Even though significant NMR‐determined structural differences exist between humic acids and the insoluble humin fractions, the recombination reproduces the original unextracted peat quite well. Applying a biopolymer mixing model to the spectra shows that humic acids have a high proportion of char‐like material that is interpreted as being derived from noncombustion polymerization or secondary synthesis during humification, a process that has been challenged by a recent soil formation model.Core Ideas Solid‐state 13C NMR of soils isolated by dilute alkali proves the existence of humic acids. Molecular mixing model and physical reconstitution both confirm the alkali extracts are real. More char‐like structures in humic acids than humin suggests secondary synthesis formation.

A dual timescale model for micro-mixing and its application in LES-TPDF simulations of turbulent nonpremixed flames

The numerical simulation of modern aero-engine combustion chamber needs accurate description of the interaction between turbulence and chemical reaction mechanism. The Large Eddy Simulation (LES) method with the Transported Probability Density Function (TPDF) turbulence combustion model is promising in engineering applications. In flame region, the impact of chemical reaction should be considered in TPDF molecular mixing model. Based on pioneer research, three new TPDF turbulence-chemistry dual time scale molecular mixing models were proposed tentatively by adding the chemistry time scale in molecular mixing model for nonpremixed flame. The Aero-Engine Combustor Simulation Code (AECSC) which is based on LES-TPDF method was combined with the three new models. Then the Sandia laboratory’s methane-air jet flames: Flame D and Flame E were simulated. Transient simulation results show that all the three new models can predict the instantaneous combustion flow pattern of the jet flames. Furthermore, the average scalar statistical results were compared with the experimental data. The simulation result of the new TPDF arithmetic mean modification model is the closest to the experimental data: the average error in Flame D is 7.6% and 6.6% in Flame E. The extinction and re-ignition phenomena of the jet flames especially Flame E were captured. The turbulence time scale and the chemistry time scale are in different order in the whole flow field. The dual time scale TPDF combustion model has ability to deal with both the turbulence effect and the chemistry reaction effect, as well as their interaction more accurately for nonpremixed flames.

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods

An extended quadrature method of moments using the β kernel density function (β-EQMOM) is used to approximate solutions to the evolution equation for univariate and bivariate composition probability distribution functions (PDFs) of a passive scalar for binary and ternary mixing. The key element of interest is the molecular mixing term, which is described using the Fokker–Planck (FP) molecular mixing model. The direct numerical simulations (DNSs) of Eswaran and Pope [“Direct numerical simulations of the turbulent mixing of a passive scalar,” Phys. Fluids 31, 506 (1988)] and the amplitude mapping closure (AMC) of Pope [“Mapping closures for turbulent mixing and reaction,” Theor. Comput. Fluid Dyn. 2, 255 (1991)] are taken as reference solutions to establish the accuracy of the FP model in the case of binary mixing. The DNSs of Juneja and Pope [“A DNS study of turbulent mixing of two passive scalars,” Phys. Fluids 8, 2161 (1996)] are used to validate the results obtained for ternary mixing. Simulations are performed with both the conditional scalar dissipation rate (CSDR) proposed by Fox [Computational Methods for Turbulent Reacting Flows (Cambridge University Press, 2003)] and the CSDR from AMC, with the scalar dissipation rate provided as input and obtained from the DNS. Using scalar moments up to fourth order, the ability of the FP model to capture the evolution of the shape of the PDF, important in turbulent mixing problems, is demonstrated. Compared to the widely used assumed β-PDF model [S. S. Girimaji, “Assumed β-pdf model for turbulent mixing: Validation and extension to multiple scalar mixing,” Combust. Sci. Technol. 78, 177 (1991)], the β-EQMOM solution to the FP model more accurately describes the initial mixing process with a relatively small increase in computational cost.

A mixing timescale model for TPDF simulations of turbulent premixed flames

Transported probability density function (TPDF) methods are an attractive modeling approach for turbulent flames as chemical reactions appear in closed form. However, molecular micro-mixing needs to be modeled and this modeling is considered a primary challenge for TPDF methods. In the present study, a new algebraic mixing rate model for TPDF simulations of turbulent premixed flames is proposed, which is a key ingredient in commonly used molecular mixing models. The new model aims to properly account for the transition in reactive scalar mixing rate behavior from the limit of turbulence-dominated mixing to molecular mixing behavior in flamelets. An a priori assessment of the new model is performed using direct numerical simulation (DNS) data of a lean premixed hydrogen–air jet flame. The new model accurately captures the mixing timescale behavior in the DNS and is found to be a significant improvement over the commonly used constant mechanical-to-scalar mixing timescale ratio model. An a posteriori TPDF study is then performed using the same DNS data as a numerical test bed. The DNS provides the initial conditions and time-varying input quantities, including the mean velocity, turbulent diffusion coefficient, and modeled scalar mixing rate for the TPDF simulations, thus allowing an exclusive focus on the mixing model. The new mixing timescale model is compared with the constant mechanical-to-scalar mixing timescale ratio coupled with the Euclidean Minimum Spanning Tree (EMST) mixing model, as well as a laminar flamelet closure by Pope and Anand (1984). It is found that the laminar flamelet closure is unable to properly capture the mixing behavior in the thin reaction zones regime while the constant mechanical-to-scalar mixing timescale model under-predicts the flame speed. The EMST model coupled with the new mixing timescale model provides the best prediction of the flame structure and flame propagation among the models tested, as the dynamics of reactive scalar mixing across different flame regimes are appropriately accounted for.

Humic acid composition and humification processes in wetland soils of a Mediterranean semiarid wetland

The present study focuses on a compositional characterization of the humic acid (HA) fraction of several wetland soils using solid-state 13C NMR spectroscopy. The data were analysed using the molecular mixing model (MMM), based on an empirical approach by Nelson and Baldock. The compositional data from HAs obtained with this model were used to obtain a wider assessment of the process of humification from comparison of total soil wetland organic matter composition and HA composition. Twenty samples of humic acids (HAs) isolated from a Mediterranean semiarid wetland (‘Tablas de Daimiel’, central Spain) were studied using elemental analysis and cross polarization magic angle spinning (CPMAS)13C nuclear magnetic resonance (NMR) spectroscopy. The NMR data were analysed with the molecular mixing model (MMM) considering up to six generic components (carbohydrate, protein, lignin, lipid, char and ‘carbonyl’). HAs are considered a conceptual mixture of these model components, and the MMM determines the proportions of the characteristic biomolecules contributing to HA composition. The composition of the HAs under study depends on local factors such as site vegetation and occurrence of fire. Correlations between the proportions of the six generic components and further comparison with those determined for the unfractionated OM (whole sample, WS), gave information on HA origin and humification mechanisms. In particular, the proportions of char and carbohydrate (R 2 0.637) and contents of lignin and protein (R 2 0.471) in the HAs were negatively correlated (P < 0.05). Significant correlations (R 2 0.439) also existed for char contents in whole sample (WS) compared to HA, and for carbohydrates in WS compared to HA (R 2 0.558). Char proportion grew in HA with respect to the WS, and carbohydrates dropped to a half on average in HA compared to WS. Two different humification mechanisms could be identified for no-fire and fire areas. In the former, HA-char was preserved selectively from char in the sample, whereas in the latter, char was newly formed by fire effect.

ChemInform Abstract: Environmental NMR: Solid‐State Methods

AbstractReview: 132 refs.

Total and pyrogenic carbon stocks in black spruce forest floors from eastern Canada

Pyrogenic carbon (PyC), a by-product of recurrent boreal wildfires, is an important component of the global soil C pool, although precise assessment of boreal PyC stock is scarce. The overall objective of this study was to estimate total C stock and PyC stock in forest floors of Eastern Canada boreal forests. We also investigated the environmental conditions controlling the stocks and characterized the composition of the forest floor layers. Forest floor samples were collected from mesic black spruce sites recently affected by fire (3–5yr) and analyzed using elemental analysis and solid state 13C nuclear magnetic resonance (NMR) spectroscopy. PyC content was further estimated using a molecular mixing model. Total C stock in forest floors averaged 5.7±2.9kgC/m2 and PyC stock 0.6±0.3kgC/m2. Total stock varied with position in the landscape, with a greater accumulation of organic material on northern aspects and lower slope positions. In addition, total stock was significantly higher in spruce-dominated forest floors than stands where jack pine was present. The PyC stock was significantly related to the atomic H/C ratio (R2 0.84) of the different organic layers. 13C NMR spectroscopy revealed a large increase in aromatic carbon in the deepest forest floor layer (humified H horizon) at the organic-mineral soil interface. The majority of the PyC stock was located in this horizon and had been formed during past high severity fires rather than during the most recent fire event.

Molecular composition of recycled organic wastes, as determined by solid-state 13C NMR and elemental analyses

Using solid state 13C NMR data and elemental composition in a molecular mixing model, we estimated the molecular components of the organic matter in 16 recycled organic (RO) wastes representative of the major materials generated in the Sydney basin area. Close correspondence was found between the measured NMR signal intensities and those predicted by the model for all RO wastes except for poultry manure char. Molecular nature of the organic matter differed widely between the RO wastes. As a proportion of organic C, carbohydrate C ranged from 0.07 to 0.63, protein C from <0.01 to 0.66, lignin C from <0.01 to 0.31, aliphatic C from 0.09 to 0.73, carbonyl C from 0.02 to 0.23, and char C from 0 to 0.45. This method is considered preferable to techniques involving imprecise extraction methods for RO wastes. Molecular composition data has great potential as a predictor of RO waste soil carbon and nutrient outcomes.

Compositional characterization of soil organic matter and hot-water-extractable organic matter in organic horizons using a molecular mixing model

Purpose Microbial decomposition of soil organic matter (SOM) is generally believed to be heterogeneous, resulting in the preferential loss of labile compounds such as carbohydrates and proteins and the accumulation of recalcitrant compounds such as lipids and lignin. However, these fractions are difficult to measure directly in soils. We examined patterns in the biomolecular composition of SOM and hot-water-extractable organic matter (HWEOM) by using a molecular mixing model (MMM) to estimate the content of carbohydrates, protein, lipids, and lignin.

Numerical Simulation of Reactive Turbulent Scalar Mixing Layer by the Random Fourier Modes Method and Lagrangian Molecular Mixing Model

A new computational scheme using Lagrangian model of the velocity and molecular mixing for the fluid particle is developed to calculate the reactive scalar field in grid generated turbulence. The model is composed of three parts. The Lagrangian velocity of fluid particle which carries the reacting species is generated by the Random Fourier Modes method. The molecular mixing model(the modified Curl's model)is used to calculate the mixing and diffusion of reactive concentration field, and the chemical reaction model is a second-order and irreversible reaction in the scalar mixing layer. It is shown that the simulated results of the first and second moments of reactive and productive species show the good agreements with of the experimental data.

The link between peat hydrology and decomposition: Beyond von Post

Summary Hydrology is central to the formation, growth and utilisation of peat soils. However, peat presents a difficult medium in which to measure hydrologic properties, due to its soft structure and high water content. The von Post scale is a widely used measure of the extent of decomposition of peat, which can be applied in the field or the laboratory without specialised equipment. von Post decomposition has been shown to correlate with hydraulic conductivity. However, it is a categorical and subjective measure of decomposition. Technological advances now enable peat chemistry to be described quantitatively and objectively. 13C nuclear magnetic resonance (NMR) is now routinely used to describe peat chemistry, and the capability of this technique has been extended by the development of the molecular mixing model (MMM). The MMM predicts the molecular composition of organic material from the spectral information provided by 13C NMR. We found significant relationships between the hydrologic properties hydraulic conductivity and water yield and peat chemistry as described by 13C NMR and the MMM. These relationships have potential application in all fields where the hydrologic properties of peat soils are of interest (i.e. peat mining, peatland restoration, catchment management) and also in modelling of peatland development and responses to climate change.

Long‐term carbon storage through retention of dissolved aromatic acids by reactive particles in soil

AbstractSoils retain large quantities of carbon, thereby slowing its return to the atmosphere. The mechanisms governing organic carbon sequestration in soil remain poorly understood, yet are integral to understanding soil‐climate feedbacks. We evaluated the biochemistry of dissolved and solid organic carbon in potential source and sink horizons across a chronosequence of volcanic soils in Hawai'i. The soils are derived from similar basaltic parent material on gently sloping volcanic shield surfaces, support the same vegetation assemblage, and yet exhibit strong shifts in soil mineralogy and soil carbon content as a function of volcanic substrate age. Solid‐state13carbon nuclear magnetic resonance spectra indicate that the most persistent mineral‐bound carbon is comprised of partially oxidized aromatic compounds with strong chemical resemblance to dissolved organic matter derived from plant litter. A molecular mixing model indicates that protein, lipid, carbohydrate, and char content decreased whereas oxidized lignin and carboxyl/carbonyl content increased with increasing short‐range order mineral content. When solutions rich in dissolved organic matter were passed through Bw‐horizon mineral cores, aromatic compounds were preferentially sorbed with the greatest retention occurring in horizons containing the greatest amount of short‐range ordered minerals. These minerals are reactive metastable nanocrystals that are most common in volcanic soils, but exist in smaller amounts in nearly all major soil classes. Our results indicate that long‐term carbon storage in short‐range ordered minerals occurs via chemical retention with dissolved aromatic acids derived from plant litter and carried along preferential flow‐paths to deeper B horizons.

Application of PDF mixing models to premixed flames with differential diffusion

Differential diffusion alters the balance of reaction and diffusion in turbulent premixed combustion, affecting the performance and emissions of combustion devices. Modelling combustion devices with Probability or Filtered Density Function (PDF or FDF) methods provides an exact treatment for the change in composition due to chemical reaction, while molecular mixing has to be modelled. Previous PDF molecular mixing models do not account for differential diffusion in a manner which satisfies realizability requirements. A new approach for treating differential diffusion, which ensures realizability, is proposed for pairwise-exchange mixing models in general, and applied in the Interaction by Exchange with the Mean (IEM) model of Dopazo [26], and in the Euclidean Minimum Spanning Tree (EMST) model of Subramaniam and Pope [5]. The new differential diffusion models are referred to as IEM-DD and EMST-DD respectively.Results from two and three-dimensional DNS of turbulent premixed methane–air combustion show that mixing rates and conditional statistics of species mass fractions depend on species diffusivities and the combustion regime. Zero-dimensional PDF model results obtained for the two-dimensional DNS case show that the EMST-DD model best reproduces the features that characterize differential diffusion in the DNS. The essential feature of the EMST-DD model, which accounts for its success in turbulent premixed combustion, is that differential mixing rates are imposed within a model which mixes locally in composition space.

Spectral fingerprinting of soil organic matter composition

Large scale environmental monitoring schemes would benefit from accurate information on the composition of soil organic matter (SOM), but so far routine procedures for describing SOM composition remain a chimera. Here, we present the initial assessment of a two step strategy for expeditious determination of SOM composition that involves: (i) building infrared fingerprints from near and mid infrared spectroscopies, two rapid and cheap yet reliable technologies; and (ii) calibrating such infrared fingerprints with multivariate chemometrics from a molecular mixing model based on the more expensive and time consuming 13C nuclear magnetic resonance technique, which discriminates five biochemical components: carbohydrate, protein, lignin, lipid and black carbon. We show fair to excellent predictive ability of the calibrated infrared fingerprints for four out of these five biochemical components, with cross-validated ratios of performance to inter-quartile distance from 3.2 to 8.3, on a small set of 23 soil samples with a wide range of organic carbon content (12–500g/kg). Multivariate calibration models were highly selective (<2% of infrared data were used for all models). However, the specificity to one particular biochemical component of the infrared wavebands automatically selected by each model was relatively low, except for lipid. Achieving direct predictions of SOM composition on unknown soil samples with infrared spectroscopy alone will require further independent validation and a larger number of samples. Overall, the implementation of our strategy at a broader scale, based on available 13C nuclear magnetic resonance soil libraries, could provide a cost effective solution for the routine assessment of SOM composition.

Sources of Terrestrial Organic Carbon in the Mississippi Plume Region: Evidence for the Importance of Coastal Marsh Inputs

High sedimentation rates along river-dominated margins make these systems important repositories for organic carbon derived from both allochthonous and autochthonous sources. Using elemental carbon/nitrogen ratios, molecular biomarker (lignin phenol), and stable carbon isotopic (bulk and compound-specific) analyses, this study examined the sources of organic carbon to the Louisiana shelf within one of the primary dispersive pathways of the Mississippi River. Surface sediment samples were collected from stations across the inner, mid, and outer Louisiana shelf, within the Mississippi River plume region, during two cruises in the spring and fall of 2000. Lignin biomarker data showed spatial patterns in terrestrial source plant materials within the river plume, such that sediments near the mouth of the Mississippi River were comparatively less degraded and richer in C4 plant carbon than those found at mid-depth regions of the shelf. A molecular and stable isotope-based mixing model defining riverine, marsh, and marine organic carbon suggested that the highest organic carbon inputs to the shelf in spring were from marine sources (55–61% marine organic carbon), while riverine organic carbon was the highest (63%) in fall, likely due to lower inputs of marine organic carbon at this time compared with the spring season. This model also indicated that marsh inputs, ranging from 19 to 34% and 3–15% of the organic carbon in spring and fall, respectively, were significantly more important sources of organic carbon on the inner Louisiana shelf than previously suggested. Finally, we propose that the decomposition of terrestrial-derived organic carbon (from the river and local wetlands sources) in mobile muds may serve as a largely unexplored additional source of oxygen-consuming organic carbon in hypoxic bottom waters of the Louisiana shelf.

Can pyrolysis-GC/MS be used to estimate the degree of thermal alteration of black carbon?

Very little is known about the macromolecular properties of biomass combustion residues referred to as black carbon (BC). Pyrolysis-gas chromatography–mass spectrometry (Py-GC/MS) was performed on: (i) peat from Spain at 400–1200 °C to investigate the effect of charring on pyrolysis fingerprint and (ii) natural charcoal from Laos in order to link molecular information to published chemical and reactivity parameters. Confirming earlier Py-GC/MS studies, the BC in the artificially charred peat and the natural charcoal produced predominantly benzene, toluene, C 2-benzenes, PAHs and benzonitriles. Furthermore, some charcoal samples produced significant amounts of phenols, methoxyphenols, carbohydrate markers, n-alkanes and n-alkenes upon pyrolysis, reflecting non-charred and weakly charred biomass. A series of pyrolysis product ratios related to the degree of dealkylation of the pyrolysis products (benzene/toluene, naphthalene/C 1-naphthalenes, C 1-naphthalenes/C 2-naphthalenes, benzofuran/C 1-benzofurans and benzonitrile/C 1-benzonitrile) increased with increasing artificial charring (peat) and, for the natural charcoal, these ratios were in accordance with established chemical and reactivity parameters related to charring intensity from other methods: proportion of aromatic C obtained from solid state 13C nuclear magnetic resonance spectroscopy (NMR), the proportion of charred material as estimated from NMR in conjunction with a molecular mixing model (NMR–MMM) and the resistance to acid dichromate oxidation. The alkyl side chains of aromatic pyrolysis products are probably inherited from short chain aliphatic C chains that cross link the predominantly aromatic building blocks of BC, and these linkages seem to disappear with increasing charring intensity. Thus, the degree of thermal alteration of BC can be discerned from the pyrolysis fragmentation pattern.