N L M m Radial grid Cubic grid
ΔUZ3ΔUZ3 ΔFZ3ΔFZ3 ΔUZ3ΔUZ3 ΔFZ3ΔFZ3
1000 1.0 (26,26,26) (32,32,32) 9.70e−10 5.28e−08 4.63e−10 3.48e−08
12 000 2.29 (54,54,54) (68,68,68) 9.56e−10 5.22e−08 4.81e−10 3.55e−08
23 000 2.84 (66,66,66) (82,82,82) 9.95e−10 5.38e−08 4.87e−10 3.56e−08
34 000 3.24 (74,74,74) (92,92,92) 9.85e−10 5.32e−08 4.92e−10 3.57e−08
AV-951 45 000 3.56 (82,82,82) (102,102,102) 9.69e−10 5.25e−08 4.88e−10 3.55e−08
56 000 3.83 (88,88,88) (110,110,110) 9.72e−10 5.30e−08 4.89e−10 3.55e−08
67 000 4.06 (92,92,92) (114,114,114) 9.87e−10 5.31e−08 5.02e−10 3.57e−08
78 000 4.27 (98,98,98) (122,122,122) 9.63e−10 5.48e−08 4.91e−10 3.89e−08
89 000 4.46 (102,102,102) (126,126,126) 9.79e−10 5.83e−08 4.98e−10 4.31e−08
100 000 4.64 (106,106,106) (132,132,132) 9.74e−10 6.24e−08 4.94e−10 4.88e−08
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Total computation times (solid), as well as computation times of short range parts (dotted), and long range parts (dashed) for the 1d-periodic case (o) and 3d-periodic case (△). Left: attended times for the total computation. We also plot exemplary behaviors where the runtime grows proportional to N (red ) and NlogNNlogN (blue □). Right: computation time scaled by the number of particles. We achieved rms energy errors of the size ≈6⋅10−10≈6⋅10−10 and rms force errors of the size ≈5⋅10−8≈5⋅10−8. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
N L M m Radial grid Cubic grid
Figure optionsDownload full-size imageDownload high-quality image (116 K)Download as PowerPoint slideprs.rt(\”abs_end\”);KeywordsIllicit drugs; Biofilms; Sewage epidemiology; Transformation kineticsNomenclature6-AM6-acetyl morphineA/V ratioratio of area of biofilms vs volume of wastewater in the sewer or sewer reactorCOCcocaineBEbenzoyl ecgonineMAmethamphetamineMDMA3,4-methylenedioxy-N-methylamphetamineLCMSMSLiquid chromatography-tandem mass spectrometry1. IntroductionAfter being consumed, illicit drugs are excreted and then transported from individual toilets to the sewage treatment plants via the sewer system. A decade ago, Daughton (2001) proposed that measuring loads of illicit drug residues in wastewater can be used as a tool to back-estimate the consumption of the corresponding illicit drugs in the communities. This approach, generally named as sewage epidemiology and first applied by Zuccato et al. (2005) to estimate the consumption of cocaine in different Italian communities, has now been used worldwide to estimate the consumption of a range of illicit drugs (Banta-Green et?al., 2009, Daughton, 2011, Thomas et?al., 2012, Irvine et?al., 2011 and van Nuijs et?al., 2011).The accuracy of this sewage epidemiology approach may be compromised by a range of uncertainties related to aspects such as wastewater sampling, sample storage, and analytical methods for illicit drugs (Lai et?al., 2011, van Nuijs et?al., 2011, Zuccato et?al., 2008 and Castiglioni et?al., 2013). Some of these recognised issues have been addressed through technical improvement related to sampling (e.g. through the use of flow proportional sampling under controlled temperature) and measurement methods of target drugs (e.g. with the use of highly sensitive methods). However, one major limitation of the sewage epidemiology approach that is yet to be fully understood and addressed concerns the transformation/degradation of illicit drug residues in the sewer system and during storage (Lai et?al., 2011, van Nuijs et?al., 2011, Zuccato et?al., 2008 and Castiglioni et?al., 2013).To address this problem, there have been studies on transformation/degradation of illicit drug residues in wastewater with an initial focus on the stability of illicit drug residues during sample storage (i.e. low temperature and long period) (Castiglioni et?al., 2006, González-Mari?o et?al., 2010, Castiglioni et?al., 2011, Gheorghe et?al., 2008 and Chiaia et al., 2008). Recently, some stability studies have started to evaluate the fate of illicit drug residues in wastewater under ambient condition (i.e. pH 7–7.5, 20 °C) (van Nuijs et?al., 2012, Bisceglia, 2010, Chen et?al., 2013 and Plósz et?al., 2013). However, those former studies only used freshly collected wastewater in glass containers as the test environment. It means that the effects of biofilms in the sewer system, which contain more biologically active organism than the wastewater, to the stability of the illicit drug residues have not been considered.A sewer system that collects and transports wastewater from residential and commercial areas typically consists of rising sewer mains and gravity sewer. Rising sewer mains normally start with a pump station to lift wastewater from low to high altitude. In contrast, gravity sewer, as its name indicates, use gravity to transport wastewater from high to low altitude. A sewer system usually requires both types of sewers but the ratio between those two sewer types is dependent on the unevenness of the land in the catchment area.Rising sewer mains are generally fully filled with wastewater and Amyloid Beta-peptide (25-35) biofilms dominate on the pipe walls. In comparison, gravity sewer is only partially filled with sewage, which may sustain both aerobic and anaerobic biofilms/sediments (Hvitved-Jacobsen, 2002). Since biofilms are rich in microorganisms, which are capable of transforming/degrading various chemical compounds, it is hypothesized that illicit drug residues can also be transformed biologically in sewers by microbes residing in biofilms. This hypothesis leads to the speculation that actual sewer conditions can have different impact on the transformation of illicit drug residues than wastewater alone due to the presence of different microbial populations in biofilms/sediments. Indeed, it has been revealed previously that sewer biofilms makes a substantially higher contribution to sulfide production compared to suspended microorganisms in wastewater (Mohanakrishnan et?al., 2009 and Gutierrez et?al., 2008). Moreover, redox condition of the sewer, i.e. aerobic or anaerobic, can also influence biological transformation processes of chemicals, which can also contribute to the overall transformation of illicit drug residues. It is thus necessary to study the fate of illicit drug residues under different sewer conditions in the presence of sewer biofilms.Also, none of the stability studies mentioned above have directly assessed the transformation of parent drugs to their metabolites, e.g. from cocaine to benzoyl ecgonine or from methamphetamine to amphetamine, because of the interference of benzoyl ecgonine or amphetamine already present in wastewater used in those studies. Since those metabolites, i.e. benzoyl ecgonine and amphetamine, are themselves used as illicit drug residues in sewage epidemiology, their formation during the residence time in the sewer system should be evaluated.This study investigated the transformation/degradation of some popular illicit drug residues in laboratory-scale sewer reactors, either under rising main or gravity sewer conditions. A control reactor without biofilms was also employed to determine the transformation in wastewater alone. The selected illicit drug residues include cocaine (COC), its metabolite benzoyl ecgonine (BE), methamphetamine (MA), MDMA and a metabolite of heroin, 6-acetyl morphine (6-AM). These illicit drug residues are usually used to estimate the consumption of COC, MA, MDMA and heroin, respectively, in sewage epidemiology. Batch tests were carried out using different sewer reactors spiked with the selected illicit drug markers. The use of deuterium labelled isotope compounds in this study helped determining the direct transformations between related illicit drug residues, which were not evaluated before. Concentrations of illicit drug residues were monitored at different time points during a period of 12 h after being spiked into the sewer reactors. The results obtained will help to clarify the impact of sewer conditions including sewer biota and redox conditions to the fate of illicit drug residues during their transport in the sewer system.2. Materials and methods2.1. Chemicals and reagentsDeuterium labelled COC, BE, MA, MDMA and 6-AM were monitored instead of the native compounds in order to trace their exclusive deuterium labelled degradation products (Table 1). All the deuterium labelled standards (COC-d3, BE-d3, MA-d8, MDMA-d5, 6-AM-d6) were purchased from Cerilliant (Texas, US). Working solutions of each deuterium labelled standards were prepared at a concentration of 5000 μg/L in methanol. All working solutions were stored at −20 °C until use. LCMS grade solvents (methanol, acetonitrile) were purchased from Merck, Germany. Deionised water was produced by a MilliQ system (Millipore, 0.22 μm filter, 18.2 mΩ cm−1).Table 1.
Chemical parameters for the bench-scale cultivation approaches and of the oxidation basin of the mine-water treatment plant.pHConcentration [mM] ofEh [mV]Iron oxidation rate [mM/h]PO43−Fe2+Fe3+Reactor with phosphatea∼184.108.40.206.0+720c∼1.1Reactor without phosphatea2.6–2.804.03.5+680c∼0.6Mine-water treatment plantb∼3n.d.3.03.0+736∼0.5daThis study; mean values of data obtained during the continuous cultivation are presented.bHedrich et al., 2011.cGeochemical modeling with PhreeqC based on measured ferrous and ferric iron concentration.dHeinzel et al., 2009b n.d. not determined.Full-size tableTable optionsView in workspaceDownload as CSVThe redox potentials of the bench-scale model and the pilot plant have a similar magnitude. The geochemical modeling with PhreeqC using the composition of the APPW-medium and the measured iron concentration yielded the same redox potential for the cultivation approach without phosphate addition and the treatment plant (data not shown). However, the calculated redox potential of the pilot plant (+680 mV) is lower than the redox potential reported by Hedrich et al. (2011). This difference maybe caused by the different way of determination. The redox potential of PHA665752 mine waters is mainly determined by the ferrous/ferric iron ratio, but the presence of further redox species in aqueous solution (e.g. nitrate/nitrite/ammonium, manganese(II)/manganese(III), arsenic(III)/arsenic(V), organic redox species) influences the redox potential as well (Sánchez Espa?a et?al., 2005 and Stumm and Morgan, 1981). Therefore, it has to be considered that the calculated redox potentials for the cultivation approaches corresponds just to the redox potential of the ferrous/ferric redox couple, whereas the redox potential for the treatment plant was measured directly and thus corresponds just to a mixed potential of all redox species existing in the mine water (Merkel and Planer-Friedrich, 2009).In the bench-scale model potassium dihydrogen phosphate was added directly into the reactor to avoid precipitation of ferrous and ferric phosphates in the medium reservoir (Maurer and Boller, 1999). Some of the dihydrogen phosphate added dissociated into protons and hydrogen phosphate. Due to the buffer capacity of hydrogen phosphate and dihydrogen phosphate present in the solution the pH during the continuous cultivation with phosphate addition was stabilized at pH 2.8 and pH variation as in the control experiment without phosphate was minimized.Although theoretically 1 mM phosphate should have been detected, only 0.2 mM phosphate was determined in the water during the cultivation. Since ferric minerals like schwertmannite, goethite, or akaganéite are known to adsorb phosphate (Chitrakar et?al., 2006 and Eskandarpour et?al., 2006) the residual added phosphate may have been adsorbed by the formed ferric minerals and/or precipitated as iron phosphate strengite (Fig. S.6) (Stumm and Morgan, 1981). Thus, it was not directly available for the microorganisms. The procedure of Altmann et al. (1971), which was used in the present study and which involves the reaction of malachite green and phosphododekamolybdate acid only detects soluble and thus bioavailable phosphate.4.2. Effect of phosphate on the microbiologyDevelopment of different microbial communities from reactors, which were inoculated with the same inoculum (Fig. 4), showed that the community composition was dependent on the phosphate addition. Since phosphate is an essential nutrient, the microorganisms are probably limited by phosphate during the cultivation without phosphate addition. Such nutrient limitations often result in the development of strategies to minimize the depletion (Harder and Dijkhuizen, 1983) and the availability of such strategies to an organism or the lack of them may have a decisive influence on the composition of a microbial community.One of such strategies is the increase of the syntheses of proteins, which are involved in the uptake and transport of the limited nutrient (Harder and Dijkhuizen, 1983). Seeger and Jerez, 1993a and Seeger and Jerez, 1993b reported modified protein syntheses for A. ferrooxidans under phosphate starvation. Genome analysis confirmed the presence of genes for a phosphate-transport system (pst genes) in A. ferrooxidans ( Valdés et al., 2008). A further strategy to antagonize the nutrient limitation is the accumulation of the limiting nutrient inside the cell ( Harder and Dijkhuizen, 1983) and in the genome of A. ferrooxidans genes involved in the polyphosphate storage have been identified ( Valdés et al., 2008).Based on the present state of the genomic analysis “Ferrovum” sp. JA12, which has recently been isolated from the water of the treatment plant ( Tischler et al. 2013), has some similarity to A. ferrooxidans with respect to phosphate uptake and storage (Mosler and Mühling, pers. communication) and thus in the strategies to deal with low phosphate concentrations. Consequently, it is so far not clear, why in the present investigation “Ferrovum” was obviously more favored by the presence of phosphate than other organisms in the microbial community.Since “F. myxofaciens” is reported as the dominating microorganism in acidic streamers ( Hallberg et?al., 2006, Rowe et?al., 2007 and Tan et?al., 2009), the continuous cultivation seems to be an important process-related parameter to favor the growth of “Ferrovum” sp. A further advantage of “F. myxofaciens” over other bacteria of the microbial community obviously is the ability to form extracellular polymeric substances (EPS) in large amounts, which result in attachment of this bacterium on surfaces and thus a reduction of a possible wash out ( Rowe and Johnson, 2008). These advantages are reflected in the dominance of “Ferrovum” sp. during the continuous cultivation independent of the phosphate addition.The significant difference in the ferrous/ferric iron ratio and thus in the redox potentials affects the capacity of the microorganisms to oxidize iron. Thus, L. ferrooxidans is able to oxidize ferrous iron up to higher redox potentials than A. ferrooxidans ( Rawlings et al., 1999). Interestingly, in the present investigation L. ferrooxidans was only detected in the phosphate-containing culture with higher redox potential, whereas A. ferrooxidans only made up a larger share of the population in the phosphate-deficient culture with lower potential. Whether this difference is due to the redox potentials or to other factors is not clear yet, and it is also not yet clear, whether or not the higher dominance of “Ferrovum” sp. in the phosphate-containing culture indicates that these bacteria can tolerate high redox potentials.Besides the effect of the phosphate addition on the diversity of the microbial community, the cell number was also influenced by phosphate addition. In the long-term cultivation the number of cells was increased and stabilized with phosphate addition compared to the approach without added phosphate (Fig. 3). This supports the hypothesis that phosphate limitation may have prevented more extensive growth of the microorganisms. Seeger and Jerez (1993b) showed a four-fold decrease of the cell number of A. ferrooxidans under phosphate starvation. The differences of the cell numbers between medium with and without phosphate increased further, when cells were reinoculated in phosphate-deficient medium. The unexpected high increase of the cell number at the beginning of the cultivation without phosphate addition, compared to the cultivation approach with phosphate addition is not clear yet. However, it seems to be a variation of the cell numbers, since the number of cells in the cultivation approach without phosphate did not increase such high in the phosphate-deficient culture in the second test series ( Fig. A5).The differences in the microbiology between the cultivation approaches without and with phosphate addition are reflected in an increased iron oxidation rate in the cultivation with phosphate addition as compared to that without phosphate. The biological influence on the iron oxidation rate was confirmed by a lack of ferrous iron oxidation during the continuous cultivation of a filter-sterilized mine water sample (Fig. A1). The increased iron oxidation rate during the cultivation with phosphate addition is obviously dependent on the presence of “Ferrovum” sp., since in the culture with phosphate “Ferrovum” sp. clearly dominated and since in addition the specific oxidation rates of ferrous iron for “F. myxofaciens” are higher than in other iron-oxidizing bacteria like A. ferrooxidans or L. ferrooxidans ( Johnson et?al., 2012 and Rowe and Johnson, 2008).This study indicates a limitation of “Ferrovum” sp. by phosphate under natural circumstances. Thus, it is possible that phosphate addition may also improve the performance of the three-step “Ferrovum”-based iron oxidation system described by Hedrich and Johnson (2012). Previous studies concerning the addition of phosphate in the pilot plant revealed no significant effect on the oxidation capacity ( Janneck et al., 2008). However, lower phosphate concentrations were added and soluble and thus bioavailable phosphate was not determined ( Janneck et al., 2008). Therefore, it would be interesting to investigate the effect of phosphate addition in the pilot plant under conditions described herein.5. ConclusionThe process of the mine-water treatment plant could be simulated in bench-scale, which allows the investigation of the system more in detail to stabilize and enhance its performance. In this study the addition of the essential nutrient phosphate resulted in an enhanced growth of the pilot plant dominating iron-oxidizing “Ferrovum” sp. and in an increase of the iron oxidation rate. Thus, this study proved the hypothesis that iron-oxidizing microorganisms occurring in acid mine waters are limited by the low phosphate concentration. In future the effect of other nutrients, which are maybe limiting for the microbial growth as well, can be studied using the bench-scale model.AcknowledgmentWe thank the BMBF for funding the research projects SURFTRAP (number: 03G0714B) and SURFTRAPII (number: 03G0821B) within the R&D-program GEOTECHNOLOGIEN.Appendix A. Supplementary dataThe following is the supplementary data related to this article:
Description and Examples of the Components of Communicative CompetenceCommunicative Competence ComponentNarrative DescriptionExample in Medical Interprofessional CommunicationGrammatical competenceConcerned with mastery of the language code itself (ie, the words and the rules).Medical terminology and jargon, order of presentation (ie, chief complaint before the history of present illness and the physical examination before the labs).Sociolinguistic competenceConcerned with appropriateness of the chosen grammar and syntax for the particular situation or context.Use of jargon may be inappropriate for discussion with nonphysician care team members.Strategy competenceConcerned with adoption of the appropriate communication strategy for the situation or context.Appropriate choice of communication type (eg, alpha text page versus e-mail versus telephone versus face-to-face) or the strategy within PD98059 given type (eg, 30-second synopsis versus 5-minute full presentation).Full-size tableTable optionsView in workspaceDownload as CSVDevelopmental Milestones• Recites facts according to a given set of rules or scripts, often directly from a template or prompt. Does not adjust communication on the basis of context, audience, or situation. Appears unaware of the social purpose of the communication.• Adjusts communication to better fit the context, audience, and situation and can present without templates or prompts, but may still err on the side of inclusion of excess detail.• Successfully tailors communication strategy and message to the audience, purpose, and context in most situations. Demonstrates awareness of the purpose of the communication; can efficiently tell a story and effectively make an argument. Beginning to improvise in unfamiliar situations.• Uses the communication strategy asthma aligns with the situation. Distills complex cases into succinct summaries tailored to audience, purpose, and context. Can improvise and has expanded strategies for dealing with difficult communication scenarios (eg, an interprofessional conflict).• Improvises in new or difficult communication scenarios. Recognized as a highly effective public speaker and a role model for the management of difficult conversations.Full-size tableTable optionsView in workspaceDownload as CSV
In a previous paper the authors presented a node-centered finite-volume ALE solver for grids undergoing edge-swapping , where the modifications occurring in the shape of the finite volumes due to the changes in the topology are recast in a continuous fashion. Such approach makes it possible to compute the solution at the subsequent time level simply by integrating the governing equations and avoiding the need of an explicit remap phase. In the present work the same finite-volume solver is extended to the case of grid refinement and coarsening. Similarly to the case of edge swapping, the insertion or Rigosertib of a node is described in terms of continuous deformation of the finite volumes associated to the computational grid. Therefore, when a vertex is inserted a new finite volume appears while it disappears when a vertex is removed.
Future extensions to viscous, thermal conducting fluid are expected to be straightforward, since the ALE formulation does not modify the viscous and thermal conductivity contributions  and . Care must be taken however in the proximity of the body surface, where very stretched boundary-layer grids made of non-simplectic elements are commonly used. Note that ALE schemes implementing shock-capturing techniques, including the present one, can be easily extended to deal with multi-material interface by e.g. the shock-capturing method of Abgrall  and modifications of medulla oblongata  and . As an alternative, thanks to the large-displacement capability of the present scheme, the material interfaces can be explicitly advected within the ALE formulation and boundary-conforming grids can be used to represent it  and . Extension to multi-material flows will be the focus of future research activities.
On the other hand, the universal Kriging PHA-739358 has been introduced by Matheron  in the field of geostatistics as a tool to interpolate discrete data considered as points of a random field trajectory. Later, this approach has been widely used in computer experiment domain , ,  and , sequential design of experiments ,  and  and global optimization . Because of the lack of a priori knowledge about the output, the Kriging model is often used in its basic configuration known as ordinary Kriging.
2. Exposure assessment
2.1. Exposure quantification and anatomical models
The human exposure is quantified by using the Specific Absorption Rate (SAR) expressed in W/kg:
View the MathML sourceSAR=σE22ρ
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In this equation σ is the conductivity of human tissue and ρ is its mass density. E is the modulus of the electric field induced in the tissue. In this paper, the exposure assessment of a pregnant woman model at the 26th week of amenorrhea (WA) is performed. The fetus model was built from the segmentation of ante-natal images . Then the obtained fetus model was inserted in a Deformable Synthetic Woman (DSW) which is initially based on a homogeneous woman model with additional basic tissues such as skin, fat, muscle and bones. This pregnant woman model was then deformed using a deformation software  in order to give her a seated position and the arms raised as if she was typing on a computer keyboard (see Fig. 1).
To understand the thermal impact to quantum effects in nano-transistors, we consider a cylinder shaped channel with a variety of gate voltages, phonon–electron interaction strengths and temperatures. It is found that an increase in the phonon–electron interaction strength or temperature leads to a decrease in channel current. However, it GDC-0449 is interesting to find out that the phonon–electron interaction has little impact to the quantum tunneling ratio.
Finally, it is worthwhile to mention that to ensure the computational accuracy and modeling reliability of the above findings, advanced numerical methods have been employed in the present work. Second order elliptic interface techniques were applied to solve the Poisson equation for the electrostatic potentials with three semiconductor–insulator geometries. The Kohn–Sham equation was solved based on the physical properties neuromuscular junction electrons have continuous and discrete spectra along transport and confined direction, respectively. The self-consistence of the coupled system was achieved by Gummel-like iterations. The performances of the nano-device were validated in terms of current–voltage curves with three types of Si/SiO2 interfaces over a wide range of source-drain or gate voltages, and different phonon energies.
We proposed a method that uses solid surface particles to correctly resolve fluid pressure forces inside thin lubricated gaps between rigid bodies which the grid alone fails to resolve, coupling together the fluid in the gap with both the fluid on the grid and the rigid bodies in order to provide a monolithic and symmetric positive-definite system. Leaving thin rigid bodies and deformable solids as future work, the current method rasterizes the boundary of each rigid body into a closed hull. When the gap between two rigid bodies is under-resolved by the grid, pressure forces are missing on grid faces that lie between two grid FIIN-3 that are rasterized into two different rigid bodies. To compute pressure forces on such grid faces, we treat each of these grid faces as two virtual solid–fluid faces and create a virtual fluid cell between the two virtual faces. To compute fluid pressure values for these virtual fluid cells, we added fluid pressure degrees of freedom to solid surface particles in the gap region and designed an interpolation operator that interpolates from the solid surface particles to the virtual fluid cells. Finally, the fluid pressure forces are computed on the virtual faces using the pressures in virtual fluid cells in the same manner as for regular solid fluid coupling grid faces.
The complexity of the flow depends on the distance from the engine. For low Mach values, the flow can be decomposed into three areas with different flow conditions: a uniform flow far from the engine, a turbulent flow (often non-linear) due to the fans and the boundary layers, and a potential flow in-between. We use this JIB-04 decomposition in our model, except for the turbulent area.
The interior part of the engine is also supposed to be behind the modal surfaces. We then consider only two domains: ΩiΩi with a potential flow and ΩeΩe with a uniform flow. The flow is an input to the problem. Matching conditions on the flow are supposed at the interface Γ∞Γ∞ between these two domains. Moreover, at ΓM1ΓM1 and ΓM2ΓM2, the flow is supposed uniform and orthogonal to the surface. It it also tangent to Γ.
2.2. Coupled problem
2.2.1. Convected Helmholtz equation
For simplicity, only one modal surface ΓMΓM is considered in the model problem instead of ΓM1ΓM1 and ΓM2ΓM2 as presented on Fig. 1. We define ΩMΩM as a semi-infinite waveguide with base ΓMΓM and oriented along the axis of the engine, see Fig. 2.
While the approach based on the long-wave model has been very successful, it Cobicistat does include limitations inherent in its formulation: in particular, the restriction to small interfacial slopes (strictly speaking, the slopes much less than unity), and therefore small contact angles. We have shown in our earlier work  that, depending on the choice of flow geometry, the comparison between the solutions of the long-wave model and of the Navier–Stokes equations may be better than expected; however, still for slopes of O(1)O(1), quantitative agreement disappears. Therefore, one would like to be able to consider wetting/dewetting problems by working outside of the long-wave limit, while still considering the most important physical effects such as fluid/solid interaction forces. These fluid/solid interactions are known to be crucial in determining stability properties of a fluid film; without their presence, a fluid film on a substrate is stable, since there are no forces in the model to destabilize it. In particular, for thin nanoscale films, fluid/solid interaction forces may be dominant. We note that the approaches based on the Derjaguin approximation to include the van der Waals or electrostatic interactions into the model in the form of a local pressure contribution (disjoining pressure) acting on the fluid/solid interface are derived under the assumption of a flat film , ,  and . Therefore these approaches cannot be trivially extended to the configurations involving large contact angles.