Modélisation du lessivage des bromures dans des cases lysimétriques par la méthode numérique des lignes

La modélisation du transport des solutés dans un milieu non-saturé repose habituellement sur l'équation de dispersion-advection (EDA). Un modèle numérique (TSOL) a été développé en couplant l'EDA avec l'équation de Richards et en incluant le prélèvement de l'eau par les plantes. La résolution numérique a été effectuée par la méthode numérique des lignes (MNL) qui présente une grande simplicité de programmation et résulte en une très bonne précision numérique. La précision de TSOL a été testée avec les résultats d'un modèle d'éléments finis (HYDRUS), et avec des données expérimentales (profils de concentration et masses de bromures récupérés) collectées pendant 195 jours dans trois cases lysimétriques installées sur un sol non remanié cultivé en pommes de terre. La comparaison entre TSOL et HYDRUS montre que la solution de la MNL est similaire à celle des éléments finis. Toutefois, pour l'ensemble des cases et des profondeurs, les modèles ont montré une surestimation des valeurs de concentration avec un écart moyen entre les concentrations mesurées et simulées par TSOL variant de 22 à 112 mg/l. Pour les cases B et C, l'erreur moyenne de biais hebdomadaire entre TSOL et les masses de bromures récupérés, était d'environ 5 mg/semaine. Dans le cas de la case A, l'erreur moyenne de biais hebdomadaire de TSOL était de 39 mg/semaine.Simulation of solute transport under transient unsaturated conditions is generally based on the dispersion-advection equation (DAE); a partial differential equation of the parabolic type under unsaturated conditions. The DAE has been solved by various numerical methods, such as finite elements and finite differences. However, these methods require advanced knowledge in mathematics and computer programming, in addition to specific adaptations to each problem in order to avoid numerical difficulties such as stability and convergence. The numerical method of lines (NML) can solve complex problems while keeping programming to a level accessible to a large number of engineers and scientists. The purpose of this article are (1) to develop and evaluate the numerical performance of a NML model (TSOL) that solves the DAE coupled with Richard's equation under unsaturated conditions; (2) to compare results of the TSOL model with those of a recognized finite elements model (HYDRUS); and (3) to validate the TSOL model with experimental data collected during 195 days under a potato field.The experimental setup was installed on September 1994 in a potato field located at Saint-Pierre, Île d'Orléans, near Québec City. It consisted on three pan lysimeters (A, B, and C) with a surface area of 0.48 m2 and a depth of 1.00 m, installed in an undisturbed sandy soil. On May 12, 1995, 15 g of KBr, dissolved in 60 ml of water, were applied uniformly over the surface of each pan lysimeter. The applied bromide was monitored until November 23, 1995. The monitoring period was divided into a first phase of 49 days, during which the soil was not cultivated and measures taken daily at 4 pm, and a second phase of 146 days during which measures were taken every Wednesday at 4 pm. The three pan lysimeters were sowded with potatoes on July 5 and harvested on September 5. Monitoring of the pan lysimeters included:1. the drained water volume; 2. the water volume sampled by the pan lysimeter; and 3. the Br- concentration of all samples.Numerical solution of the governing equations was obtained by the NML which belongs to the semi-discret methods consisting in discretising all independent variables except time, which is considered continuous for initial conditions problems. The discretisation of the DAE spatial variables was done by finite differences and resulted in a system of ordinary differential equations solved by LSODES (Livermore Solver for Ordinary Differential Equations Sparse); a solver used for systems with a sparse jacobian. The sparse nature of the jacobian results from our numerical procedure which solves simultaneously the DAE and Richard's equation.The initial simulation time was fixed to May 12, 1995 at 4 pm and final time to November 23, 1995 at 4 pm with an hourly time step. The total depth of the pan lysimeter was simulated with a uniform internodal space of 1.0 cm. For each pan lysimeter, the initial pressure profile was measured by five pairs of tensiometers at depths of 7.5, 22.5, 45.0, 70.0 and 100.0 cm. The total mass of bromide applied was distributed equally over the first three upper nodes, and converted to concentration using the water content. At the soil surface, boundary condition for Richard's equation was taken as the hourly amount of rain fall (from planting to harvest), and as the net hourly water flux (from harvest until the end of the monitoring period). For the DAE, the boundary condition at the soil surface was of the third type. At the bottom of the pan lysimeters, a contant pressure head was assigned, which was the mean pressure measured by the deepest tensiometer; for concentration, a boundary condition of zero gradient was assigned.For the two simulated variables (soil water bromide concentration and recovered mass of bromide), results of TSOL and HYDRUS were similar, showing an over-estimation of bromide concentration profiles but similar drained masses of bromide except lysimeter A, for which a large over-estimation was observed. This over-estimation may be explained by the presence of cracks between the soil and the plastic film surrounding the lysimeter. These cracks may allow a quick surface water flow along the sides during heavy rainfall. Because the solute was initially applied over all of the surface area of the lysimeters, a fraction of the solute might have migrated with the flowing water, and the remaining fraction by the soil matrix. The water flowing through cracks will quickly reach the bottom of the lysimeters. For all pan lysimetres and soil depths, the mean absolute error for weekly soil solution concentration profiles was 96 mg/l and the mean bias error 80 mg/l. For the mass of bromide recovered in lysimeters B and C, the weekly absolute mean error was 7 mg/week and the mean bias error 5 mg/week. For lysimeter A, the weekly absolute mean error and the mean bias error were the same, that is 39 mg/week.For the simulation period, the numerical mass balance was negligible for the two models. However, the simulation time was longer for TSOL than for HYDRUS (18 versus 13 min). This difference is explained by the completely implicit differentiation scheme used by HYDRUS compared to the Backward Differentiation Formula used by LODES which is more complex, but frees the user from checking timestep precision. Considering the ease of programming and the resulting numerical precision, the NML has proven very effective in solving the solute transport equations in unsaturated conditions

Understanding the origins of the intrinsic dead-layer effect in nanocapacitors

Thin films of high-permittivity dielectrics are considered ideal candidates for realizing high charge density nanosized capacitors for use in next generation energy storage and nanoelectronic applications. The experimentally observed capacitance of such film nanocapacitors is, however, an order of magnitude lower than expected. This dramatic drop in capacitance is attributed to the so called dead layer - a low-permittivity layer at the metal-dielectric interface in series with the high-permittivity dielectric. The exact nature of the dead layer and the reasons for its origin still remain somewhat unclear. Based on insights gained from recently published ab initio work on SrRuO3/SrTiO3/SrRuO3 and our first principle simulations on Au/MgO/Au and Pt/MgO/Pt nanocapacitors, we construct an analytical model that isolates the contributions of various physical mechanisms to the intrinsic dead layer. In particular we argue that strain-gradients automatically arise in very thin films even in absence of external strain inducers and, due to flexoelectric coupling, are dominant contributors to the dead layer effect. Our theoretical results compare well with existing as well as our own ab initio calculations and suggest that inclusion of flexoelectricity is necessary for qualitative reconciliation of atomistic results. Our results also hint at some novel remedies for mitigating the dead layer effect.Comment: 17 pages, 6 figure

A general wavelet-based profile decomposition in the critical embedding of function spaces

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be expressed as a finite sum of translations and dilations of functions $(\phi_l)_{l>0}$ such that the remainder converges to zero in $Y$ as the number of functions in the sum and $n$ tend to $+\infty$. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space $X=\dot H^s$ into the $Y=L^p$ in $d$ dimensions with $0<s=d/2-d/p$, and then generalized by Jaffard to the case where $X$ is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular we identify two generic properties on the spaces $X$ and $Y$ that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of $X$ and $Y$ satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older and BMO spaces.Comment: 24 page

From PEF to PBF: what difference does the longer alkyl chain make a computational spectroscopy study of poly (butylene 2,5-furandicarboxylate)

This work explores the conformational preferences and the structureproperty correlations of poly(butylene 2,5-furandicarboxylate) (PBF), a longer chain analogue of the most well-known biobased polyester from the furan family, poly(ethylene 2,5-furandicarboxylate) (PEF). A thorough computational spectroscopic study–including infrared, Raman and inelastic neutron scattering spectroscopy, combined with discrete and periodic density functional theory calculations–allowed the identification of dominant structural motifs in the amorphous and crystalline regions. Discrete calculations and vibrational spectroscopy of semi-crystalline and amorphous samples strongly support the predominance of gauche, trans, gauche conformations of the butylene glycol fragment in both the crystalline and amorphous domains. In what concerns the furandicarboxylate fragment, amorphous domains are dominated by syn,syn conformations, while in the crystalline domains the anti,anti forms prevail. A possible crystalline structure–built from these conformational preferences and including a network of C-H···O hydrogen bond contacts—was optimized using periodic density functional theory. This proposed crystal structure avoids the unrealistic structural features of the previously proposed X-ray structure, provides an excellent description of the inelastic neutron scattering spectrum of the semi-crystalline form, and allows the correlation between microscopic structure and macroscopic properties of the polymer.publishe

Zn treatment effects on biological potential of fennel bulbs as affected by in vitro digestion process

Zn treatment effects on the stability of polyphenols, MDA (malondialdehyde) content, antioxidant and lipoxygenase inhibition activities of two varieties of fennel bulbs were studied by using an in vitro gastrointestinal digestion model. Likewise, the effect of Zn on viability cells of E. coli was also performed. The results revealed that high amounts of total phenolic and flavonoid compounds were released during the digestion process, especially after the intestinal phase. Additionally, the antioxidant and lipoxygenase inhibitory activity were affected by the gastrointestinal digestion process and seems to be correlated with total phenol contents. On the other hand, the viability of E. coli was not affected by the activity of our tested bulbs during passage through the artificial digestion model, but the treated bulbs activity contribute relatively to the inhibition growth of bacteria. The survival of E. coli in fennel bulbs was challenged with simulated gastrointestinal fluids and the results showed that the E. coli strains, despite having experienced a viability reduction at the intestinal phase, were able to overcome the exposure to the gastrointestinal synthetic fluids. This E. coli ability reinforces the need for good hygienic measures to assure safe fresh produce, even for those that are rich in antibacterial compounds.info:eu-repo/semantics/publishedVersio

On a family of numerical models for couple stress based flexoelectricity for continua and beams

A family of numerical models for the phenomenological linear flexoelectric theory for continua and their particularisation to the case of three-dimensional beams based on a skew-symmetric couple stress theory is presented. In contrast to the standard strain gradient flexoelectric models which assume coupling between electric polarisation and strain gradients, we postulate an electric enthalpy in terms of linear invariants of curvature and electric field. This is achieved by introducing the axial (mean) curvature vector as a strain gradient measure. The physical implication of this assumption is many-fold. Firstly, analogous to the standard strain gradient models, for isotropic (non-piezoelectric) materials it allows constructing flexoelectric energies without breaking material’s centrosymmetry. Secondly, unlike the standard strain gradient models, nonuniform distribution of volumetric part of strains (volumetric strain gradients) do not generate electric polarisation, as also confirmed by experimental evidence to be the case for some important classes of flexoelectric materials. Thirdly, a state of plane strain generates out of plane deformation through strain gradient effects. Finally, under this theory, extension and shear coupling modes cannot be characterised individually as they contribute to the generation of electric polarisation as a whole. As a first step, a detailed comparison of the developed couple stress based flexoelectric model with the standard strain gradient flexoelectric models is performed for the case of Barium Titanate where a myriad of simple analytical solutions are assumed in order to quantitatively describe the similarities and dissimilarities in effective electromechanical coupling under these two theories. From a physical point of view, the most notable insight gained is that, if the same experimental flexoelectric constants are fitted in to both theories, the presented theory in general, reports up to 200% stronger electromechanical conversion efficiency. From the formulation point of a view, the presented flexoelectric model is also competitively simpler as it eliminates the need for high order strain gradient and coupling tensors and can be characterised by a single flexoelectric coefficient. In addition, three distinct mixed flexoelectric variational principles are presented for both continuum and beam models that facilitate incorporation of strain gradient measures in to a standard finite element scheme while maintaining the C0 continuity. Consequently, a series of low and high order mixed finite element schemes for couple stress based flexoelectricity are presented and thoroughly benchmarked against available closed form solutions in regards to electromechanical coupling efficiency. Finally, nanocompression of a complex flexoelectric conical pyramid for which analytical solution cannot be established is numerically studied where curvature induced necking of the specimen and vorticity around the frustum generate moderate electric polarisation

Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

We investigate the equations of anisotropic incompressible viscous fluids in $\R^3$, rotating around an inhomogeneous vector $B(t, x_1, x_2)$. We prove the global existence of strong solutions in suitable anisotropic Sobolev spaces for small initial data, as well as uniformlocal existence result with respect to the Rossby number in the same functional spaces under the additional assumption that $B=B(t,x_1)$ or $B=B(t,x_2)$. We also obtain the propagation of the isotropic Sobolev regularity using a new refined product law.Comment: 25 pages, to appear in Journal of Dynamics and Differential Equation

Highly Efficient Elimination of Colorectal Tumor-Initiating Cells by an EpCAM/CD3-Bispecific Antibody Engaging Human T Cells

With their resistance to genotoxic and anti-proliferative drugs and potential to grow tumors and metastases from very few cells, cancer stem or tumor-initiating cells (TICs) are a severe limitation for the treatment of cancer by conventional therapies. Here, we explored whether human T cells that are redirected via an EpCAM/CD3-bispecific antibody called MT110 can lyse colorectal TICs and prevent tumor growth from TICs. MT110 recognizes EpCAM, a cell adhesion molecule expressed on TICs from diverse human carcinoma, which was recently shown to promote tumor growth through engagement of elements of the wnt pathway. MT110 was highly potent in mediating complete redirected lysis of KRAS-, PI3 kinase- and BRAF-mutated colorectal TICs, as demonstrated in a soft agar assay. In immunodeficient mice, MT110 prevented growth of tumors from a 5,000-fold excess of a minimally tumorigenic TIC dose. T cells engaged by MT110 may provide a potent therapeutic means to eradicate TICs and bulk tumor cells derived thereof

Iodine-125 brachytherapy for brain tumours - a review

Iodine-125 brachytherapy has been applied to brain tumours since 1979. Even though the physical and biological characteristics make these implants particularly attractive for minimal invasive treatment, the place for stereotactic brachytherapy is still poorly defined