Search results for "equation"
showing 10 items of 4219 documents
Establishing soil loss tolerance: an overview
2016
Soil loss tolerance is a criterion for establishing if a soil is potentially subjected to erosion risk, productivity loss and if a river presents downstream over-sedimentation or other off-site effects are present at basin scale. At first this paper reviews the concept of tolerable soil loss and summarises the available definitions and the knowledge on the recommended values and evaluating criteria. Then a threshold soil loss value, at the annual temporal scale, established for limiting riling was used for defining the classical soil loss tolerance. Finally, some research needs on tolerable soil loss are listed.
Modeling the acid-base properties of molybdate(VI) in different ionic media, ionic strengths and temperatures, by EDH, SIT and Pitzer equations
2017
This paper reports the results of a study on the determination of the protonation constants of MoO42 −, in NaClaq, NaNO3aq, KClaq, at different ionic strengths (0 < I/mol dm− 3 ≤ 5.0 in NaClaq, 0 < I/mol dm− 3 ≤ 3.0 in NaNO3aq and KClaq) and temperatures (278.15 ≤ T/K ≤ 318.15 in NaClaq, only 298.15 K in NaNO3aq and KClaq), by potentiometric (ISE-H+ glass electrode) and spectrophotometric (UV/Vis) titrations. After a critical analysis of results and literature findings, the proposed speciation model takes into account the formation of two monomeric and four heptameric species, namely: MoO4H−, MoO4H2, (MoO4)7H86 −, (MoO4)7H95 −, (MoO4)7H104 − and (MoO4)7H113 −. Due to the complexity of…
Propagation of spatiotemporal solitons in dissipative media
2010
This thesis presents a semi-analytical approach for the search of (3+1)D spatio-temporal soliton solutions of the complex cubic-quintic Ginzburg-Landau equation (GL3D).We use a semi-analytical method called collective coordinate approach, to obtain an approximate profile of the unknown pulse field. This ansatz function is chosen to be a function of a finite number of parameters describing the light pulse.By applying this collective corrdinate procedure to the GL3D equation, we obtain a system of variational equations which give the evolution of the light bullet parameters as a function of the propagation distance. We show that the collective coordinate approach is uncomparably faster than t…
Numerical study of soliton stability, resolution and interactions in the 3D Zakharov–Kuznetsov equation
2021
International audience; We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is L-2-subcritical, and thus, solutions exist globally, for example, in the H-1 energy space.We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in Farah et al. (0000) for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of de…
Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
2017
International audience; We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the 'energy' parameter E. We show that as |E| -> infinity, NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when |E| is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied.
Zero viscosity limit of the Oseen equations in a channel
2001
Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics.
Primary and secondary distributions after a small-amplitude potential step at disk electrode coated with conducting film
2011
Abstract The set of equations and boundary conditions for the “primary potential/current distribution” after a small-amplitude potential step has been analyzed for a film-coated disk electrode in contact with an electrolyte. The solution of these equations provides the overall short-time resistance of this system, Rtot, which is determined by the short-time resistance of the electrolyte solution in contact with the bare disk electrode, Rs, and the short-time film resistance to the current passage in the normal direction, R f = L f / κ f π r o 2 (ro, disk radius; Lf, film thickness; κf, its specific conductivity). The deviation of Rtot from the sum of these resistances, Rs + Rf, originates f…
Acid versus base peptization of mesoporous nanocrystalline TiO2 films: functional studies in dye sensitized solar cells
2005
We report an analysis of the influence of acid/base conditions employed in the synthesis of TiO2 nanoparticles upon the performance of dye sensitised photoelectrochemical solar cells fabricated from these particles. The functional properties of the TiO2 nanoparticles in these devices are investigated by potential step chronoamperometry, transient laser spectroscopy, and photovoltaic device characterisation. We find that base peptization conditions employed in the sol–gel fabrication of the TiO2 nanoparticles result in a reduction in film electron density under negative applied bias, correlated with slower interfacial recombination losses and a higher device open circuit voltage.