Search results for "equation"
showing 10 items of 4219 documents
Predicting breakthrough of vanadium in fixed-bed absorbent columns with complex groundwater chemistries: A multi-component granular ferric hydroxide−…
2020
Granular ferric hydroxide (GFH) is often used for fixed bed adsorbent (FBA) columns in groundwater purification units around the world to remove arsenate contaminations. Groundwater can contain also other toxic (e.g., antimonite and vanadate) and non-toxic oxo-anions (phosphate and silicic acid) that are known to affect FBA lifetimes. Therefore, understanding the breakthrough of toxic compounds intended for removal by FBA is essential to their design, and is important to predict accurately breakthrough curves (BTCs) for FBAs in waterworks to plan future operating costs. Rapid small-scale column tests (RSCCT) and pilot-scale FBA were used to simulate vanadate BTCs for complex groundwater che…
On the properties of the radiosity equation near corners
2003
The radiosity equation is an integral equation of the second kind which describes the energy exchange by radiation between surfaces in R3. It is assumed that all surfaces are Lambertian reflectors and that all emitters are diffusive emitters. The radiosity equation plays an important role for the calculation of photo realistic images with the help of computers. Many surfaces which are used in practical calculations are only piecewise smooth and contain edges or corners. In this contribution we present regularity results for the solution of the radiosity equation in the vicinity of corners. The space of piecewise continuous functions is not suitable for this equation and we construct a new f…
On the fusion problem for degenerate elliptic equations
1995
Let F be a relatively closed subset of a Euclidean domain Ω. We investigate when solutions u to certain elliptic equations on Ω/F are restrictions of solutions on all of Ω. Specifically, we show that if ∂F is not too large, and u has a suitable decay rate near F, then u can be so extended.
Edelstein-Suzuki-type resuls for self-mappings in various abstract spaces with application to functional equations
2016
Abstract The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.
Dense matter with eXTP
2019
In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics o…
Derivation of Models for Thin Sprays from a Multiphase Boltzmann Model
2017
We shall review the validation of a class of models for thin sprays where a Vlasov type equation is coupled to an hydrodynamic equation of Navier–Stokes or Stokes type. We present a formal derivation of these models from a multiphase Boltzmann system for a binary mixture: under suitable assumptions on the collision kernels and in appropriate asymptotics (resp. for the two different limit models), we prove the convergence of solutions to the multiphase Boltzmann model to distributional solutions to the Vlasov–Navier–Stokes or Vlasov–Stokes system. The proofs are based on the procedure followed in Bardos et al. (J Stat Phys 63:323–344 (1991), [2]) and explicit evaluations of the coupling term…
Tetraalkylammonium Cations Conduction through a Single Nanofluidic Diode: Experimental and Theoretical Studies
2017
[EN] We describe experimentally and theoretically the concentration-dependent conduction of tetraalkylammonium (TAA+) cations through a nanofluidic diode fabricated in a polymer membrane via asymmetric track-etching techniques. This single-pore membrane exhibits current rectification characteristics because of the ionized carboxylate groups on the pore surface. We use aqueous solutions of potassium (K+ ), ammonium (A+ ), tetramethylammonium (TMA+ ), tetraethylammonium (TEA+ ), and tetrabutylammonium (TBA+ ) ions with concentrations ranging from 50 to 500 mM under acidic (pH 3.5) and physiological (pH 6.5) conditions. Compared with the K+ and A+ ions, the TMA+ , TEA+ , and TBA+ ions show rel…
Characterization of traditional artificial patinas on copper using the voltammetry of immobilized particles
2020
[EN] The voltammetry of immobilized particles methodology (VIMP) is used to characterize the composition of artificial patinas on copper. The voltammetric response of carbonate-, nitrate-, chloride-, sulfate-, and sulfide-based patinas is described using sub-microsamples attached to graphite electrodes in contact with aqueous acetate buffer. Patina-characteristic voltammetric profiles are obtained for the different artificial patinas that can be recognized using the generalized Tafel analysis of the voltammetric curves. VIMP data could also provide layer-by-layer information about composition and compactness/crystallinity of the patinas for which a simplified theoretical modeling is present…
A High-Resolution Penalization Method for large Mach number Flows in the presence of Obstacles
2009
International audience; A penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkman-penalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this method to theoretical results and to simulations with Fluent software. Our work indicates that this technique can be very promising in applications to complex flows.
Implicit-explicit and explicit projection schemes for the unsteady incompressible Navier–Stokes equations using a high-order dG method
2017
Abstract A modified version of the projection scheme [19] is proposed, which does not show a lower limit for the time step in contrast to the limits of stability observed numerically for some projection type schemes. An advantage of the proposed scheme is that the right-hand side of the Poisson equation for the pressure is independent of the time step. An explicit version of the current scheme is also provided besides the implicit-explicit one. For the implicit-explicit version, we retain divergence of the viscous terms on the right-hand side of the Poisson equation in order to achieve a higher accuracy for low Reynolds number flows. In this way, we also ensure that the Poisson equation wit…