Search results for " numerical analysis"
showing 10 items of 106 documents
A degenerating convection-diffusion system modelling froth flotation with drainage
2022
Abstract Froth flotation is a common unit operation used in mineral processing. It serves to separate valuable mineral particles from worthless gangue particles in finely ground ores. The valuable mineral particles are hydrophobic and attach to bubbles of air injected into the pulp. This creates bubble-particle aggregates that rise to the top of the flotation column where they accumulate to a froth or foam layer that is removed through a launder for further processing. At the same time, the hydrophilic gangue particles settle and are removed continuously. The drainage of liquid due to capillarity is essential for the formation of a stable froth layer. This effect is included into a previous…
A generalized Newton iteration for computing the solution of the inverse Henderson problem
2020
We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step, and no further expensive cross-correlations. Numerical experiments…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
The Effects of Orography on the Extratropical Transition of Tropical Cyclones: A Case Study of Typhoon Sinlaku (2008)
2018
Abstract Extratropical transition (ET) can cause high-impact weather in midlatitude regions and therefore constitutes an ongoing threat at the end of a tropical cyclone’s (TC) life cycle. Most of the ET events occur over the ocean, but some TCs recurve and undergo ET along coastal regions; however, the latter category is less investigated. Typhoon Sinlaku (2008), for example, underwent ET along the southern coast of Japan. It was one of the typhoons that occurred during the T-PARC field campaign, providing unprecedented high-resolution observational data. Sinlaku is therefore an excellent case to investigate the impact of a coastal region, and in particular orography, on the evolution of ET…
TRADITION AND MODERNITY OF CATALAN VAULTS: HISTORICAL AND STRUCTURAL ANALYSIS
2012
Il lavoro analizza da diversi punti di vista un particolare tipo di strutture voltate noto come volte catalane (bóveda tabicada) e la tecnica costruttiva correlata. Le volte catalane sono volte realizzate da strati alterni di mattoni e malta, caratterizzate da un esiguo spessore in relazione alle altre dimensioni. Il primo passo presentato nel lavoro è quello di investigare tutti gli aspetti storici al fine di inquadrare sia la tipologia che la tecnica costruttiva correlata all'interno della storia dell'architettura e di individuare le ragioni di un così grande successo lungo i secoli. Successivamente, è stata effettuata una campagna di indagini sperimentali, che completa una precedente, su…
Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation
2023
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrödinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of …
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
2019
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
Entropy dissipation of moving mesh adaptation
2012
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. There have been though only few results on the mathematical analysis of these schemes due to the lack of proper tools that incorporate both the time evolution and the mesh adaptation step of the overall algorithm. In this paper we provide a method to perform the analysis of the mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient condition…
A constructive theory of shape
2021
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…