Search results for "Boundary value problem"
showing 10 items of 551 documents
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
On the solution of a parabolic PDE involving a gas flow through a semi-infinite porous medium
2021
Abstract Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, for…
Constraining electric resistivity tomography by direct push electric conductivity logs and vibracores: An exemplary study of the Fiume Morto silted r…
2018
The inversion of geoelectric data is nonunique. Therefore, electric resistivity tomography (ERT) usually results in different subsurface models that fit observed apparent resistivity values equally well. To reduce the uncertainty, constraints on the geometry and resistivity of subsurface structures can be incorporated into the ERT inversion. We test different ways of constraining ERT by applying (1) improved starting models, (2) structural constraints, and (3) structural and resistivity constraints. A priori information is needed for these approaches, which is acquired from direct push electrical conductivity (DP-EC) logs and vibracores in our study. We found that adapting high vertical re…
Effects of different boundary conditions and palaeotopographies on the onshore response of tsunamis in a numerical model – A case study from western …
2016
Abstract Hydrodynamic numerical models are essential in modern tsunami hazard assessment. They allow the economical simulation of possible tsunami scenarios for areas at risk and provide reliable and detailed insights into local onshore dynamics. This is especially true when simulations are calibrated with field traces of past tsunami inundation events. Following this approach, the current study focuses on palaeotsunami events indicated by sedimentary and geomorphological field traces in the northern Gulf of Kyparissia (NW Greece). Based on three different digital elevation models (DEM) – reflecting the recent and two palaeotopographies – various tsunami wave constellations according to the…
Benchmarking numerical models of brittle thrust wedges
2016
International audience; We report quantitative results from three brittle thrust wedge experiments, comparing numerical resultsdirectly with each other and with corresponding analogue results. We first test whether the participatingcodes reproduce predictions from analytical critical taper theory. Eleven codes pass the stable wedgetest, showing negligible internal deformation and maintaining the initial surface slope upon horizontaltranslation over a frictional interface. Eight codes participated in the unstable wedge test that examinesthe evolution of a wedge by thrust formation from a subcritical state to the critical taper geometry. Thecritical taper is recovered, but the models show two…
Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets
2017
We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of equal-spin Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. This additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and results in the generation of spontaneous superconducting currents and phase shifts in various geometr…
Dynamic Modeling of Planar Multi-Link Flexible Manipulators
2021
A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.
Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method
2019
Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…
A singular elliptic equation and a related functional
2021
We study a class of Dirichlet boundary value problems whose prototype is [see formula in PDF] where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on [see formula in PDF] whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Diffusion through thin membranes: Modeling across scales
2016
From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesosco…