A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Raytcho Lazarov ◽  
Petr Vabishchevich
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Numerical Study ◽  
Homogeneous Equation ◽  
Fractional Boundary Conditions ◽  
Homogeneous Elliptic Equation

AbstractWe consider the homogeneous equation

Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

2004 ◽  
Vol 134 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Mónica Clapp ◽  
Manuel Del Pino ◽  
Monica Musso
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Critical Exponent ◽  
Bounded Domain ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Homogeneous Elliptic Equation

We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

scholarly journals A numerical study of the impact perforation of sandwich panels with graded hollow sphere cores

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110094
Author(s):  
Ibrahim Elnasri ◽  
Han Zhao
Keyword(s):  
Boundary Conditions ◽  
Hollow Sphere ◽  
Sandwich Panel ◽  
Numerical Study ◽  
Sandwich Panels ◽  
Hopkinson Bar ◽  
Core Density ◽  
The Core ◽  
The Impact ◽  
Force Displacement

In this study, we numerically investigate the impact perforation of sandwich panels made of 0.8 mm 2024-T3 aluminum alloy skin sheets and graded polymeric hollow sphere cores with four different gradient profiles. A suitable numerical model was conducted using the LS-DYNA code, calibrated with an inverse perforation test, instrumented with a Hopkinson bar, and validated using experimental data from the literature. Moreover, the effects of quasi-static loading, landing rates, and boundary conditions on the perforation resistance of the studied graded core sandwich panels were discussed. The simulation results showed that the piercing force–displacement response of the graded core sandwich panels is affected by the core density gradient profiles. Besides, the energy absorption capability can be effectively enhanced by modifying the arrangement of the core layers with unclumping boundary conditions in the graded core sandwich panel, which is rather too hard to achieve with clumping boundary conditions.

scholarly journals Numerical Study of Three-Dimensional Surface Jets Emerging from a Fishway Entrance Slot

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1079
Author(s):  
Lena Mahl ◽  
Patrick Heneka ◽  
Martin Henning ◽  
Roman B. Weichert
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Free Water ◽  
Lateral Wall ◽  
Lateral Spreading ◽  
Propagation Length ◽  
Vertical Slot ◽  
Surface Jets

The efficiency of a fishway is determined by the ability of immigrating fish to follow its attraction flow (i.e., its jet) to locate and enter the fishway entrance. The hydraulic characteristics of fishway entrance jets can be simplified using findings from widely investigated surface jets produced by shaped nozzles. However, the effect of the different boundary conditions of fishway entrance jets (characterized by vertical entrance slots) compared to nozzle jets must be considered. We investigate the downstream propagation of attraction jets from the vertical slot of a fishway entrance into a quiescent tailrace, considering the following boundary conditions not considered for nozzle jets: (1) slot geometry, (2) turbulence characteristics of the approach flow to the slot, and (3) presence of a lateral wall downstream of the slot. We quantify the effect of these boundary conditions using three-dimensional hydrodynamic-numeric flow simulations with DES and RANS turbulence models and a volume-of-fluid method (VoF) to simulate the free water surface. In addition, we compare jet propagation with existing analytical methods for describing jet propagations from nozzles. We show that a turbulent and inhomogeneous approach flow towards a vertical slot reduces the propagation length of the slot jet in the tailrace due to increased lateral spreading compared to that of a jet produced by a shaped nozzle. An additional lateral wall in the tailrace reduces lateral spreading and significantly increases the propagation length. For highly turbulent flows at fishway entrances, the RANS model tends to overestimate the jet propagation compared to the transient DES model.

scholarly journals FRACTAL DIMENSION OF SPIN-GLASSES INTERFACES IN DIMENSION d = 2 AND d = 3 VIA STRONG DISORDER RENORMALIZATION AT ZERO TEMPERATURE

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550042 ◽  
Author(s):  
CÉCILE MONTHUS
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Spin Glasses ◽  
Periodic Boundary ◽  
Domain Walls ◽  
Numerical Study ◽  
Periodic Boundary Conditions ◽  
Zero Temperature ◽  
Low Dimensions ◽  
Strong Disorder

For Gaussian Spin-Glasses in low dimensions, we introduce a simple Strong Disorder renormalization at zero temperature in order to construct ground states for Periodic and Anti-Periodic boundary conditions. The numerical study in dimensions [Formula: see text] (up to sizes [Formula: see text]) and [Formula: see text] (up to sizes [Formula: see text]) yields that Domain Walls are fractal of dimensions [Formula: see text] and [Formula: see text], respectively.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

Numerical Study of the Effect of Geometry and Boundary Conditions on the Collapse Behaviour of Stocky Stiffened Panels

2012 ◽  
Vol 154 (A2) ◽  
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ultimate Strength ◽  
Material Properties ◽  
Finite Element Modelling ◽  
Numerical Study ◽  
Fe Analysis ◽  
Stiffened Panels ◽  
Element Modelling ◽  
Geometric Configurations

This study aims at studying different configurations of the stiffened panels in order to identify robust configurations that would not be much sensitive to the imprecision in boundary conditions that can exist in experimental set ups. A numerical study is conducted to analyze the influence of the stiffener’s geometry and boundary conditions on the ultimate strength of stiffened panels under uniaxial compression. The stiffened panels with different combinations of mechanical material properties and geometric configurations are considered. The four types of stiffened panels analysed are made of mild or high tensile steel and have bar, ‘L’ and ‘U’ stiffeners. To understand the effect of finite element modelling on the ultimate strength of the stiffened panels, four types of FE models are investigated in FE analysis including 3 bays, 1/2+1+1/2 bays, 1+1 bays and 1 bay with different boundary conditions.

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

Sign in / Sign up

Export Citation Format

Share Document