On Mathematical Models of the Dynamics of Three-Dimensional Elastic Bodies. Part 2. Bodies with Discretely Observable Initial Boundary Condition

2017 ◽  
Vol 49 (9) ◽  
pp. 20-28
Author(s):  
Vladimir Antonovich Stoyan ◽  
Stepan T. Danysh
Keyword(s):  
Boundary Condition ◽  
Mathematical Models ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Elastic Bodies ◽  
Initial Boundary Condition

scholarly journals Linear parabolic equations with venttsel initial boundary conditions

1994 ◽  
Vol 50 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Yi Zeng ◽  
Yousong Luo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Engineering Problem ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Boundary Condition ◽  
Linear Parabolic Equations

The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.

scholarly journals Global Solutions for the Kuramoto-Sivashinsky Equation Posed on Unbounded 3D Grooves

2021 ◽  
pp. 293-303
Author(s):  
N.A. Larkin
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Three Dimensional ◽  
Global Solutions ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Global Strong Solutions ◽  
Initial Boundary Value ◽  
Sivashinsky Equation

Initial boundary value problems for the three-dimensional Kuramoto-Sivashinsky equation posed on unbounded 3D grooves (that may serve as mathematical models for wildfires) were considered. The existence and uniqueness of global strong solutions as well as their exponential decay have been established.

scholarly journals Comparison between analytical, numerical, and experimental results of grouping effects in droplet streams

2017 ◽  
Author(s):  
Norbert Roth ◽  
Hassan Gomaa ◽  
Alon Livne ◽  
David Katoshevski ◽  
Bernhard Weigand
Keyword(s):  
Numerical Simulation ◽  
Boundary Condition ◽  
Direct Numerical Simulation ◽  
Initial Boundary ◽  
Experimental Results ◽  
Controllable System ◽  
Initial Boundary Condition ◽  
Linear Behaviour ◽  
Monodisperse Droplet ◽  
Monodisperse Droplets

Grouping of droplets was studied in monodisperse droplet streams. This very controllable system allows to studybasic effects. In experiments droplet streams with monodisperse droplets were generated, however, with initially two different inter droplet spacing. A larger inter droplet spacing is followed by a little bit smaller one, which is followed by a larger one and so on. Due to this initial boundary condition groups of two droplets form, which approach each other and finally coagulate. It was found, that the velocity of the droplet approach is linearly dependent on the spacing between the droplets. This process was simulated by direct numerical simulation using the in-house code FS3D. The results of the simulations show the  ame linear behaviour. For larger computational domains thenumerical results approach the experimental results.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4685

Boundary Condition Design to Heat a Moving Object at Uniform Transient Temperature Using Inverse Formulation

2004 ◽  
Vol 126 (3) ◽  
pp. 619-626 ◽  
Author(s):  
Hakan Ertu¨rk ◽  
Ofodike A. Ezekoye ◽  
John R. Howell
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Design Problem ◽  
Manufacturing Industry ◽  
Three Dimensional ◽  
Chemical Deposition ◽  
Iterative Solution ◽  
Conveyor Belt ◽  
Temperature History ◽  
Transient Temperature

The boundary condition design of a three-dimensional furnace that heats an object moving along a conveyor belt of an assembly line is considered. A furnace of this type can be used by the manufacturing industry for applications such as industrial baking, curing of paint, annealing or manufacturing through chemical deposition. The object that is to be heated moves along the furnace as it is heated following a specified temperature history. The spatial temperature distribution on the object is kept isothermal through the whole process. The temperature distribution of the heaters of the furnace should be changed as the object moves so that the specified temperature history can be satisfied. The design problem is transient where a series of inverse problems are solved. The process furnace considered is in the shape of a rectangular tunnel where the heaters are located on the top and the design object moves along the bottom. The inverse design approach is used for the solution, which is advantageous over a traditional trial-and-error solution where an iterative solution is required for every position as the object moves. The inverse formulation of the design problem is ill-posed and involves a set of Fredholm equations of the first kind. The use of advanced solvers that are able to regularize the resulting system is essential. These include the conjugate gradient method, the truncated singular value decomposition or Tikhonov regularization, rather than an ordinary solver, like Gauss-Seidel or Gauss elimination.

scholarly journals Bootstrapping boundary-localized interactions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Connor Behan ◽  
Lorenzo Di Pietro ◽  
Edoardo Lauria ◽  
Balt C. van Rees
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Parameter Space ◽  
Three Dimensional ◽  
Conformal Boundary ◽  
Dimensional Boundary ◽  
Dirichlet And Neumann Conditions ◽  
Boundary Fields ◽  
Boundary Dynamics

Abstract We study conformal boundary conditions for the theory of a single real scalar to investigate whether the known Dirichlet and Neumann conditions are the only possibilities. For this free bulk theory there are strong restrictions on the possible boundary dynamics. In particular, we find that the bulk-to-boundary operator expansion of the bulk field involves at most a ‘shadow pair’ of boundary fields, irrespective of the conformal boundary condition. We numerically analyze the four-point crossing equations for this shadow pair in the case of a three-dimensional boundary (so a four-dimensional scalar field) and find that large ranges of parameter space are excluded. However a ‘kink’ in the numerical bounds obeys all our consistency checks and might be an indication of a new conformal boundary condition.

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