Surface Simulation Algorithm Streamlining by the Brownian Motion Method on the Criterion of Iterations Number Minimizing

2017 ◽  
Vol 5 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Брылкин ◽  
Yuriy Brylkin
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Geometric Model ◽  
Navier Stokes ◽  
Space Forms ◽  
High Enthalpy ◽  
Fractal Surfaces ◽  
Torus Knot ◽  
Necessary And Sufficient ◽  
Motion Method

The paper has been devoted to construction of geometric model for real surface’s compartment at micro- and nanoscales with known fractal dimension. Receiving data on the real surface’s fractal dimension has been considered in [8; 9; 11; 13; 20]. Fractal dimension as a relief development measure has been accepted for the necessary and sufficient condition of the model construction. As is known, for a flying vehicle’s appearance the comprehensive characteristics research is performed with ground work in aerodynamic tubes, and numerical simulation. Similarly, a fragment of product’s heat protection is tested in high-enthalpy facilities for research of physico-chemical processes in the boundary layer, as well as for confirmation of calculations of interactions between rarefied gas’s particles and the surface. In this work has been performed the analysis of geometrical interpretations of algorithms for the fractal surfaces formation based on the Brownian motion method, proposed to use in calculations by Monte Carlo and Navier-Stokes methods. A point choice leading to construction of secant or tangent planes to space forms has been assigned as an element of randomness per iteration. All proposed algorithms lead to construction of surfaces with fractal dimension D ≈ 2.5, but by different iterations number. A tendency to reduce the iterations number required to achieve a specific fractal dimension by increasing the capacity of many lines for plane compartment digitalization has been revealed. The best result has been obtained by construction of projections for section of surface called a torus knot [19, 22]. Visualization was carried out in ASCON Kompas 3Dv.14 program on algorithms results in MathCAD environment.

scholarly journals Detailed Modeling of Cork-Phenolic Ablators in Preparation for the Post-flight Analysis of the QARMAN Re-entry CubeSat

2021 ◽  
Author(s):  
Claudio Miccoli ◽  
Alessandro Turchi ◽  
Pierre Schrooyen ◽  
Domenic D’Ambrosio ◽  
Thierry Magin
Keyword(s):  
Fluid Dynamics ◽  
Thermal Protection ◽  
A Priori ◽  
European Space Agency ◽  
Thermal Response ◽  
Accurate Method ◽  
Navier Stokes ◽  
Advection Equation ◽  
High Enthalpy ◽  
Space Agency

AbstractThis work deals with the analysis of the cork P50, an ablative thermal protection material (TPM) used for the heat shield of the qarman Re-entry CubeSat. Developed for the European Space Agency (ESA) at the von Karman Institute (VKI) for Fluid Dynamics, qarman is a scientific demonstrator for Aerothermodynamic Research. The ability to model and predict the atypical behavior of the new cork-based materials is considered a critical research topic. Therefore, this work is motivated by the need to develop a numerical model able to respond to this demand, in preparation to the post-flight analysis of qarman. This study is focused on the main thermal response phenomena of the cork P50: pyrolysis and swelling. Pyrolysis was analyzed by means of the multi-physics Computational Fluid Dynamics (CFD) code argo, developed at Cenaero. Based on a unified flow-material solver, the Volume Averaged Navier–Stokes (VANS) equations were numerically solved to describe the interaction between a multi-species high enthalpy flow and a reactive porous medium, by means of a high-order Discontinuous Galerkin Method (DGM). Specifically, an accurate method to compute the pyrolysis production rate was implemented. The modeling of swelling was the most ambitious task, requiring the development of a physical model accounting for this phenomenon, for the purpose of a future implementation within argo. A 1D model was proposed, mainly based on an a priori assumption on the swelling velocity and the resolution of a nonlinear advection equation, by means of a Finite Difference Method (FDM). Once developed, the model was successfully tested through a matlab code, showing that the approach is promising and thus opening the way to further developments.

TORUS KNOTS EMBODYING CURVATURE AND TORSION IN AN OTHERWISE FEATURELESS CONTINUUM

2011 ◽  
Vol 20 (12) ◽  
pp. 1723-1739 ◽  
Author(s):  
J. S. AVRIN
Keyword(s):  
Elementary Particle ◽  
General Relativity ◽  
Geometric Model ◽  
The Other ◽  
Particle Model ◽  
Torus Knots ◽  
Torus Knot ◽  
The Subject ◽  
Curvature And Torsion ◽  
The Relationship

The subject is a localized disturbance in the form of a torus knot of an otherwise featureless continuum. The knot's topologically quantized, self-sustaining nature emerges in an elementary, straightforward way on the basis of a simple geometric model, one that constrains the differential geometric basis it otherwise shares with General Relativity (GR). Two approaches are employed to generate the knot's solitonic nature, one emphasizing basic differential geometry and the other based on a Lagrangian. The relationship to GR is also examined, especially in terms of the formulation of an energy density for the Lagrangian. The emergent knot formalism is used to derive estimates of some measurable quantities for a certain elementary particle model documented in previous publications. Also emerging is the compatibility of the torus knot formalism and, by extension, that of the cited particle model, with general relativity as well as with the Dirac theoretic notion of antiparticles.

Estimation of Fractal Dimension in Different Color Model

2018 ◽  
Vol 8 (1) ◽  
pp. 75-93
Author(s):  
Sumitra Kisan ◽  
Sarojananda Mishra ◽  
Ajay Chawda ◽  
Sanjay Nayak
Keyword(s):  
Fractal Dimension ◽  
Color Space ◽  
Vital Role ◽  
Color Images ◽  
Color Spaces ◽  
Fractal Surfaces ◽  
Test Operation ◽  
Novel Method ◽  
Rgb Color Space ◽  
Different Color

This article describes how the term fractal dimension (FD) plays a vital role in fractal geometry. It is a degree that distinguishes the complexity and the irregularity of fractals, denoting the amount of space filled up. There are many procedures to evaluate the dimension for fractal surfaces, like box count, differential box count, and the improved differential box count method. These methods are basically used for grey scale images. The authors' objective in this article is to estimate the fractal dimension of color images using different color models. The authors have proposed a novel method for the estimation in CMY and HSV color spaces. In order to achieve the result, they performed test operation by taking number of color images in RGB color space. The authors have presented their experimental results and discussed the issues that characterize the approach. At the end, the authors have concluded the article with the analysis of calculated FDs for images with different color space.

Influencing Parameters of Tip Blowing Interacting With Rotor Tip Flow

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Cyril Guinet ◽  
André Inzenhofer ◽  
Volker Gümmer
Keyword(s):  
Geometric Model ◽  
Axial Compressor ◽  
Axial Flow ◽  
Navier Stokes ◽  
Axial Position ◽  
Design Parameters ◽  
Stall Margin ◽  
Casing Treatment ◽  
Transonic Compressor ◽  
Casing Treatments

The design space of axial-flow compressors is restricted by stability issues. Different axial-type casing treatments (CTs) have shown their ability to enhance compressor stability and to influence efficiency. Casing treatments have proven to be effective, but there still is need for more detailed investigations and gain of understanding for the underlying flow mechanism. Casing treatments are known to have a multitude of effects on the near-casing 3D flow field. For transonic compressor rotors, these are more complex, as super- and subsonic flow regions alternate while interacting with the casing treatment. To derive design rules, it is important to quantify the influence of the casing treatment on the different tip flow phenomena. Designing a casing treatment in a way that it antagonizes only the deteriorating secondary flow effects can be seen as a method to enhance stability while increasing efficiency. The numerical studies are carried out on a tip-critical rotor of a 1.5-stage transonic axial compressor. The examined recirculating tip blowing casing treatment (TBCT) consists of a recirculating channel with an air off-take above the rotor and an injection nozzle in front of the rotor. The design and functioning of the casing treatment are influenced by various parameters. A variation of the geometry of the tip blowing, more specifically the nozzle aspect ratio, the axial position, or the tangential orientation of the injection port, was carried out to identify key levers. The tip blowing casing treatment is defined as a parameterized geometric model and is automatically meshed. A sensitivity analysis of the respective design parameters of the tip blowing is carried out on a single rotor row. Their impact on overall efficiency and their ability to improve stall margin are evaluated. The study is carried out using unsteady Reynolds-averaged Navier–Stokes (URANS) simulations.

scholarly journals Stable commutator length in amalgamated free products

2015 ◽  
Vol 07 (04) ◽  
pp. 693-717 ◽  
Author(s):  
Tim Susse
Keyword(s):  
Geometric Model ◽  
Free Products ◽  
Cyclic Groups ◽  
Amalgamated Free Products ◽  
Torus Knot ◽  
Knot Complements ◽  
Stable Commutator Length ◽  
Free Abelian Groups ◽  
Commutator Length ◽  
Boundary Mapping

We show that stable commutator length is rational on free products of free abelian groups amalgamated over ℤk, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parametrize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. Further, we use the methods developed to show that in free products of cyclic groups the stable commutator length of a fixed word varies quasirationally in the orders of the free factors.

A multivariate Weierstrass–Mandelbrot function

1985 ◽  
Vol 400 (1819) ◽  
pp. 331-350 ◽  
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Fractional Brownian Motion ◽  
Continuum Limit ◽  
Small Length ◽  
Stochastic Description ◽  
Fractal Surfaces ◽  
Higher Dimensional ◽  
The Many ◽  
The Continuum

The univariate Weierstrass–Mandelbrot function is generalized to many variables to model higher dimensional stochastic processes such as undersea topography. Because this topography is difficult to measure at small length scales over the many large regions that affect long-ranged acoustic propagation in the ocean, one needs a stochastic description that can be extrapolated to both large and small features. Fractal surfaces are a convenient framework for such a description. Computer-generated plots for the two-variable case are presented. It is shown that in the continuum limit the multivariate function is equivalent to the multivariate fractional Brownian motion.

SKOROKHOD EMBEDDINGS IN BOUNDED TIME

2011 ◽  
Vol 11 (02n03) ◽  
pp. 215-226 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
PHILIPP STRACK
Keyword(s):  
Brownian Motion ◽  
Time Horizon ◽  
Sufficient Conditions ◽  
Stopping Time ◽  
Fixed Time ◽  
Stopping Times ◽  
Embedding Problem ◽  
Brownian Motion With Drift ◽  
Necessary And Sufficient ◽  
Skorokhod Embedding Problem

This article deals with the Skorokhod embedding problem in bounded time for the Brownian motion with drift Xt = κt + Wt: Given a probability measure μ we aim at finding a stopping time τ such that the law of Xτ is μ, and τ is almost surely smaller than some given fixed time horizon T > 0. We provide necessary and sufficient conditions on the distribution μ for the existence of such bounded stopping times.

A Numerical Model for Brownian Motions of Nano-Particles in Supersonic and Hypersonic Impactors

2006 ◽  
Author(s):  
Azam Zare ◽  
Omid Abouali ◽  
Goodarz Ahmadi
Keyword(s):  
Brownian Motion ◽  
Collection Efficiency ◽  
Operating Conditions ◽  
The Body ◽  
Nano Particles ◽  
Navier Stokes ◽  
Computer Simulation Model ◽  
Micro Particles ◽  
Deposition Processes ◽  
Energy Equations

In this paper, transport and deposition processes of nano-particles in supersonic and hypersonic impactors were investigated using a computational modeling approach. Axisymmetric forms of the compressible Navier-Stokes and energy equations were solved and the airflow and thermal condition in the impactor including the upstream nozzle were evaluated. A computer simulation model for solving the Lagrangian particle equation of motion including all the relevant forces was developed. The importance of the accurate modeling of the Brownian motion of nano-particles was further emphasized. The motion of nano- and micro-particles in the supersonic and hypersonic impactors were then simulated and the impactor capture efficiencies under various operating conditions were studied. For dilute particle concentrations, the assumption of one-way interaction was used. Particular attention was given to proper evaluation of the Brownian motion of the nano-particles in the upstream nozzle and in the body of impactor. The simulation results for collection efficiency were found to be in good agreement with experimental data. In particular, the model accurately predicted the loss of the nano-particles in the upstream nozzle due to their Brownian motion.

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