Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640025 ◽  
Author(s):  
Mamadou Sango ◽  
Tesfalem Abate Tegegn
Keyword(s):  
Harmonic Analysis ◽  
Existence Result ◽  
Three Dimensional ◽  
Regularity Result ◽  
Heat Equations ◽  
Analysis Tools ◽  
Large Numbers ◽  
Magnetohydrodynamics Equation ◽  
Stochastic Heat Equations ◽  
Time Existence

We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.

scholarly journals Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wensheng Wang ◽  
Xiaoying Chang ◽  
Wang Liao
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Harmonic Analysis ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Colored Noise ◽  
Asymptotic Distributions ◽  
Heat Equations ◽  
Stochastic Heat Equations

Let u α , d = u α , d t , x ,   t ∈ 0 , T , x ∈ ℝ d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process u α , d , in time, having infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.

Harmonic Analysis on Low Quality Tidal Data

2014 ◽  
Author(s):  
Joost den Haan
Keyword(s):  
Harmonic Analysis ◽  
Three Dimensional ◽  
Measurement Data ◽  
Tidal Energy ◽  
Energy Yield ◽  
Profile Measurement ◽  
Current Profile ◽  
Tidal Power ◽  
Data Set ◽  
Tidal Forcing

The aim of the study is to devise a method to conservatively predict a tidal power generation based on relatively short current profile measurement data sets. Harmonic analysis on a low quality tidal current profile measurement data set only allowed for the reliable estimation of a limited number of constituents leading to a poor prediction of tidal energy yield. Two novel, but very different approaches were taken: firstly a quasi response function is formulated which combines the currents profiles into a single current. Secondly, a three dimensional vectorial tidal forcing model was developed aiming to support the harmonic analysis with upfront knowledge of the actual constituents. The response based approach allowed for a reasonable prediction. The vectorial tidal forcing model proved to be a viable start for a full featuring numerical model; even in its initial simplified form it could provide more insight than the conventional tidal potential models.

scholarly journals Multiple-Image Encryption Algorithm Based on the 3D Permutation Model and Chaotic System

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 660 ◽  
Author(s):  
Xiaoqiang Zhang ◽  
Xuesong Wang
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Three Dimensional ◽  
Multiple Image ◽  
External Mode ◽  
Large Numbers ◽  
Permutation Model ◽  
Magic Cube ◽  
Exclusive Or ◽  
Image Encryption Algorithm

Large numbers of images are produced in many fields every day. The content security of digital images becomes an important issue for scientists and engineers. Inspired by the magic cube game, a three-dimensional (3D) permutation model is established to permute images, which includes three permutation modes, i.e., internal-row mode, internal-column mode, and external mode. To protect the image content on the Internet, a novel multiple-image encryption symmetric algorithm (block cipher) with the 3D permutation model and the chaotic system is proposed. First, the chaotic sequences and chaotic images are generated by chaotic systems. Second, the sender permutes the plain images by the 3D permutation model. Lastly, the sender performs the exclusive OR operation on permuted images. The simulation and algorithm comparisons display that the proposed algorithm possesses desirable encryption images, high security, and efficiency.

scholarly journals Some properties of non-linear fractional stochastic heat equations on bounded domains

2017 ◽  
Vol 102 ◽  
pp. 86-93 ◽  
Author(s):  
Mohammud Foondun ◽  
Ngartelbaye Guerngar ◽  
Erkan Nane
Keyword(s):  
Heat Equations ◽  
Bounded Domains ◽  
Non Linear ◽  
Stochastic Heat Equations

scholarly journals Significance of Nonsimilar Numerical Simulations in Forced Convection from Stretching Cylinder Subjected to External Magnetized Flow of Sisko Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jifeng Cui ◽  
Umer Farooq ◽  
Ahmed Jan ◽  
Murtada K. Elbashir ◽  
Waseem Asghar Khan ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Frictional Heating ◽  
Fluid Velocity ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Axial Direction ◽  
High Viscosity ◽  
Heat Equations ◽  
Dimensionless Numbers ◽  
Sisko Fluid

The practice of flowing effort is participating in various industries especially in nutrition productions all around the world. These fluids practices are utilized extensively in nutrition handling productions by making use of sticky liquids to produce valuable food manufactured goods in bulk. Nevertheless, such productions ought to guarantee that involved equipment such as pipelines are maintained clean as well as are cleared out for the efficient movement of fluids. The nonsimilar characteristics of involuntary convection from circular cylinder stretching in the axial direction subjected to an external flow of Sisko fluid characterized by the freely growing boundary layers (BL) are presented in this research. A circular cylinder is submerged in a stationary fluid. The axial stretching of the cylinder causes external fluid flow. The magnetic force of strength ″ B 0 ″ is enforced in the transverse direction. Because of the fluid's high viscosity, frictional heating due to viscous dissipation is quite significant. The flow is three dimensional but with no circumferential variations. The governing equations for axisymmetric flow that include the mass balance, x -momentum, and heat equation are modeled through conservation laws. The dimensionless system is developed by employing appropriate nonsimilar transformations. The numerical analyses are presented by adapting local nonsimilarity via finite-difference (FDM)-based MATLAB algorithm bvp4c. The characteristics of dimensionless numbers are determined by graphs that are plotted on momentum and heat equations. The nonsimilar simulations have been compared with the existing local similar solutions. Fluid velocity is increased as the material and curvature parameters are increased, resulting in improved heat transfer. The deviation in skin friction and local Nusselt number against the various dimensionless numbers is also analyzed.

Nonlinear Neumann boundary value problem for semilinear heat equations with critical power nonlinearities

2021 ◽  
pp. 1-35
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina ◽  
Pavel I. Naumkin ◽  
Takayoshi Ogawa
Keyword(s):  
Boundary Value Problem ◽  
Large Time ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Heat Equations ◽  
Semilinear Heat Equation ◽  
Neumann Boundary Value Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We study the nonlinear Neumann boundary value problem for semilinear heat equation ∂ t u − Δ u = λ | u | p , t > 0 , x ∈ R + n , u ( 0 , x ) = ε u 0 ( x ) , x ∈ R + n , − ∂ x u ( t , x ′ , 0 ) = γ | u | q ( t , x ′ , 0 ) , t > 0 , x ′ ∈ R n − 1 where p = 1 + 2 n , q = 1 + 1 n and ε > 0 is small enough. We investigate the life span of solutions for λ , γ > 0. Also we study the global in time existence and large time asymptotic behavior of solutions in the case of λ , γ < 0 and ∫ R + n u 0 ( x ) d x > 0.

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