scholarly journals Influence of the hypermagnetic field noise on the baryon asymmetry generation in the symmetric phase of the early universe

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Maxim Dvornikov ◽  
Victor B. Semikoz
Keyword(s):  
Early Universe ◽  
Fluid Velocity ◽  
Baryon Asymmetry ◽  
Navier Stokes ◽  
Electroweak Phase Transition ◽  
Navier Stokes Equation ◽  
Advection Term ◽  
Induction Equation ◽  
Field Noise ◽  
Symmetric Phase

AbstractWe study a matter turbulence caused by strong random hypermagnetic fields (HMFs) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier–Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of $$e_\mathrm {R,L}$$ e R , L and $$\nu _{e_\mathrm {L}}$$ ν e L , we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the ‘t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

scholarly journals Mathematical modelling of fluid flow in electromagnetically stirred weld pool

2021 ◽  
Vol 1201 (1) ◽  
pp. 012025
Author(s):  
K Enger ◽  
M G Mousavi ◽  
A Safari
Keyword(s):  
Fluid Flow ◽  
Grain Refinement ◽  
Weld Pool ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Turbulent Fluid Flow ◽  
Flow Modelling ◽  
Weld Parameters ◽  
The Relationship

Abstract In this paper, a mathematical model has been proposed to study the relationship between electromagnetic stirring (EMS) weld parameters and the mode of fluid flow on grain refinement of AA 6060 weldments. For this purpose, fluid flow modelling using Navier-Stokes equation is described first, and then, the proposed mathematical approach has been discussed in detail. For demonstration, calculations to determine the fluid velocity in the weld pool of thin plate AA6060 were performed. The application of the model on the experimental results indicates that the best grain refinement is achieved at a transition mode from laminar to turbulent fluid flow.

scholarly journals A MAGNETOHYDRODYNAMIC STUDY OF BEHAVIOR IN AN ELECTROLYTE FLUID USING NUMERICAL AND EXPERIMENTAL SOLUTIONS

2012 ◽  
Vol 11 (1-2) ◽  
pp. 53
Author(s):  
L. P. Aoki ◽  
M. G. Maunsell ◽  
H. E. Schulz
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Fluid Velocity ◽  
Flow Analysis ◽  
Test Chamber ◽  
Cross Product ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Vector Density ◽  
The Magnetic Field

This article examines a rectangular closed circuit filled with an electrolyte fluid, known as macro pumps, where a permanent magnet generates a magnetic field and electrodes generate the electric field in the flow. The fluid conductor moves inside the circuit under magnetohydrodynamic effect (MHD). The MHD model has been derived from the Navier Stokes equation and coupled with the Maxwell equations for Newtonian incompressible fluid. Electric and magnetic components engaged in the test chamber assist in creating the propulsion of the electrolyte fluid. The electromagnetic forces that arise are due to the cross product between the vector density of induced current and the vector density of magnetic field applied. This is the Lorentz force. Results are present of 3D numerical MHD simulation for newtonian fluid as well as experimental data. The goal is to relate the magnetic field with the electric field and the amounts of movement produced, and calculate de current density and fluid velocity. An u-shaped and m-shaped velocity profile is expected in the flows. The flow analysis is performed with the magnetic field fixed, while the electric field is changed. Observing the interaction between the fields strengths, and density of the electrolyte fluid, an optimal configuration for the flow velocity isdetermined and compared with others publications.

GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS

2007 ◽  
Vol 17 (07) ◽  
pp. 1039-1063 ◽  
Author(s):  
A. MELLET ◽  
A. VASSEUR
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Fluid Velocity ◽  
Planck Equation ◽  
Coupled System ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equation ◽  
Reflection Boundary ◽  
Fokker Planck

We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

Boundary Layers

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Boundary Layer ◽  
Fluid Velocity ◽  
One Dimension ◽  
Navier Stokes ◽  
Analytic Approximation ◽  
Navier Stokes Equation ◽  
Velocity Gradients ◽  
Thin Region ◽  
Large Velocity ◽  
Different Dimensions

It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’s equations to one dimension. They can then be solved numerically. A convergent analytic approximation was also found by H. Weyl. The drag on a flat plate can now be derived, resolving d’Alembert’s paradox. When the boundary is too long, Prandtl’s theory breaks down: the boundary layer becomes turbulent or separates from the wall.

Investigation into Fluid Velocity Field of Wedge-Shaped Gap in Grinding

2010 ◽  
Vol 37-38 ◽  
pp. 593-598 ◽  
Author(s):  
Chang He Li ◽  
Zhen Lu Han ◽  
Jing Yao Li
Keyword(s):  
Velocity Field ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Surface Velocity ◽  
Navier Stokes ◽  
Coolant Fluid ◽  
Navier Stokes Equation ◽  
Part Surface ◽  
Peripheral Surface ◽  
Fluid Velocity Field

In the grinding process, grinding fluid is delivered for the purposes of chip flushing, cooling, lubrication and chemical protection of work surface. Hence, the conventional method of flood delivering coolant fluid by a nozzle in order to achieve high process performance purposivelly. However, hydrodynamic fluid pressure can be generated ahead of the grinding zone due to the wedge effect between wheel peripheral surface and part surface. In this paper, a theoretical fluid velocity field modeling is presented for flow of coolant fluid of wedge-shaped gap in flood delivery surface grinding, which is based on navier-stokes equation and continuous formulae. The numerical simulation results showed that the velocity in the x direction was dominant and the side-leakage in the y direction existed. The velocity in the z direction was smaller than the others because of the assumption of laminar flow. The smaller the gap is, the larger the velocity in the x direction. The magnitude of the velocity is also proportional to the surface velocity of the wheel.

scholarly journals New Necessary Conditions for the Well-Posedness of Steady Bioconvective Flows and Their Small Perturbations

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 205
Author(s):  
Aníbal Coronel ◽  
Fernando Huancas ◽  
Alex Tello ◽  
Marko Rojas-Medar
Keyword(s):  
Weak Solutions ◽  
Flow Problem ◽  
Necessary Conditions ◽  
Fluid Velocity ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Small Perturbations ◽  
The Galerkin Method ◽  
Bioconvective Flow

We introduce new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of the weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem. Our analysis is based on the application of the Galerkin method, and the system considered consists of three equations: the nonlinear Navier–Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. The boundary conditions are homogeneous and of zero-flux-type, for the cases of fluid velocity and microorganism concentration, respectively.

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