scholarly journals Incoherent localized structures and hidden coherent solitons from the gravitational instability of the Schrödinger-Poisson equation

2021 ◽  
Vol 104 (5) ◽  
Author(s):  
Josselin Garnier ◽  
Kilian Baudin ◽  
Adrien Fusaro ◽  
Antonio Picozzi
Keyword(s):  
Poisson Equation ◽  
Gravitational Instability ◽  
Localized Structures

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

scholarly journals Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu
Keyword(s):  
Poisson Equation ◽  
Existence Result ◽  
Critical Growth ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Number Of Solutions ◽  
Concentration Behavior ◽  
The Relationship ◽  
Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

Research on the application of 3D reconstruction technology in traditional handicraft design

2021 ◽  
pp. 002072092110052
Author(s):  
GuoLong Zhang
Keyword(s):  
Poisson Equation ◽  
Optimization Algorithm ◽  
Three Dimensional ◽  
Reconstruction Algorithm ◽  
Social Production ◽  
Design Constraint ◽  
Reconstruction Process ◽  
Key Steps ◽  
Shielding Design ◽  
Reconstruction Model

The use of computer technology for three-dimensional (3 D) reconstruction is one of the important development directions of social production. The purpose is to find a new method that can be used in traditional handicraft design, and to explore the application of 3 D reconstruction technology in it. Based on the description and analysis of 3 D reconstruction technology, the 3 D reconstruction algorithm based on Poisson equation is analyzed, and the key steps and problems of the method are clarified. Then, by introducing the shielding design constraint, a 3 D reconstruction algorithm based on shielded Poisson equation is proposed. Finally, the performance of two algorithms is compared by reconstructing the 3 D image of rabbit. The results show that: when the depth value of the algorithm is 11, the surface of the rabbit image obtained by the proposed optimization algorithm is smoother, and the details are more delicate and fluent; under different depth values, with the increase of the depth value, the number of vertices and faces of the two algorithms increase, and the optimal depth values of 3 D reconstruction are more than 8. However, the proposed optimization algorithm has more vertices, and performs better in the reconstruction process; the larger the depth value is, the more time and memory are consumed in 3 D reconstruction, so it is necessary to select the appropriate depth value; the shielding parameters of the algorithm have a great impact on the fineness of the reconstruction model. The larger the parameter is, the higher the fineness is. In a word, the proposed 3 D reconstruction algorithm based on shielded Poisson equation has better practicability and superiority.

Domain wall dynamics: Growth laws, localized structures and stable droplets

2007 ◽  
Vol 146 (1) ◽  
pp. 71-86 ◽  
Author(s):  
D. Gomila ◽  
P. Colet ◽  
M. S. Miguel ◽  
G.-L. Oppo
Keyword(s):  
Domain Wall ◽  
Domain Wall Dynamics ◽  
Localized Structures ◽  
Growth Laws
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