Mixed characteristic problem for motion of a granular and additively compressible medium

1978 ◽  
Vol 19 (2) ◽  
pp. 236-239 ◽  
Author(s):  
I. S. Degtyarev
Keyword(s):  
Compressible Medium ◽  
Mixed Characteristic ◽  
Characteristic Problem

scholarly journals A pathological case of the C1 conjecture in mixed characteristic

2018 ◽  
Vol 167 (01) ◽  
pp. 61-64 ◽  
Author(s):  
INDER KAUR
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Projective Curve ◽  
Free Sheaf ◽  
Smooth Projective Curve ◽  
Mixed Characteristic ◽  
Locally Free Sheaf ◽  
Fixed Rank ◽  
Pathological Case

AbstractLet K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

Study on Cavity Growth in Uniaxial Tension of ZK60 Magnesium Alloy

2007 ◽  
Vol 353-358 ◽  
pp. 687-690
Author(s):  
Yan Dong Yu ◽  
De Liang Yin ◽  
Bao You Zhang
Keyword(s):  
Volume Fraction ◽  
Cavity Growth ◽  
Experimental Studies ◽  
Superplastic Forming ◽  
Cavity Radius ◽  
Analysis Software ◽  
Mixed Characteristic ◽  
Substantial Growth ◽  
Zk60 Magnesium Alloy ◽  
Electronic Microscope

Cavity growth is a typical microstructure feature in superplastic forming (SPF) of materials. Substantial growth and interlink of cavities in superplastic deformation usually lead to reduction in elongation, even to failure. Consequently, it is necessary to investigate the mechanism and model of cavity growth. In this paper, experimental studies on cavity growth were carried out by means of superplastic tension of ZK60 magnesium alloys. Scanning electronic microscope (SEM) was employed for observation of fractography. Experimental cavity radius and volume fraction were determined by optical microscopy and corresponding picture-based analysis software. It is found that, the fractured surfaces after a superplastic elongation have a mixed characteristic of intergranular cavities and dimples. Further, the cavity growth is identified to follow a exponentially increasing mode.

On One Nonlinear Variant of the Nonlocal Characteristic Problem

2015 ◽  
Vol 206 (4) ◽  
pp. 406-412
Author(s):  
M. Menteshashvili ◽  
R. Bitsadze
Keyword(s):  
Characteristic Problem

Comparison of the numerical and self-similar solutions of Sedov’s problem on a point explosion in gas

2020 ◽  
Vol 15 (3-4) ◽  
pp. 212-216
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Gas Dynamics ◽  
Numerical Solutions ◽  
Similarity Theory ◽  
Compressible Medium ◽  
Initial Moment ◽  
Point Explosion ◽  
Perfect Gas ◽  
Gas Dynamics Equations ◽  
Self Similar ◽  
Similar Solutions

Comparative analysis of solutions of Sedov’s problem of a point explosion in gas for the plane case, obtained by the analytical method and using the open software package of computational fluid dynamics OpenFOAM, is carried out. A brief analysis of methods of dimensionality and similarity theory used for the analytical self-similar solution of point explosion problem in a perfect gas (nitrogen) which determined by the density of uncompressed gas, magnitude of released energy, ratio of specific heat capacities and by the index of geometry of the explosion is given. The system of one-dimensional gas dynamics equations for a perfect gas includes the laws of conservation of mass, momentum, and energy is used. It is assumed that at the initial moment of time there is a point explosion with instantaneous release of energy. Analytical self-similar solutions for the Euler and Lagrangian coordinates, mass velocity, pressure, temperature, and density in the case of plane geometry are given. The numerical simulation of considered process in sonicFoam solver of OpenFOAM package built on the PISO algorithm was performed. For numerical modeling the system of differential equations of gas dynamics is used, including the equations of continuity, Navier-Stokes motion for a compressible medium and conservation of internal energy. Initial and boundary conditions were selected in accordance with the obtained analytical solution using the setFieldsDict, blockMeshDict, and uniformFixedValue utilities. The obtained analytical and numerical solutions have a satisfactory agreement.

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