• 천문학논총
• /
• 제20권1호
• /
• pp.37-42
• /
• 2005

The problem for the collapse of isothermal and rotational self-gravitational viscous disk is considered. We derive self-similar solutions for the cases in the inner and outer regions of the self-gravitational viscous disk. We show that surface density depends on ${\sigma}_0/r$ in the outer region of the disk using a slow accretion approximation. The ratio of a modified viscous parameter in the outer region of the disk to that in the inner region is 0.042. We resorted to numerical solutions of governing equations of the self-gravitational disk to find out profiles of ${\sigma}$, u and ${\upsilon}$ in terms of x. Their profiles were rapidly changed around the innermost region of the self-gravitational disk. It indicates that a new object was formed in the most inner region of the disk.

• 대한수학회보
• /
• 제61권3호
• /
• pp.699-715
• /
• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

• Journal of Astronomy and Space Sciences
• /
• 제22권2호
• /
• pp.139-146
• /
• 2005

A model of advection-dominated accretion flows has been highlighted in the last decade. Most of calculations are based on self-similar solutions of equations governing the accreting flows. We revisit self-similar solutions of the simplest form of advection-dominated accretion flows. We explore the parameter space thoroughly and seek another category of self-similar solutions. In this study we allow the parameter f less than zero, which denotes the fraction of energy transported through advection. We have found followings: 1. For f > 0, in real ADAF solutions the ratio of specific heats ${\gamma}$ satisfies 1 < ${\gamma}$ < 5/3 for O ${\leq}$ f ${\leq}$ 1. On the other hands, in wind solutions a rotating disk does not exist. 2. For f < 0, in real ADAF solutions with ${\epsilon}$ greater than zero ${\gamma}$ requires rather exotic range, that is, ${\gamma}$ < 1 or ${\gamma}$ > 5/3. When -5/2 < ${\epsilon}$' < 0, however, allowable ${\gamma}$ can be found in ${\gamma}$ < 5/3, in which case 4{\Omega}_0$,_ is imaginary. 3. For a negative $u_0$,+ with f > 0, solutions are only allowed with exotic ${\gamma}$, that is, 1 < ${\gamma}$ or ${\gamma}$ > (5f/2-5/3)/(5f/2-1)when O < f < 2/5, (5f/2-5/3)/(5f/2-1) < ${\gamma}$ < 1 when f > 2/5. Since ${\epsilon}$' is negative, 4{\Omega}_0$,+ is again an imaginary quantity. For a negative $u_0$,+ with f < 0, ${\gamma}$ is allowed in 1 < 7 < (5|f|/2 + 5/3)/(5|f|/2 + 1). We briefly discuss physical implications of what we have found.

• 대한수학회보
• /
• 제47권1호
• /
• pp.29-37
• /
• 2010

We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

• 대한수학회보
• /
• 제52권6호
• /
• pp.1945-1962
• /
• 2015

This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity vanishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave solution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.

• Journal of Astronomy and Space Sciences
• /
• 제18권1호
• /
• pp.1-6
• /
• 2001

In this paper we investigate the properties of advection-dominated accretion flows (ADAFs) in case that outflows carry away infalling matter with its angular momentum and energy. Positive Bernoulli number in ADAFs allow a fraction of the gas to be expelled in a form of outflows. The ADAFs are also unstable to convection. We present self-similar solutions for advection-dominated accretion flows in the presence of outflows from the accretion flows(ADIOS). The axisymmetric flow is treated in variables integrated over polar sections and the effects of outflows on the accretion flow are parameterized for possible configurations compatible with the one dimensional self-similar ADAF solution. We explicitly derive self-similar solutions of ADAFs in the presence of outflows and show that the strong outflows in the accretion flows result in a flatter density profile, which is similar to that of the convection-dominated accretion flows(CDAFs) in which convection transports the angular momentum inward and the energy outward. There two different versions of the ADAF model should show similar behaviors in X-ray spectrum to some extent. Even though the two models may show similar behaviors, they should be distinguishable due to different physical properties. We suggest that for a central object of which mass is known these two different accretion flow should have different X-ray flux value due to deficient matter in the wind model.

• 천문학논총
• /
• 제17권1호
• /
• pp.11-14
• /
• 2002

Our examination of the relations of spherically symmetric accretion on a massive point object to viscous drag, neglecting gas pressure and using self-similar transformation, shows the behaviors of the asymptotic solutions? in the regions near to and far from the center. The viscosity reduces the free-fall velocity by the factor $(1\;+\;\zeta) ^{-1}$, and causes flattening in the density distribution. Therefore, the viscosity leads to the reduction of the mass accretion rate.

• 천문학논총
• /
• 제18권1호
• /
• pp.21-24
• /
• 2003

The problem of the collapse of a self gravitating disk is here considered. We show self-similar solutions for the above problem under a modified viscous parameter. Surface density depends on r$^m$ in the inner region, where m is -1.6. Therefore growing central mass goes on without mass inflow to the system.

• Structural Engineering and Mechanics
• /
• 제20권3호
• /
• pp.335-346
• /
• 2005

The T-stress of cracks in elastic sheets is solved by using the fractal finite element method (FFEM). The FFEM, which had been developed to determine the stress intensity factors of cracks, is re-applied to evaluate the T-stress which is one of the important fracture parameters. The FFEM combines an exterior finite element model with a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. The higher order Williams series is used to condense the large numbers of nodal displacements at the inner model near the crack tip to a small set of unknown coefficients. Numerical examples revealed that the present approach is simple and accurate for calculating the T-stresses and the stress intensity factors. Some errors of the T-stress solutions shown in the previous literature are identified and the new solutions for the T-stress calculations are presented.

• Journal of the korean society of oceanography
• /
• 제31권2호
• /
• pp.75-88
• /
• 1996

The analytic and numerical solution of the 1$\frac{1}{2}$-layer and 2$\frac{1}{2}$-layer models are derived. The large coastal-sea level drop and the fast westward speed of the anticyclonic gyre due to strong offshore winds using two ocean models are investigated. The models are forced by wind stress fields similar in structure to the intense mountain-pass jets(${\sim}$20 dyne/$cm^{2}$) that appear in the Gulfs of Tehuantepec and Papagayo in the Central America for periods of 3${\sim}$7 days. Analytic and numerical solutions compare favorably with observations, the large sea-level drop (${\sim}$30 cm) at the coast and the fast westward propagation speeds (${\sim}$13 km/day) of the gyres. The coastal sea-level drop is enhanced by several factors: horizontal mixing, enhanced forcing, coastal geometry, and the existence of a second active layer in the 2$\frac{1}{2}$-layer model. Horizontal mixing enhances the sea-level drop because the coastal boundary layer is actually narrower with mixing. The forcing ${\tau}$/h is enhanced near the coast where h is thin. Especially, in analytic solutions to the 2$\frac{1}{2}$-layer model the presence of two baroclinic modes increases the sea-level drop to some degree. Of theses factors the strengthened forcing ${\tau}$/h has the largest effect on the magnitude of the drop, and when all of them are included the resulting maximum drop is -30.0 cm, close to observed values. To investigate the processes that influence the propagation speeds of anticyclonic gyre, several test wind-forced calculations were carried out. Solutions to dynamically simpler versions of the 1$\frac{1}{2}$-layer model show that the speed is increased both by ${\beta}$-induced self-advection and by larger h at the center ofthe gyres. Solutions to the 2$\frac{1}{2}$-layer model indicate that the lower-layer flow field advects the gyre westward and southward, significantly increasing their propagation speed. The Papagayo gyre propagates westward at a speed of 12.8 km/day, close to observed speeds.