On the Stability of Most General Exact Solution for Isentropic Superdense Stars

2005 ◽  
Vol 8 (1) ◽  
pp. 60-62
Author(s):  
Dhuha Majeed Saleh ◽  
◽  
Abdul Samee A. Al-Janabi ◽  
M. K. Jasim ◽  
◽  
...  
Keyword(s):  
Exact Solution ◽  
Superdense Stars ◽  
The Stability

An exact solution in the stability of m. h. d. Couette flow

1972 ◽  
Vol 327 (1569) ◽  
pp. 269-278 ◽  
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Couette Flow ◽  
Stability Problem ◽  
Axial Magnetic Field ◽  
Narrow Gap ◽  
Mhd Stability ◽  
Arbitrary Magnetic Field ◽  
The Stability ◽  
Conducting Cylinders

The MHD stability problem for dissipative Couette flow in a narrow gap between corotating, conducting cylinders with an axial magnetic field is solved exactly. Results are presented for an arbitrary magnetic field; in particular, previous results on the zero and infinite magnetic field limits are verified.

Stability of Bödewadt flow

2005 ◽  
Vol 363 (1830) ◽  
pp. 1181-1187 ◽  
Author(s):  
Sharon O MacKerrell
Keyword(s):  
Exact Solution ◽  
Theoretical Study ◽  
Stokes Equations ◽  
Basic Flow ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Asymptotic Investigation ◽  
Wave Angle ◽  
The Stability

The stability of the flow produced over an infinite stationary plane in a fluid rotating with uniform angular velocity at an infinite distance from the plane is considered. The basic flow is an exact solution of the Navier–Stokes equations making it amenable to theoretical study. An asymptotic investigation is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally can be described by a linear inviscid stability analysis. The prediction obtained for the wave angle of the disturbances is found to agree well with the available experimental and numerical results.

On the Stability of the Impact Damper

1966 ◽  
Vol 33 (3) ◽  
pp. 586-592 ◽  
Author(s):  
S. F. Masri ◽  
T. K. Caughey
Keyword(s):  
Exact Solution ◽  
Stability Analysis ◽  
Asymptotically Stable ◽  
Impact Damper ◽  
The Stability ◽  
The Impact

The exact solution for the symmetric two-impacts-per-cycle motion of the impact damper is derived analytically, and its asymptotically stable regions are determined. The stability analysis defines the zones where the modulus of all the eigenvalues of a certain matrix relating conditions after each of two consecutive impacts is less than unity.

The Galerkin method applied to convective instability problems

1968 ◽  
Vol 33 (1) ◽  
pp. 201-208 ◽  
Author(s):  
Bruce A. Finlayson
Keyword(s):  
Exact Solution ◽  
Time Dependence ◽  
Galerkin Method ◽  
Convective Instability ◽  
Fluid Layer ◽  
Oscillatory Instability ◽  
Rotating Fluid ◽  
Exponential Time ◽  
The Stability ◽  
The Galerkin Method

The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory instability can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.

On the stability of the asymptotic suction boundary-layer profile

1965 ◽  
Vol 23 (4) ◽  
pp. 715-735 ◽  
Author(s):  
T. H. Hughes ◽  
W. H. Reid
Keyword(s):  
Exact Solution ◽  
Stability Problem ◽  
Adjoint Problem ◽  
Analytical Continuation ◽  
Neutral Stability ◽  
The Stability ◽  
Asymptotic Suction ◽  
Linear Stability Problem ◽  
Original Treatment ◽  
General Method

This paper presents a discussion of some aspects of the linear stability problem for the asymptotic suction profile. An exact solution of the inviscid equation is first obtained in terms of the usual hypergeometric function and its analytical continuation. This exact solution provides both a corrected version of an earlier treatment by Freeman and an independent check on the more general method suggested for solving the inviscid equation numerically. Various approximations to the characteristic equation, and hence to the curve of neutral stability, are then considered. In particular, it is found that, in a consistent asymptotic treatment of the related adjoint problem, at least one viscous correction to the singular inviscid solution must be considered. Based on the present results for the adjoint problem, it is suggested that Tollmien's original treatment of the viscous corrections must be slightly modified.

scholarly journals The elastic stability of a thin twisted strip—II

1937 ◽  
Vol 161 (905) ◽  
pp. 197-220 ◽  
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Main Part ◽  
Fourier Expansion ◽  
Elastic Stability ◽  
Numerical Work ◽  
The Stability ◽  
Good Agreement

I—In a previous paper the present writer discussed both theoretically and experimentally the equilibrium and elastic stability of a thin twisted strip, and the results obtained by the theory were found to be in good agreement with observation. It has, however, been pointed out by Professor Southwell, F. R. S., that the solution of the stability equations which was given in that paper may only be regarded as an approximate solution for, although it satisfies exactly the differential equations and two boundary conditions along the edge of the strip, it only satisfies the two remaining boundary conditions approximately. The author has also noticed that the coefficients n a m in the Fourier expansion of θ 2 cos mθ which were used in A are incorrect when m = 0, and this has led to errors in the numerical work so that the values of ᴛb 2 / π 2 h which are given in Table I of A are wrong. In the present paper a solution of the stability equations is obtained which satisfies all the boundary conditions. This solution is very much more complicated than the approximate solution and much greater labour is required for the numerical work. The numerical work for the approximate solution of A has also been revised and the corrected results are given in 9, 10. It is found that the results for the approximate solution are in good agreement with those obtained from the exact solution and that both agree moderately well with the experimental results which are given in A. The main part of this paper is an extension of the previous work and is concerned with the stability of a thin twisted strip when it is subjected to a tension along its length. The theory has been compared with experiment and satisfactorily good agreement between them was found.

scholarly journals Exact Solution of Impulse Response to a Class of Fractional Oscillators and Its Stability

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Ming Li ◽  
S. C. Lim ◽  
Shengyong Chen
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Impulse Response ◽  
Fractional Order ◽  
System Analysis ◽  
Stability Behavior ◽  
Single Degree ◽  
Fractional Oscillator ◽  
The Stability ◽  
Typical Model

Oscillator of single-degree-freedom is a typical model in system analysis. Oscillations resulted from differential equations with fractional order attract the interests of researchers since such a type of oscillations may appear dramatic behaviors in system responses. However, a solution to the impulse response of a class of fractional oscillators studied in this paper remains unknown in the field. In this paper, we propose the solution in the closed form to the impulse response of the class of fractional oscillators. Based on it, we reveal the stability behavior of this class of fractional oscillators as follows. A fractional oscillator in this class may be strictly stable, nonstable, or marginally stable, depending on the ranges of its fractional order.

The Alculation Method of Stable Bearing Capacity of Portal Frame

2013 ◽  
Vol 351-352 ◽  
pp. 329-336 ◽  
Author(s):  
Xu Chen ◽  
Hui Min Li
Keyword(s):  
Exact Solution ◽  
Bearing Capacity ◽  
Carrying Capacity ◽  
Lateral Displacement ◽  
Reference Value ◽  
Frame Structure ◽  
Concentrated Force ◽  
Portal Frame ◽  
Calculation Results ◽  
The Stability

In recent years, the portal frame structure in the actual project has been widely used, but using the finite element method calculation of stable bearing capacity of portal frame is more complex, and very difficult to the design and construction personnel. With the known stability of the cantilever column carrying capacity and the vertex of the lateral displacement under concentrated force, the establishment of the ratio of the portal frame stability capacity and the stability of the cantilever column carrying capacity both in the same concentrated force vertex lateral displacement than the relationship between the structural mechanics solver to seek out frame to the lateral displacement of the vertex under concentrated force, obtained by computing the stability capacity of the portal frame, and with the exact solution comparison and found that the methods of theoretical calculation results coincide with the exact solution, and then get an easy way of solving the portal frame stable bearing capacity. After numerical example, this method is simple, easy to master, and it has important reference value.

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