Brown方程的分歧解与初始成畴问题

初始成畴问题是一个典型的分歧问题。通过标度变换使铁磁体的尺寸参数显现在自由能表达式和Brown方程中。推广应用分歧理论的微扰法,求出了Brown方程的最小正分歧点和从此点发出的分歧解。分析了单畴态和分歧解的稳定性,据此对初始成畴临界尺寸和初始成畴行为进行了研究。结论指出,临界尺寸是尺寸参数的最小正分歧点,其近旁的初始成畴过程或者沿着分歧解连续地进行,或者是一个不连续的跃变。给出了相应的判据。此外,还得到了严格单畴临界尺寸上下限的一个估计,以及在特殊情况下这种临界尺寸的精确结果。 关键词：

BIFURCATION SOLUTIONS OF BROWN'S EQUATION AND PROBLEM OF FORMATION OF INCIPIENT MAGNETIC DOMAIN

The problem of formation of incipient magnetic domain in the scheme of Brown's equation is one of the typical problems of bifurcation. A scale transformation is introduced, so that the size of a ferromagnetic body appears explicitly as a parameter in the expressions of free energy and Brown's equation. We generalize the perturbation method in bifurcation theory to study the initial bifurcation of Brown's equation. After an analysis of the stability of single-domain state and bifurcation solutions, we arrived at the conclusion that the critical size of incipient domain formation equals to the smallest positive bifurcation point of size parameter and the process of incipient domain formation takes place either continuously following the bifurcation solutions starting from this bifurcation point or discontinuously with a jump at this point. The criteria for discriminating the continuity and discontinuity of such a transition were given. In addition, we also obtained the lower and upper limits of the precise critical size of single-domain, and also its exact value in particular cases.