BRIEF NOTES Response of a Nonlinear System Under Combined Parametric and Forcing Excitation

In this Note we study a nonlinear second-order system subjected to combined parametric and forcing excitations. The paper may be regarded as an extension of 3 In The results of The system to be studied is governed by M is a small parameter. In addition to equation It consists of two parts. One is the 1/2-order subharmonic oscillation with amplitude coefficients A and B. The second part is a forced oscillation which has the same frequency as the external excitation. For the stationary amplitudes^/! and B we get from We immediately see that A = B = 0 is a solution of (5) regardless whether g = 0 or not, because is = is ~ 0 for A = B = 0, even wheng 9^ 0, as it can be seen from (6). The solution A =B = 0 corresponds, of course, to a response which is devoid of the 1/2-order subharmonic. In solving (5) for A ^ 0, B ^ 0 there are two basic difficulties. One has to do with the sgn xo term and, hence, all the j-factors in (5). As A and B are still unknown at the outset the term cannot be calculated explicitly. Only for g = 0 can The second difficulty is in finding an efficient way of solving Substituting Where the coefficients po,. • . , qa are functions of X. By requiring that these two equations must have a common root, the value of X is determined. The condition which the coefficients of (9) have to fulfill is that a certain determinant which is called the resultant of the two polynomials [7, p. 175] With the value of X determined from (10) by means of a numerical iteration we evaluate the roots of the two polynomials of (9) and pick that root which is common to both. Having obtained B, we calculate A from In this manner the influence of all the parameters on the stationary response amplitude may be studied. As already mentioned A = B = Journal of Applied Mechanics MARCH 1977 / 17

High order amplitude equation for steps on creep curve

We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential equations describing the evolution of three types of dislocations. The transition to the instability has been shown to be via Hopf bifurcation leading to limit cycle solutions with respect to physically relevant drive parameters. Here we use reductive perturbative method to extract an amplitude equation of up to seventh order to obtain an approximate analytic expression for the order parameter. The analysis also enables us to obtain the bifurcation (phase) diagram of the instability. We find that while supercritical bifurcation dominates the major part of the instability region, subcritical bifurcation gradually takes over at one end of the region. These results are compared with the known experimental results. Approximate analytic expressions for the limit cycles for different types of bifurcations are shown to agree with their corresponding numerical solutions of the equations describing the model. The analysis also shows that high order nonlinearities are important in the problem. This approach further allows us to map the theoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.

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Expression of the SST receptor 2 in uveal melanoma is not a prognostic marker

Introduction: Uveal melanoma (UM) cells and neurohormone-producing cells both originate from the neural crest. Somatostatin receptors subtype 2 (SSTR2) are over-expressed in several tumors, often from neuroendocrine origin, and synthetic antagonists like octreotide and octreotate are being used as diagnostic or therapeutic agents. We investigated the SSTR2 expression in UM, and determined whether this expression was related to prognosis of the disease. Materials and methods: UM cell lines and fresh primary UM samples were tested for SSTR2 expression by autoradiography (AR) using 125I-Tyr3-octreotate. Furthermore, UM cell lines were analyzed for SSTR2 mRNA expression with quantitative real-time RT-PCR. Results: Using AR, cell-surface SSTR2 expression was demonstrated in two UM metastatic cell lines, but no expression was detected in three cell lines derived from primary UM. However, all primary and metastatic UM cell lines showed mRNA expression levels for SSTR2 using quantitative real-time RT-PCR. Only three of 14 primary UM demonstrated moderate SSTR2 expression, and this expression was not significantly associated with tumor-free survival or any tested prognostic factor. Conclusions: Based on the rare and low expression of SSTR2 found in primary UM specimens and in UM cell lines, we conclude that SSTR2 is not widely expressed in UM. Furthermore, SSTR2 expression was not associated with tumor-free survival and prognostic factors. Therefore SSTR2 is not suited as prognostic marker or therapeutic target in UM