Kuvvetli Nonlineer Sistemler İçin Çok Ölçekli Lindstedt Poincare Tekniği

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Çok ölçekli metot ve Lindstedt-Poincare tekniğinin birleştirilmesi esasına dayanan yeni bir perturbasyon metodu ortaya atılmıştır. Yeni metot lineer sönümlü osilatör, Duffing denklemi, sönümlü kübik nonlineer denklem, kuadratik ve kübik nonlineer denklem ve zorlamalı Duffing denklemine uygulanmıştır. Klasik çok ölçekli metot ve yeni metodu kullanarak yaklaşık analitik çözümler elde edilmiştir. Bu çözümler ana denklemin sayısal çözümü ile karşılaştırılmıştır. Yeni metot kuvvetli nonlineer sistemler için çok iyi sonuçlar vermiştir.A new perturbation method combining the Method of Multiple Scales and Lindstedt Poincare techniques is proposed. The new method is applied to Linear damped oscillator, Duffing equation, damped cubic nonlinear equation, an equation with quadratic and cubic nonlinearities and forced Duffing equation. Approximate analytical solutions are obtained using the classical Multiple scales method and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. The new method produces much better results for strong nonlinearities

The genetic architecture of membranous nephropathy and its potential to improve non-invasive diagnosis

Membranous Nephropathy (MN) is a rare autoimmune cause of kidney failure. Here we report a genome-wide association study (GWAS) for primary MN in 3,782 cases and 9,038 controls of East Asian and European ancestries. We discover two previously unreported loci, NFKB1 (rs230540, OR = 1.25, P = 3.4 × 10-12) and IRF4 (rs9405192, OR = 1.29, P = 1.4 × 10-14), fine-map the PLA2R1 locus (rs17831251, OR = 2.25, P = 4.7 × 10-103) and report ancestry-specific effects of three classical HLA alleles: DRB1*1501 in East Asians (OR = 3.81, P = 2.0 × 10-49), DQA1*0501 in Europeans (OR = 2.88, P = 5.7 × 10-93), and DRB1*0301 in both ethnicities (OR = 3.50, P = 9.2 × 10-23 and OR = 3.39, P = 5.2 × 10-82, respectively). GWAS loci explain 32% of disease risk in East Asians and 25% in Europeans, and correctly re-classify 20-37% of the cases in validation cohorts that are antibody-negative by the serum anti-PLA2R ELISA diagnostic test. Our findings highlight an unusual genetic architecture of MN, with four loci and their interactions accounting for nearly one-third of the disease risk

Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators

Strongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions. © 2017 Walter de Gruyter GmbH, Berlin/Boston