A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid becomes solidified by heat transfer to a plane mold of finite thickness. Heat flux drawn from the lower surface of the mold is approximately uniform, but contains a small sinusoidal perturbation in one space dimension. Numerical results are obtained for the consequent sinusoidal perturbation ...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

A comprehensive assessment is made of transient and asymptotic two-dimensional perturbation growth in compressible shear flow using unbounded constant shear and the Couette problem as examples. The unbounded shear flow example captures the essential dynamics of the rapid transient growth processes at high Mach numbers, while excitation by nonmodal mechanisms of nearly neutral modes supported by...

We demonstrate experimentally that a periodic perturbation on a partially spatially incoherent optical beam induces modulation instability that depends strongly on the perturbation periods as well as on the strength of the nonlinearity and the degree of spatial coherence. At a fixed value of the nonlinearity and coherence, the incoherent modulation instability has a maximum growth at a preferre...

Let H and H + H be positive deenite matrices. It was shown by Barlow and Demmel, and Demmel and Veseli c that if one takes a component-wise approach one can prove much stronger bounds on i (H)== i (H++H) and the components of the eigenvectors of H and H++H than by using the standard norm-wise perturbation theory. Here a uniied approach is presented that improves on the results of Barlow, Demmel...

Galaxy cluster peculiar velocities can be inferred from high–sensitivity, high–resolution multiple–frequency observations in the 30 to 400 GHz range. While galaxy cluster counts and power spectra are sensitive to the growth factor, peculiar velocities are sensitive to the time–derivative of the growth factor and are hence complementary. Using linear perturbation theory, we forecast constraints ...

Through cyclic regeneration, feather stem cells are molded into different shapes under different physiological states. With its distinct morphology, context-dependent growth, and experimental manipulability, the feather provides a rich model to study growth control, regeneration, and morphogenesis in vivo. Recent examples include novel insights revealed by transient perturbation with chemothera...

Transient energy growth of disturbances to co-rotating vortex pairs is investigated in an analysis where vortex core expansion and vortex merging are included. The dynamics of pairs are compared to those of individual vortices in order to highlight the effect of vortex interaction. Three typical vortex pair cases are studied, with the pairs comprised respectively of individually asymptotically ...