ni number. Further, this surfactant mode instability shifts toward low wave numbers with critical Marangoni number for instability scaling with wave number in a particular fashion. We used this scaling and carried out an asymptotic analysis to capture this instability in low wave-number limit. Depending on S and Bo, we observed the existence of a stable gap in terms of Ma where both the eigen-modes remain stable. Our results indicate that for a given Bond number, the width of stable gap in terms of Ma decreases with decrease in S and the stable gap vanishes when S is sufficiently small. The effect of increasing Bond number (or equivalently, the strength of basic flow) is found to be stabilizing for the film flow configuration.We study dynamic magnetic behavior in the vicinity of the dynamic phase transition (DPT) for a suitable series of samples that have different Curie temperatures T_C, which thus enables us to experimentally explore the role of the reduced temperature T/T_C in the DPT. For this purpose, we fabricate Co_1-xRu_x epitaxial thin films with uniaxial in-plane anisotropy by means of sputter deposition in the concentration range 0.0≤x≤0.26. All samples are ferromagnetic at room temperature, exhibit an abrupt magnetization reversal along their easy axis, and represent a unique T_C and thus T/T_C ratio according to their Ru concentration. The dynamic magnetic behavior is measured by using an ultrasensitive transverse magneto-optical detection method and the resulting dynamic states are explored as a function of the applied magnetic field amplitude H_0 and period P, as well as an additional bias field H_b, which is the conjugate field of the dynamic order parameter Q. Our experimental results demonstrate that the qualitative behavior of the dynamic phase diagram is independent of the T/T_C ratio and that for all T/T_C values we observe metamagnetic anomalies in the dynamic paramagnetic state, which do not exist in the corresponding thermodynamic phase diagram. However, quantitatively, these metamagnetic anomalies are very strongly dependent on the T/T_C ratio, leading to an about 20-fold increase of large metamagnetic fluctuations in the paramagnetic regime as the T/T_C ratio increases from 0.37 to 0.68. Also, the phase space range in which these anomalous metamagnetic fluctuations occur extends closer and closer to the critical point as T/T_C increases.In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time τ at the critical point increases with system size L in power-law fashion τ∼L^z, which defines the critical dynamical exponent z. We show that this also holds for the two-dimensional bond-diluted Ising model in the regime p>p_c, where p is the parameter denoting the bond concentration, but with a dynamical critical exponent z(p) which shows a strong p dependence. Moreover, we show numerically that z(p), as obtained from the autocorrelation of the total magnetization, diverges when the percolation threshold p_c=1/2 is approached z(p)-z(1)∼(p-p_c)^-2. We refer to this observed extremely fast increase of the correlation time with size as super slowing down. Independent measurement data from the mean-square deviation of the total magnetization, which exhibits anomalous diffusion at the critical point, support this result.A pulse traveling on a uniform nondissipative chain of N masses connected by springs is soon destructured by dispersion. Here it is shown that a proper modulation of the masses and the elastic constants makes it possible to obtain a periodic dynamics and a perfect transmission of any kind of pulse between the chain ends, since the initial configuration evolves to its mirror image in the half period. This makes the chain behave as a Newton's cradle. By a known algorithm based on orthogonal polynomials one can numerically solve the general inverse problem leading from the spectrum to the dynamical matrix and then to the corresponding mass-spring sequence, so yielding all possible "perfect cradles." As quantum linear systems obey the same dynamics of their classical counterparts, these results also apply to the quantum case For instance, a wave function localized at one end would evolve to its mirror image at the opposite chain end.We discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model.Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates k for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in k(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log(k) vs F that leads to incorrect landscape parameter determination. To correct the measured k(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Exarafenib datasheet Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected k(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.