Effective Reducibility of a Class of Linear Differential Equations with Quasiperiodic Coefficients

In this paper we consider the effective reducibility of the following linear differential equation: , where A is a constant matrix, Q(t,?) is quasiperiodic in t, and ? is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to , where R* is exponentially small in ?.

Effects of Reduced Frequency on Network Configuration and Synchronization Transition

Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced frequency＇, a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.

Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects

A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.

Biogenic volatile organic compound analyses by PTR-TOF-MS: Calibration, humidity effect and reduced electric field dependency

Green leaf volatiles（GLVs） emitted by plants after stress or damage induction are a major part of biogenic volatile organic compounds（BVOCs）. Proton transfer reaction time-of-flight mass spectrometry（PTR-TOF-MS） is a high-resolution and sensitive technique for in situ GLV analyses, while its performance is dramatically influenced by humidity, electric field,etc. In this study the influence of gas humidity and the effect of reduced field（E/N） were examined in addition to measuring calibration curves for the GLVs. Calibration curves measured for seven of the GLVs in dry air were linear, with sensitivities ranging from 5 to10 ncps/ppbv（normalized counts per second/parts per billion by volume）. The sensitivities for most GLV analyses were found to increase by between 20% and 35% when the humidity of the sample gas was raised from 0% to 70% relative humidity（RH） at 21°C, with the exception of（E）-2-hexenol. Product ion branching ratios were also affected by humidity,with the relative abundance of the protonated molecular ions and higher mass fragment ions increasing with humidity. The effect of reduced field（E/N） on the fragmentation of GLVs was examined in the drift tube of the PTR-TOF-MS. The structurally similar GLVs are acutely susceptible to fragmentation following ionization and the fragmentation patterns are highly dependent on E/N. Overall the measured fragmentation patterns contain sufficient information to permit at least partial separation and identification of the isomeric GLVs by looking at differences in their fragmentation patterns at high and low E/N.