On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Poroelastic toughening in polymer gels: A theoretical and numerical study

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.     

Operation principle of self-phase compensated optical waveguide isolator

A theory is developed for the self-phase compensated optical waveguide isolator recently reported in the literature. The operation principle of such device is explained in terms of synchronization of phase and power conversion. The effect of balancing phase mismatches of the two convertors on achieving a proper percentage of mode conversion is revealed. The way to make use of the phase mismatches of different sections to accommodate the different requirements in phase relationship for the reciprocal and nonreciprocal mode convertors is discussed. The theory is extended to the case where phase compensator is used. It is demonstrated that the introduction of phase compensator separates the adjustment of phase from the adjustment of power for the mode convertors so that relaxes fabrication tolerances of such devices. An isolator consists of three phase mismatched waveguide sections is designed and simulated. The simulation results confirm the self-phase compensation theory.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Prediction of High Performance Fibers Strength Using Back Propagation Neural Network

Nowadays, quantification of the effects of basic parameters such as precursor, temperature oxidation, residence time, low temperature carbonization (LTC) and high temperature carbonization (HTC) on production process polyacrylonitrile based carbon fibers is not completely understood. In this way, there is not a completely theoretical model that accomplishes to quantitatively describe production process carbon fibers very accurately which needs to be used by engineers in design, simulation and operation of that process. This paper presents the development of a back propagation neural network model for the prediction of carbon fibers produced from PAN fibers. The model is based on experimental data. The precursors, temperature oxidation, residence time, LTC and HTC have been considered as the input parameters and the strength as output parameter to develop the model. The developed model is then compared with experimental results and it is found that the results obtained from the neural network model are accurate in predicting the strength of carbon fibers.     

Alkaloids Analysis of Habranthus cardenasianus (Amaryllidaceae), Anti-Cholinesterase Activity and Biomass Production by Propagation Strategies

Plants in the Amaryllidaceae family synthesize a diversity of bioactive alkaloids. Some of these plant species are not abundant and have a low natural multiplication rate. The aims of this work were the alkaloids analysis of a Habranthus cardenasianus bulbs extract, the evaluation of its inhibitory activity against cholinesterases, and to test several propagation strategies for biomass production. Eleven compounds were characterized by GC-MS in the alkaloid extract, which showed a relatively high proportion of tazettine. The known alkaloids tazettine, haemanthamine, and the epimer mixture haemanthidine/6-epi-haemanthidine were isolated and identified by spectroscopic methods. Inhibitory cholinesterases activity was not detected. Three forms of propagation were performed: bulb propagation from seed, cut-induced bulb division, and micropropagated bulbs. Finally, different imbibition and post-collection times were evaluated in seed germination assays. The best propagation method was cut-induced bulb division with longitudinal cuts into quarters (T1) while the best conditions for seed germination were 0-day of post-collection and two days of imbibition. The alkaloids analyses of the H. cardenasianus bulbs showed that they are a source of anti-tumoral alkaloids, especially pretazettine (tazettine) and T1 is a sustainable strategy for its propagation and domestication to produce bioactive alkaloids.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

Femtosecond laser pulse train effect on Doppler profile of cesium resonance lines

We present direct observation of the velocity-selective optical pumping of the Cs ground state hyperfine levels induced by the femtosecond (fs) laser oscillator centered at either D2 (6 ²S_1/2↦6 ²P_3/2, 852 nm) or D1 (6 P_1/2, 894 nm) cesium line. We utilized previously developed modified direct frequency comb spectroscopy (DFCS) which uses a fixed frequency comb for the excitation and a weak cw scanning probe laser centered at the ¹³³Cs 6 ²S_1/2↦6 ²P_3/2 transition (D2 line) for ground levels population monitoring. The frequency comb excitation changes the usual Doppler absorption profile into a specific periodic, comblike structure. The mechanism of the velocity selective population transfer between the Cs ground state hyperfine levels induced by fs pulse train excitation is verified in a theoretical treatment of the multilevel atomic system subjected to a pulse train resonant field interaction.     

Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods

In this brief review, an overview about recent efforts to simulate the spectroscopic signatures of chiral molecules is given with focus on real time propagation approaches to solve the time-dependent Schrödinger equation. In particular the simulation of electric circular dichroism spectra and vibrational Raman optical activity is discussed. In comparison to linear absorption spectra, where only the response of the electric dipole moment is necessary, the response of the magnetic dipole moment and electric quadrupole moment is more intricate. Issues such as gauge origin dependence, basis set dependence, non-local potentials and the dipole approximation are addressed.