Reprint of : Connection between wave transport through disordered 1D waveguides and energy density inside the sample: A maximum-entropy approach

We study the average energy – or particle – density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.     

Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties

Mechanical problems involving an interphase between two well-defined, and eventually different, materials are of interest. The aim of this paper is to present a simplified model that, for low frequency regime, is appropriate for this situation: an interface model with elastic and inertial properties. We present, together with the equations of motion, an identification procedure that is valid for any mass density profile along the thickness of the interphase. For evaluating the accuracy of the model, computations of the reflection coefficients in some relevant cases are shown. Besides, a finite element method is used as a benchmark for both the high and low frequency regimes. It is worth to be noted that the numerical test has been inspired by the problem of the interphase that is formed at the bone-implant boundary.     

Application of the transmission line matrix method for outdoor sound propagation modelling – Part 1: Model presentation and evaluation

The present paper deals with an original time-domain approach applied to outdoor sound propagation under meteorological effects. The transmission line matrix method, based on the Huygens’ principle, had already been validated over impedant grounds and complex topography. The presented formulation proposes to take into account meteorological effects (wind speed and temperature) through the relative sound speed. The necessary wavefront direction is determined through the calculation of the averaged intensity vector direction. A good agreement is found between simulations of both the transmission line matrix and parabolic equation methods. A relevant use of the method is shown in the framework of environmental acoustics and initial applications are proposed in Part 2.     

Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

We consider the infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm (mDGH2) system. The infinite propagation speed is derived for the corresponding solution with compactly supported initial data that does not have compact support any longer in its lifespan.     

Modeling the Effect of Injection Molding Process Parameters on Warpage Using Neural Network Theory

A back propagation artificial neural network (BPANN) prediction model for warpage of injection-molded polypropylene was developed based on an orthogonal design method. The BPANN model was trained by the input and output data obtained from the moldflow software platform simulations. It is proved that the BPANN model can predict the warpage with reasonable accuracy. Utilizing the BPANN model, the effects of the process parameters, packing pressure (Pp), melt temperature (T_me), mold temperature (T_mo), packing time (t_p), cooling time (t_c), and fill pressure (p_f), on the warpage were investigated. The most important process parameter affecting the warpage was Pp, and the second most important was T_me. The rest of the process parameters, T_mo, t_p, t_c, and p_f, were found to be relatively less influential. Warpage increased with elevating T_mo. In contrast, an increase in Pp and T_me caused the warpage to decrease.     

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.     

A novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.     

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.     

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.