On Internal Fracture of Solids

Initiation and propagation of internal fracture in solid

On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

"This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random power series around the regular¿singular point 1. A theorem on the existence and uniqueness of Lp(omega) solution to the random Legendre differential equation on the intervals (-1,1) and (1,3) is obtained. The hypotheses assumed are simple: initial conditions in Lp(omega) and random input A in L infinite(omega) (this is equivalent to A having absolute moments that grow at most exponentially). Thus, this paper extends the deterministic theory to a random framework. Uncertainty quantification for the solution stochastic process is performed by truncating the random series and taking limits in Lp(omega). In the numerical experiments, we approximate its expectation and variance for certain forms of the differential equation. The reliability of our approach is compared with Monte Carlo simulations and generalized polynomial chaos expansions.Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de ValènciaCalatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045S11214Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Wong, E., & Hajek, B. (1985). Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. doi:10.1007/978-1-4612-5060-9Nouri, K., & Ranjbar, H. (2014). Mean Square Convergence of the Numerical Solution of Random Differential Equations. Mediterranean Journal of Mathematics, 12(3), 1123-1140. doi:10.1007/s00009-014-0452-8Lupulescu, V., O’Regan, D., & ur Rahman, G. (2014). Existence results for random fractional differential equations. Opuscula Mathematica, 34(4), 813. doi:10.7494/opmath.2014.34.4.813Villafuerte, L., & Chen-Charpentier, B. M. (2012). A random differential transform method: Theory and applications. Applied Mathematics Letters, 25(10), 1490-1494. doi:10.1016/j.aml.2011.12.033Licea, J. A., Villafuerte, L., & Chen-Charpentier, B. M. (2013). Analytic and numerical solutions of a Riccati differential equation with random coefficients. Journal of Computational and Applied Mathematics, 239, 208-219. doi:10.1016/j.cam.2012.09.040Lang, S. (1997). Undergraduate Analysis. Undergraduate Texts in Mathematics. doi:10.1007/978-1-4757-2698-5Cortés, J.-C., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., & Villanueva, R.-J. (2013). Solving Continuous Models with Dependent Uncertainty: A Computational Approach. Abstract and Applied Analysis, 2013, 1-10. doi:10.1155/2013/983839Calatayud, J., Cortés, J. C., Jornet, M., & Villanueva, R. J. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences, 41(18), 9618-9627. doi:10.1002/mma.531

The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems

We study the influence of a DC bias voltage V on quantum interference corrections to the measured differential conductance in metallic mesoscopic wires and rings. The amplitude of both universal conductance fluctuations (UCF) and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger than the Thouless energy. The enhancement persists even in the presence of inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages electron-phonon collisions lead to the amplitude decaying as a power law for the UCF and exponentially for the ABE. We obtain good agreement of the experimental data with a model which takes into account the decrease of the electron phase-coherence length due to electron-electron and electron-phonon scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in Europhysics Letter

Analysis of a segmented brushless PM machine utilising soft magnetic composites

© Copyright 2007 IEEESoft magnetic composites (SMC) is a magnetic material which offers the potential for innovative machine geometries and lower cost manufacturing. This paper examines the finite-element analysis and performance prediction of a segmented brushless permanent magnet machine based on SMC. Experimental results including the back-EMF waveform, iron loss and performance characteristics are used to validate the simulation results

Random Hermite differential equations: Mean square power series solutions and statistical properties

This paper deals with the construction of random power series solution of second order linear differential equations of Hermite containing uncertainty through its coefficients and initial conditions. Under appropriate hypotheses on the data, we establish that the constructed random power series solution is mean square convergent. We provide conditions in order to obtain random polynomial solutions and, as a consequence, random Hermite polynomial are introduced. Also, the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given. Finally, we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including Monte Carlo simulation. © 2011 Elsevier Inc. All rights reserved.This work has been partially supported by the Spanish M.C.Y.T. and FEDER grants MTM2009-08587, DPI2010-20891-C02-01 as well as the Universitat Politecnica de Valencia grant PAID-06-09 (Ref. 2588).Calbo Sanjuán, G.; Cortés López, JC.; Jódar Sánchez, LA. (2011). Random Hermite differential equations: Mean square power series solutions and statistical properties. Applied Mathematics and Computation. 218(7):3654-3666. https://doi.org/10.1016/j.amc.2011.09.008S36543666218

Bank erosion survey of the main stem of the Kankakee River in Illinois and Indiana

"Contract report 2001-01"--Cover."March 2001.""Conservation 2000 Ecosystem Project.""Prepared for the Illinois Department of Natural Resources.""Contributors: David T.W. Soong, Erin Bauer, William C. Bogner, and Jim Slowikowski.

Macroscopic transport by synthetic molecular machines

Nature uses molecular motors and machines in virtually every significant biological process, but demonstrating that simpler artificial structures operating through the same gross mechanisms can be interfaced with—and perform physical tasks in—the macroscopic world represents a significant hurdle for molecular nanotechnology. Here we describe a wholly synthetic molecular system that converts an external energy source (light) into biased brownian motion to transport a macroscopic cargo and do measurable work. The millimetre-scale directional transport of a liquid on a surface is achieved by using the biased brownian motion of stimuli-responsive rotaxanes (‘molecular shuttles’) to expose or conceal fluoroalkane residues and thereby modify surface tension. The collective operation of a monolayer of the molecular shuttles is sufficient to power the movement of a microlitre droplet of diiodomethane up a twelve-degree incline.

A matched study of surgically treated stage IB adenosquamous carcinoma and adenocarcinoma of the uterine cervix

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72055/1/j.1525-1438.1993.03040245.x.pd

Measurement of the Transverse-Longitudinal Cross Sections in the p (e,e'p)pi0 Reaction in the Delta Region

Accurate measurements of the p(e,e?p)pi0 reaction were performed at Q^2=0.127(GeV/c)^2 in the Delta resonance energy region. The experiments at the MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam with the out of plane magnetic spectrometer system (OOPS). In this paper we report the first simultaneous determination of both the TL and TL? (``fifth" or polarized) cross sections at low Q^{2} where the pion cloud contribution dominates the quadrupole amplitudes (E2 and C2). The real and imaginary parts of the transverse-longitudinal cross section provide both a sensitive determination of the Coulomb quadrupole amplitude and a test of reaction calculations. Comparisons with model calculations are presented. The empirical MAID calculation gives the best overall agreement with this accurate data. The parameters of this model for the values of the resonant multipoles are |M_{1+}(I=3/2)|= (40.9 \pm 0.3)10^{-3}/m_pi, CMR= C2/M1= -6.5 \pm 0.3%, EMR=E2/M1=-2.2 \pm 0.9%, where the errors are due to the experimental uncertainties.Comment: 10 pages, 3 figures, minor corrections and addition