A two-phase composite in simple shear: Effective mechanical anisotropy development and localization potential

We present a combined shape and mechanical anisotropy evolution model for a two-phase inclusion-bearing rock subject to large deformation. A single elliptical inclusion embedded in a homogeneous but anisotropic matrix is used to represent a simplified shape evolution enforced on all inclusions. The mechanical anisotropy develops due to the alignment of elongated inclusions. The effective anisotropy is quantified using the differential effective medium (DEM) approach. The model can be run for any deformation path and an arbitrary viscosity ratio between the inclusion and host phase. We focus on the case of simple shear and weak inclusions. The shape evolution of the representative inclusion is largely insensitive to the anisotropy development and to parameter variations in the studied range. An initial hardening stage is observed up to a shear strain of gamma = 1 irrespective of the inclusion fraction. The hardening is followed by a softening stage related to the developing anisotropy and its progressive rotation toward the shear direction. The traction needed to maintain a constant shear rate exhibits a fivefold drop at gamma = 5 in the limiting case of an inviscid inclusion. Numerical simulations show that our analytical model provides a good approximation to the actual evolution of a two-phase inclusion-host composite. However, the inclusions develop complex sigmoidal shapes resulting in the formation of an S-C fabric. We attribute the observed drop in the effective normal viscosity to this structural development. We study the localization potential in a rock column bearing varying fraction of inclusions. In the inviscid inclusion case, a strain jump from gamma = 3 to gamma = 100 is observed for a change of the inclusion fraction from 20% to 33%.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

Validity of the acoustic approximation in full-waveform seismic crosshole tomography

Acoustic waveform inversions are an increasingly popular tool for extracting subsurface information from seismic data. They are computationally much more efficient than elastic inversions. Naturally, an inherent disadvantage is that any elastic effects present in the recorded data are ignored in acoustic inversions. We investigate the extent to which elastic effects influence seismic crosshole data. Our numerical modeling studies reveal that in the presence of high contrast interfaces, at which P-to-S conversions occur, elastic effects can dominate the seismic sections, even for experiments involving pressure sources and pressure receivers. Comparisons of waveform inversion results using a purely acoustic algorithm on synthetic data that is either acoustic or elastic, show that subsurface models comprising small low-to-medium contrast (?30%) structures can be successfully resolved in the acoustic approximation. However, in the presence of extended high-contrast anomalous bodies, P-to-S-conversions may substantially degrade the quality of the tomographic images. In particular, extended low-velocity zones are difficult to image. Likewise, relatively small low-velocity features are unresolved, even when advanced a priori information is included. One option for mitigating elastic effects is data windowing, which suppresses later arriving seismic arrivals, such as shear waves. Our tests of this approach found it to be inappropriate because elastic effects are also included in earlier arriving wavetrains. Furthermore, data windowing removes later arriving P-wave phases that may provide critical constraints on the tomograms. Finally, we investigated the extent to which acoustic inversions of elastic data are useful for time-lapse analyses of high contrast engineered structures, for which accurate reconstruction of the subsurface structure is not as critical as imaging differential changes between sequential experiments. Based on a realistic scenario for monitoring a radioactive waste repository, we demonstrated that acoustic inversions of elastic data yield substantial distortions of the tomograms and also unreliable information on trends in the velocity changes.

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose.

On the approximation of the subgrid scale for systems of equations

Postprint (published version)

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

Laser-Ultraviolet-A induced ultra weak photon emission in human skin cells: A biophotonic comparison between keratinocytes and fibroblasts

Photons participate in many atomic and molecular interactions and processes. Recent biophysical research has discovered an ultraweak radiation in biological tissues. It is now recognized that plants, animal and human cells emit this very weak biophotonic emission which can be readily measured with a sensitive photomultiplier system. UVA laser induced biophotonic emission of cultured cells was used in this report with the intention to detect biophysical changes between young and adult fibroblasts as well as between fibroblasts and keratinocytes. With suspension densities ranging from 1-8x106 cells/ml, it was evident that an increase of the UVA-laser-light induced photon emission intensity could be observed in young as well as adult fibroblastic cells. By the use of this method to determine ultraweak light emission, photons in cell suspensions in low volumes (100 mu l) could be detected, in contrast to previous procedures using quantities up to 10 ml. Moreover, the analysis has been further refined by turning off the photomultiplier system electronically during irradiation leading to the first measurements of induced light emission in the cells after less than 10 mu s instead of more than 100 milliseconds. These significant changes lead to an improvement factor up to 106 in comparison to classical detection procedures. In addition, different skin cells as fibroblasts and keratinocytes stemining from the same donor were measured using this new highly sensitive method in order to find new biophysical insight of light pathways. This is important in view to develop new strategies in biophotonics especially for use in alternative therapies.

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation, which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one-dimensional diffusion. The validity of this approximation, based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.

A consistent extension of the local spin density approximation to account for quantum dot mass and dielectric mismatches

A consistent extension of local spin density approximation (LSDA) to account for mass and dielectric mismatches in nanocrystals is presented. The extension accounting for variable effective mass is exact. Illustrative comparisons with available configuration interaction calculations show that the approach is also very reliable when it comes to account for dielectric mismatches. The modified LSDA is as fast and computationally low demanding as LSDA. Therefore, it is a tool suitable to study large particle systems in inhomogeneous media without much effort.

Capturing Weak Signals for Foresight Building

Tulevaisuuden hahmottamisen merkitys heikkojen signaalien avulla on korostunut viime vuosien aikana merkittävästi,koska yrityksen liiketoimintaympäristössä tapahtuvia muutoksia on ollut yhä vaikeampaa ennustaa historian perusteella. Liiketoimintaympäristössä monien muutoksien merkkejä on ollut nähtävissä, mutta niitä on ollut vaikea havaita. Heikkoja signaaleja tunnistamalla ja keräämällä sekä reagoimalla tilanteeseen riittävän ajoissa, on mahdollista saavuttaa ylivoimaista kilpailuetua. Kirjallisuustutkimus keskittyy heikkojen signaalien tunnistamisen haasteisiin liiketoimintaympäristöstä, signaalien ja informaation kehittymiseen sekä informaation hallintaan organisaatiossa. Kiinnostus näihin perustuu tarpeeseen määritellä heikkojen signaalien tunnistamiseen vaadittava prosessi, jonka avulla heikot signaalit voidaan huomioida M-real Oyj:n päätöksenteossa. Kirjallisuustutkimus osoittaa selvästi sen, että heikkoja signaaleita on olemassa ja niitä pystytään tunnistamaan liiketoimintaympäristöstä. Signaaleja voidaan rikastuttaa yrityksessä olevalla tietämyksellä ja hyödyntää edelleen päätöksenteossa. Vertailtaessa sekä kirjallisuustutkimusta että empiiristä tutkimusta tuli ilmi selkeästi tiedon moninaisuus; määrä,laatu ja tiedonsaannin oikea-aikaisuus päätöksenteossa. Tutkimuksen aikana kehittyi prosessimalli tiedon suodattamiselle, luokittelulle ja heikkojen signaalien tunnistamiselle. Työn edetessä prosessimalli kehittyi osaksi tässä työssä kehitettyä kokonaisuutta 'Weak Signal Capturing' -työkalua. Monistamalla työkalua voidaan kerätä heikkoja signaaleja eri M-realin liiketoiminnan osa-alueilta. Tietoja systemaattisesti kokoamalla voidaan kartoittaa tulevaisuutta koko M-realille.

The Development of Weak Signal Concept

Tämän hetken trendit kuten globalisoituminen, ympäristömme turbulenttisuus, elintason nousu, turvallisuuden tarpeen kasvu ja teknologian kehitysnopeus korostavatmuutosten ennakoinnin tarpeellisuutta. Pysyäkseen kilpailukykyisenä yritysten tulee kerätä, analysoida ja hyödyntää liiketoimintatietoa, jokatukee niiden toimintaa viranomaisten, kilpailijoiden ja asiakkaiden toimenpiteiden ennakoinnissa. Innovoinnin ja uusien konseptien kehittäminen, kilpailijoiden toiminnan arviointi, asiakkaiden tarpeet muun muassa vaativatennakoivaa arviointia. Heikot signaalit ovat keskeisessä osassa organisaatioiden valmistautumisessa tulevaisuuden tapahtumiin. Opinnäytetyön tarkoitus on luoda ja kehittää heikkojen signaalien ymmärrystä ja hallintaa sekäkehittää konseptuaalinen ja käytännöllinen lähestymistapa ennakoivan toiminnan edistämiselle. Heikkojen signaalien tyyppien luokittelu perustuu ominaisuuksiin ajan, voimakkuuden ja liiketoimintaan integroinnin suhteen. Erityyppiset heikot signaalit piirteineen luovat reunaehdot laatutekijöiden keräämiselle ja siitä edelleen laatujärjestelmän ja matemaattiseen malliin perustuvan työvälineen kehittämiselle. Heikkojen signaalien laatutekijät on kerätty yhteen kaikista heikkojen signaalien konseptin alueista. Analysoidut ja kohdistetut laatumuuttujat antavat mahdollisuuden kehittää esianalyysiä ja ICT - työvälineitä perustuen matemaattisen mallin käyttöön. Opinnäytetyön tavoitteiden saavuttamiseksi tehtiin ensin Business Intelligence -kirjallisuustutkimus. Hiekkojen signaalien prosessi ja systeemi perustuvat koottuun Business Intelligence - systeemiin. Keskeisinä kehitysalueina tarkasteltiin liiketoiminnan integraatiota ja systemaattisen menetelmän kehitysaluetta. Heikkojen signaalien menetelmien ja määritelmien kerääminen sekä integrointi määriteltyyn prosessiin luovat uuden konseptin perustan, johon tyypitys ja laatutekijät kytkeytyvät. Käytännöllisen toiminnan tarkastelun ja käyttöönoton mahdollistamiseksi toteutettiin Business Intelligence markkinatutkimus (n=156) sekä yhteenveto muihin saatavilla oleviin markkinatutkimuksiin. Syvähaastatteluilla (n=21) varmennettiin laadullisen tarkastelun oikeellisuus. Lisäksi analysoitiin neljä käytännön projektia, joiden yhteenvedot kytkettiin uuden konseptin kehittämiseen. Prosessi voidaan jakaa kahteen luokkaan: yritysten markkinasignaalit vuoden ennakoinnilla ja julkisen sektorin verkostoprojektit kehittäen ennakoinnin struktuurin luonnin 7-15 vuoden ennakoivalle toiminnalle. Tutkimus rajattiin koskemaan pääasiassa ulkoisen tiedon aluetta. IT työvälineet ja lopullisen laatusysteemin kehittäminen jätettiin tutkimuksen ulkopuolelle. Opinnäytetyön tavoitteena ollut heikkojen signaalien konseptin kehittäminen toteutti sille asetetut odotusarvot. Heikkojen signaalien systemaattista tarkastelua ja kehittämistyötä on mahdollista edistää Business Intelligence - systematiikan hyödyntämisellä. Business Intelligence - systematiikkaa käytetään isojen yritysten liiketoiminnan suunnittelun tukena.Organisaatioiden toiminnassa ei ole kuitenkaan yleisesti hyödynnetty laadulliseen analyysiin tukeutuvaa ennakoinnin weak signals - toimintaa. Ulkoisenja sisäisen tiedon integroinnin ja systematiikan hyödyt PK -yritysten tukena vaativat merkittävää panostusta julkishallinnon rahoituksen ja kehitystoiminnan tukimuotoina. Ennakointi onkin tuottanut lukuisia julkishallinnon raportteja, mutta ei käytännön toteutuksia. Toisaalta analysoitujen case-tapausten tuloksena voidaan nähdä, ettei organisaatioissa välttämättä tarvita omaa projektipäällikköä liiketoiminnan tuen kehittämiseksi. Business vastuun ottamiseksi ja asiaan sitoutumiseen on kuitenkin löydyttävä oikea henkilö

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.