Finite Slope Research Articles

Transfer of Multivariate Calibrations between Four Near-Infrared Spectrometers Using Orthogonal Signal Correction

The transfer of partial least squares (PLS) calibration models among four near-infrared spectrometers was investigated for the quantitative analysis of thermoset resin polymers. A comparative study of second derivatives, multiplicative scatter correction, finite impulse response filtering, slope and bias correction, model updating (MU), and orthogonal signal correction (OSC) was conducted to determine which processing methods achieved model transferability. It is shown that OSC and MU were superior to the other calibration transfer methods, leading to very robust PLS models with enhanced predictive ability. It is also shown that the transfer results obtained with OSC were not significantly different from those obtained with model updating.

Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation

According to the Bagnold hypothesis for equilibrium bed load transport, a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical, or threshold, value associated with incipient motion of grains. It was shown in a companion paper [Seminara et al., 2002], however, that the Bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose. An investigation of this failure resulted in a demonstration of its lack of validity even for nearly horizontal beds. The constraint is here replaced with an entrainment formulation, according to which a dynamic equilibrium is maintained by a balance between entrainment of bed grains into the bed load layer and deposition of bed load grains onto the bed. The entrainment function is formulated so that the entrainment rate is an increasing function of the excess of the fluid shear stress at the bed over the threshold value. The formulation is implemented with the aid of a unique set of laboratory data that characterizes equilibrium bed load transport at relatively low shear stresses for streamwise angles of bed inclination varying from nearly 0° to 22°. The formulation is shown to provide a description of bed load transport on nearly horizontal beds that fits the data as well as that resulting from the Bagnold constraint. The entrainment formulation has the added advantage of not requiring the unrealistically high dynamic coefficient of Coulomb friction resulting from the Bagnold constraint. Finally, the entrainment formulation provides reasonable and consistent results on finite streamwise and transverse bed slopes, even those at which the Bagnold formulation breaks down completely.

Irregular elastic half-plane gravity problem

Abstract The analytic solution for stresses in an elastic half-plane with an irregular boundary under gravity is derived in this study. The geometry is treated using a mapping function rationalized from the Schwarz–Christoffel transformation and the complex variable method along with the Cauchy integral is used in the derivation. Both Cauchy and logarithmic types of singular integrals, as well as ordinary integrals are evaluated. The body force potential is determined using a restraint condition on horizontal stress at the surface at infinity. The stress functions are decomposed into two parts: a non-holomorphic and a holomorphic one, and are obtained in closed form. Half-planes with finite slopes and steps are considered. Stress concentrations at the toes of slopes of different angles, stress distributions, directions and magnitudes of principal stresses and the Drucker–Prager stress under various internal frictional angles are shown and variation of stresses caused by excavation for slope angles of 30° and 60° is investigated.

Oscillatory Flows over a Permeable Wavy Boundary

ABSTRACTIn this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.

Overconvergent modular forms and the Fontaine-Mazur conjecture

We prove a conjecture of Fontaine and Mazur on modularity of representations of G ℚ which are potentially semi-stable at p, for representations coming from finite slope, overconvergent eigenforms. We also give an application of our technique to a question of Gouvea on overconvergence of certain modular forms. If ρ is a suitable representation of G ℚ,S on a two dimensional vector space over a finite field product of 𝔾 m and the S a finite set of primes – we construct a rigid analytic subspace of the universal deformation space of ρ, which is defined by a purely representation theoretic condition, and contains the eigencurve of Coleman-Mazur. Conjecturally, it is equal to this curve.

Capillary condensation in a disordered mesoporous medium: a grand canonical Monte Carlo study

The adsorption of rare gases in a disordered mesoporous silica glass has been studied by means of grand canonical Monte Carlo (GCMC) simulation. A series of porous samples has been obtained by using an off-lattice 3D reconstruction method recently introduced to reproduce topological and morphological properties of correlated disordered porous materials such as Vycor. The off-lattice functional of 115m2g−1 Vycor is applied to a simulation box containing silicon and oxygen atoms of cubic cristoballite with a homothetic reduction in order to obtain porous samples with mean pore size around 35 Å and specific surface around 220 m2 g−1. A realistic surface chemistry is then obtained by saturating all the dangling oxygen bonds with hydrogen. Some topological properties of the different 3D reconstructions of the Vycor-like material are analysed using chord length distributions and small angle scattering data. The GCMC Ar, Kr and Xe adsorption/desorption isotherms are calculated at different temperatures. At sufficiently low temperatures, they exhibit a capillary condensation transition with an adsorption branch having a finite slope accompanied by a hysteresis loop upon desorption. It has been shown on a set of simulated argon isotherms, that evolution with temperature of the GCMC results is similar to experiment. At the temperature at which the hysteresis loop disappears, it was found that the compressibility of the dense liquid-like phase at the maximum of the so-called hysteretic coexistence curves increases significantly. In the low pressure and temperature domain, different adsorption scenarios can be interpreted on the basis of a Zisman-type of criterion for wetting. The BET surface area is shown to be strongly related to this criterion. At higher pressure, it was found that the pore size distribution obtained by using the standard BJH analysis applied to both simulated adsorption and desorption data qualitatively reproduces the main features of the chord length distribution.

Evolutionary speed of species invasions.

Successful invasion may depend of the capacity of a species to adjust genetically to a spatially varying environment. This research modeled a species invasion by examining the interaction between a quantitative genetic trait and population density. It assumed: (I) a quantitative genetic trait describes the adaptation of an individual to its local ecological conditions; (2) populations far from the local optimum grow more slowly than those near the optimum; and (3) the evolution of a trait depends on local population density, because differences in local population densities cause asymmetrical gene flow. This genetics-density interaction determined the propagation speed of populations. Numerical simulations showed that populations spread by advancing as two synchronic traveling waves, one for population density and one for trait adaptation. The form of the density wave was a step front that advances homogenizing populations at their carrying capacity; the adaptation wave was a curve with finite slope that homogenizes populations at full adaptation. The largest speed of population expansion, for a dimensionless analysis, corresponded to an almost homogeneous spatial environment when this model approached an ecological description such as the Fisher-Skellam's model. A large genetic response also favored faster speeds. Evolutionary speeds, in a natural scale, showed a wide range of rates that were also slower compared to models that only consider demographics. This evolutionary speed increased with high heritability, strong stabilizing selection, and high intrinsic growth rate. It decreased for steeper environmental gradients. Also indicated was an optimal dispersal rate over which evolutionary speed declined. This is expected because dispersal moves individuals further, but homogenizes populations genetically, making them maladapted. The evolutionary speed was compared to observed data. Furthermore, a moderate increase in the speed of expansion was predicted for ecological changes related to global warming.

Linear temperature dependence of lower critical field inMgB2

The lower critical field $H_{c1}$ has been carefully measured on a well shaped cylindrical sample of the new superconductor $MgB_2$ fabricated by high pressure synthesis. The penetration depth $\lambda$ is calculated from the $H_{c1}$ data. It is found that a linear relation of $H_{c1}(T)$ appears in whole temperature region below $T_c$. Furthermore a finite slope of $dH_{c1}/dT$ and $d\lambda(T)/dT$ remains down to the lowest temperature (2 K). These are inconsistent with the expectation for a widely thought s-wave superconductivity in $MgB_2$.

Critical fields and specific heat ofLuNi2B2C

We have measured the upper critical magnetic field, lower critical magnetic field, and low-temperature specific heat of ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ Our upper critical-field measurements above $\ensuremath{\sim}2\mathrm{K}$ are consistent with earlier measurements by other groups. The upper critical field exhibits a finite slope as $\stackrel{\ensuremath{\rightarrow}}{T}0,$ and we discuss possible origins of this very unusual behavior. We observe a linear temperature dependence for the lower critical field of our single-crystal sample, a temperature dependence that disagrees with earlier measurements on polycrystals and suggests that the lower critical field may be anisotropic. The Sommerfeld coefficient increases with magnetic field as ${H}^{\ensuremath{\epsilon}}$ with $\ensuremath{\epsilon}=0.63\ifmmode\pm\else\textpm\fi{}0.12$ in qualitative agreement with earlier work. The temperature dependence of the zero-field electronic specific heat is exponential well below ${T}_{c}.$ We discuss our results in light of recent proposals of both anisotropic s-wave and d-wave superconductivity for ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ Our data seem most consistent with strong-coupling superconductivity and a weakly anisotropic s-wave energy gap.

A Grand Canonical Monte Carlo study of argon adsorption/condensation in mesoporous silica glasses

We have studied adsorption of argon in a mesoporous silica controlled porous glass (CPG) over a wide range of temperatures by means of Grand Canonical Monte Carlo (GCMC) simulation. A numerical sample of the CPG adsorbent has been obtained by using an off-lattice reconstruction method recently introduced to reproduce topological and morphological properties of correlated disordered porous materials. The off-lattice functional of Vycor is applied to a simulation box containing silicon and oxygen atoms of cubic cristoballite with a homothetic reduction factor of 2.5 so as to obtain 36 Å CPG samples. The Ar adsorption/desorption isotherms are calculated at 77, 87, 100, 120 and 130 K. They exhibit a hysteresis loop characteristic of the capillary condensation phenomenon. As often encountered in gas adsorption experiments with this type of porous solid, the adsorption branch is characterized by a finite slope, in contrast to that theoretically obtained in simple geometries such as slits and cylinders. As the temperature increases, the hysteresis loop is displaced toward the higher (reduced) pressure range and shrinks in agreement with experiment; the temperature, Tcc, for which the isotherm is fully reversible is 132.7 K. This behavior is similar to that found for slit-shaped or cylindrical pores for which the capillary condensation/evaporation transition is found to be first order. We have shown that the hysteretic coexistence curve obtained from desorption data is characteristic of disordered systems with energetic heterogeneity. In the system of reduced units (ρcc and Tcc, where ρcc is the confined fluid density at Tcc), we have also found that the hysteretic coexistence curves close to Tcc for polar and non-polar fluids in silica ordered and disordered mesoporous sytems of the same mean pore size, fall on a single master curve.

Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model

In this work, we introduce a restricted ballistic deposition model with symmetric growth rules that favors the formation of local finite slopes. It is the simplest model which, even without including a diffusive relaxation mode of the interface, leads to a macroscopic groove instability. By employing a finite-size scaling of numerical simulation data, we determine the scaling behavior of the surface structure grown over a one-dimensional substrate of linear size L. We found that the surface profile develops a macroscopic groove with the asymptotic surface width scaling as , with . The early-time dynamics is governed by the scaling law , with . We further investigate the sensitivity to initial conditions of the present model by applying damage spreading techniques. We find that the early-time distance between two initially close surface configurations grows in a ballistic fashion as , but a slower Brownian-like scaling ( ) sets up for evolution times much larger than a characteristic time scale .

Reliability analysis of slopes using fuzzy sets theory

Abstract The stability assessment of slopes is difficult because of many uncertainties. Possibilistic approach using fuzzy sets allows for a logical and systematic analysis of the uncertainties. In this paper an attempt has been made to present a new approach for the stability analysis of slopes incorporating fuzzy uncertainty. Uncertain parameters are expressed as fuzzy sets. A methodology has been presented in the study to process the fuzzy uncertainties in a slope reliability analysis. Fuzzy uncertainty is incorporated in the estimated probability of failure. A numerical example of the finite earth slope problem illustrates the methodology. The approach allows assessment of the likelihood that a particular slope section will have a higher failure probability than the failure probability of the ‘critical’ deterministic failure surface.

Numerical Modelling Of Turbulent Airflow Over Water Waves

A nonlinear numerical model is developed for turbulent boundary-layer flowover a train of water waves of finite amplitude or slope. The airflow isassumed to be steady, two-dimensional, and neutrally-stratified. The wavesurface is assumed to be aerodynamically rough and flow conditions at thewave surface are prescribed. The numerical model used in this study adoptsthree turbulence closure schemes with different degrees of physicalcompleteness. Two of these are second-order schemes, whichare believed to describe turbulent flow more completely than thesimpler closures used in most previous studies. Although models with all turbulence closures agree qualitatively in the prediction of the amplitude of the surface normal stress perturbation, the lower- and higher-order closures differ significantly in predictions of phase, and hence the form drag and energy transfer rate between wind and waves. Our model results are in reasonable agreement with field and laboratory measurements, although predicted energy transfer rates are generally at the low end of the range of experimental values. Cases with airflow at various angles to the wave direction are also considered.

The energetics of surface-alloy formation: an embedded-atom-method,second-order-expansion study

Chemical ordering and clustering instabilities in alloys are governed by theFourier transform of the effective pair interactions, V(k). We make useof a second-order-expansion formalism, based upon embedded-atom-methodinteratomic potentials, to calculate chemical and elastic contributions toV(k) for monolayer surface alloys on single-crystal substrates. It isdemonstrated that the elastic contribution to V(k) is characterized bya finite slope at the origin, consistent with continuum models which predictthat V(k)∝-|k| for small wavevectors. As a consequence,the global minimum in V(k) always occurs at finite k, andtherefore compositional instabilities in ultrathin surface-alloy films aregenerally of an ordering (as opposed to clustering, k = 0) type.

Sediment-discharge vector in a turbulent flow above an eroded bottom

The problem of determination of sediment discharge by a turbulent flow of a fluid above an eroded surface of an arbitrary relief with a finite slope of the bottom is considered. The surface of the bottom separates a stationary granular medium (sand) from a moving two-phase mixture of a fluid and solid particles. The medium is set into motion under the action of shear stress of the fluid. The medium obeys Coulomb's friction law for a granular medium and Prandtl's law of turbulent friction of the fluid. As a result of solving the boundary-value problem for the motion of a two-phase mixture of a fluid and solid particles, a generic formula for sediment discharges is derived. The sediment-discharge vector is expressed through the vector of shear stress on the bottom, the vector of the slope of the bottom, and the distribution function of the solid particles in the bottom layer for an arbitrary relief of the bottom with a finite slope. It is shown that the sediment discharge depends weakly on the detailed distribution of particles in the bottom layer. Conditions of failure of the bottom surface are obtained. The sediment-discharge formula allows one to derive a closed system of equations that determines the process of bottom erosion in the river or channel bed.

A Grand Canonical Monte-Carlo Study of Argon Adsorption/Condensation in Mesoporous Silica Glasses: Application to the Characterization of Porous Materials

AbstractWe have studied adsorption of argon in a mesoporous silica Controlled Porous Glass (CPG) means of Grand Canonical Monte-Carlo (GCMC) simulation. A numerical sample of the CPG adsorbent has been obtained by using an off-lattice reconstruction method recently introduced to reproduce topological and morphological properties of correlated disordered porous materials. The off-lattice functional of (100 m2/g)-Vycor is applied to a simulation box containing silicon and oxygen atoms of cubic cristoballite with an homothetic reduction of factor 2.5 so to obtain 30Å-CPG sample. A realistic surface chemistry is then obtained by saturating all oxygen dangling bonds with hydrogen. The Ar, Kr and Xe adsorption/desorption isotherms are calculated at different temperatures. At sufficiently low temperature, they exhibit a capillary condensation transition with a finite slope by contrast to that theoretically predicted for simple pore geometriessuch as slits and cylinders. In the low pressure and temperature domain, we have identified different adsorption scenarios, which can be interpreted on the basis of a Zisman-type of criterium for wetting. We demonstrate that the BET surface area is strongly related to this criterion. At higher pressure, we demonstrate that the pore size distribution obtained by using the standard BJH analysis applied to both adsorption and desorption data qualitatively reproduces the main features of the chord length distribution.

Thermal Oxidation of Si Nanoparticles Grown by Plasma-Enhanced CVD

ABSTRACTNanoparticles of amorphous silicon were grown by plasma-enhanced CVD. Their high hydrogen content has a great influence on the oxidation kinetics. Oxidation experiments done in a thermo-balance show that during a heating ramp under oxygen the onset of oxidation shifts to higher temperatures when hydrogen content is reduced by annealing. Apparently this higher oxidation rate of the as-grown particles is due to the great density of dangling bonds that are left behind just after the hydrogen is desorpted. This fact is supported by analyzing the oxidation dynamics under isothermal conditions. At lower temperature, when oxidation takes place just after hydrogen desorption, the oxidation transient begins with a finite slope which indicates that oxidation is not diffusion controlled. On the other hand, at higher temperatures, activation energy of the parabolic rate constant indicates that the oxide layer formed is less protective than the oxide layer formed on crystalline silicon.

Propagation of Obliquely Incident Tsunamis on a Slope Part I: Amplification of Tsunamis on a Continental Slope

A new analytical solution of tsunami which is obliquely incident on a continental slope is derived based on the linear shallow water wave theory. The model of a continental slope consists of a finite constant slope and a bottom of uniform depth and has a vertical wall at the shoreline. Because of the existence of the vertical wall, another function can be taken as one of the fundamental solutions on a slope in addition to the confluent hypergeometric function M. Based on the solution obtained, the characteristics of tsunami amplification on a continental slope are discussed in terms of the conditions of the incidence. The magnitude of the amplification can be predicted with several parameters of wave incidence, such as, the incident angle and the relative incident-wave length to the topography. Especially, when a tsunami is incident almost parallel to the slope, we found that there exists distinctive amplifications for particular parameters characterizing the incident wave. The effect of the existence of the vertical wall is also discussed. The characteristics of amplification also depend much on the position of the vertical wall.

Slope stability analysis by finite elements

The majority of slope stability analyses performed in practice still use traditional limit equilibrium approaches involving methods of slices that have remained essentially unchanged for decades. This was not the outcome envisaged when Whitman & Bailey (1967) set criteria for the then emerging methods to become readily accessible to all engineers. The finite element method represents a powerful alternative approach for slope stability analysis which is accurate, versatile and requires fewer a priori assumptions, especially, regarding the failure mechanism. Slope failure in the finite element model occurs 'naturally' through the zones in which the shear strength of the soil is insufficient to resist the shear stresses. The paper describes several examples of finite element slope stability analysis with comparison against other solution methods, including the influence of a free surface on slope and dam stability. Graphical output is included to illustrate deformations and mechanisms of failure. It is argued that the finite element method of slope stability analysis is a more powerful alternative to traditional limit equilibrium methods and its widespread use should now be standard in geotechnical practice. En grande majorité, les analyses de stabilité de pente menées dans la pratique continuent à utiliser les méthodes traditionnelles d'équilibre limite et des systèmes de tranches qui n'ont pratiquement pas changé depuis des dizaines d'années. Ce n'était pas le résultat envisagé quand Whitman et Bailey (1967) ont établi des critères pour que ces méthodes alors émergeantes puissent devenir facilement accessibles à tous les ingénieurs. La méthode d'éléments finis qui représente une alternative puissante pour les analyses de stabilité de pente, est exacte, polyvalente et demande moins d'hypothèses ‘a priori’, surtout en ce qui concerne les mécanismes de rupture. La rupture de pente dans le modèle à éléments finis se produit ‘naturellement’ à travers des zones dans lesquelles la résistance au cisaillement du sol est insuffisante pour résister aux contraintes tangentielles. Cet exposé décrit plusieurs exemples d'analyses de stabilité de pente utilisant les éléments finis et établit des comparaisons avec d'autres méthodes, comme l'influence d'une surface libre sur la stabilité d'une pente et d'une digue. Nous joignons une représentation graphique pour illustrer les déformations et mécanismes de rupture. Nous avançons que la méthode d'éléments finis pour analyser la stabilité des pentes constitue une alternative plus puissante aux méthodes traditionnelles d'équilibre limite et que son utilisation devrait maintenant devenir une pratique standard en géotechnique.

Resonant scattering of edge waves by longshore periodic topography: finite beach slope

The resonant scattering of low-mode progressive edge waves by small-amplitude longshore periodic depth perturbations superposed on a plane beach has recently been investigated using the shallow water equations (Chen & Guza 1998). Coupled evolution equations describing the variations of edge wave amplitudes over a finite-size patch of undulating bathymetry were developed. Here similar evolution equations are derived using the full linear equations, removing the shallow water restriction of small (2N + 1)θ, where N is the maximum mode number considered and θ is the unperturbed planar beach slope angle. The present results confirm the shallow water solutions for vanishingly small (2N + 1)θ and allow simple corrections to the shallow water results for small but finite (2N + 1)θ. Additionally, multi-wave scattering cases occurring only when (2N + 1)θ = O(1) are identified, and detailed descriptions are given for the case involving modes 0, 1, and 2 that occurs only on a steep beach with θ = π/12.