Finite Slices Research Articles

On Finite Domains Based Slices in the Structure of Superintuitionistic Predicate Logics, Preview

The article presents a series of closely related papers that together make up a single piece of work, devoted to the description of a hierarchy of slices in the structure of superintuitionistic predicate logics and making probably the first attempt to transfer to the predicate case Hosoi's hierarchy of (finite) slices for the structure of superintuitionistic propositional logics.

Fluid retention on miscible viscous fingering of finite slices in porous media with dead-end pores

One of the key factors for low efficiency in miscible displacements is viscous fingering (VF), a hydrodynamic instability when a less-viscous fluid displaces a more-viscous one. While leading to large unswept areas by VF, it is widely believed that in swept areas the displaced fluid is 100% cleaned up. This is however not true considering the fluid retention caused by non-negligible dead-end pores in porous media. Here, we investigate by highly accurate numerical simulation the effects of fluid retention on VF of a finite slice. We employ a dead-end pore model that is different from the classical convection–diffusion equation. We find porous medium first acts as a sink and then a source of displaced fluids in newly swept areas, which substantially affects VF dynamics and leads to much more uncleaned displaced fluids in swept areas. Our research provides new insights into the roles of porous media in VF research community.

Dynamic Bayesian Network for Predicting Tunnel-Collapse Risk in the Case of Incomplete Data

Collapse is one of the most dangerous aspects of drilling–blasting construction in highway tunnels. To accurately control tunnel-collapse risk, a multistate dynamic Bayesian network (DBN) evaluation method for highway tunnel collapse based on parameter learning was proposed. First, by analyzing the risk mechanism of tunnel construction, the initial BN model was established based on the causal relationship between risk factors and construction risk in hydrogeological conditions, construction technology, and construction management. Next, the construction process was discretized into finite time slices. In consideration of the fuzzy uncertainty of nodes, node polymorphism was introduced to construct a multistate DBN. Then, 50 typical tunnel-collapse cases were taken as sample data, and the conditional probability distribution of initial BN was derived using parameter learning based on the expectation-maximization (EM) algorithm. Using DBN reasoning and sensitivity analysis, the dynamic risk probability and the dominant factors of tunnel collapse were predicted. Finally, the DBN model was fed back with the measured cumulative values and velocity of the crown settlement, which updated the dynamic risk probability assessment results. In analyzing the collapse probability of Jinzhupa tunnel passing through the angular unconformity contact zone as an example, the results demonstrated that dynamic risk assessment results combined with monitoring data could better reflect the reality of construction contingencies, providing real-time risk management guidance.

Analysis of layered rectangular plates under thermo-mechanical loads considering temperature-dependent material properties

The analytical solutions are presented for the distributions of temperature, displacements, and stresses in simply-supported layered rectangular plates under thermo-mechanical loads. The material properties of every layer are temperature-dependent. A slice model is presented for discretization: dividing every layer into finite thin slices, the material properties within each slice are assumed to be uniform. The temperature varies along the thickness and follows the one-dimensional (1-D) heat conduction equations. An iterative algorithm is proposed for the prediction of the 1-D temperature field. Then, the exact three-dimensional (3-D) thermoelasticity theory and the transfer matrix technique are applied for the prediction of the displacement and stress fields in the plate. The influences of temperature can be divided into two parts: producing thermal deformations and thermal stresses and affecting the deformations and stresses induced by mechanical loads. Finally, the influences of the surface temperature and the layer thickness ratio on the thermo-mechanical responses of a sandwich plate are studied in detail.

Assessment of natural frequency of installed offshore wind turbines using nonlinear finite element model considering soil-monopile interaction

A nonlinear finite element model is developed to examine the lateral behaviors of monopiles, which support offshore wind turbines (OWTs) chosen from five different offshore wind farms in Europe. The simulation is using this model to accurately estimate the natural frequency of these slender structures, as a function of the interaction of the foundations with the subsoil. After a brief introduction to the wind power energy as a reliable alternative in comparison to fossil fuel, the paper focuses on concept of natural frequency as a primary indicator in designing the foundations of OWTs. Then the range of natural frequencies is provided for a safe design purpose. Next, an analytical expression of an OWT natural frequency is presented as a function of soil-monopile interaction through monopile head springs characterized by lateral stiffness KL, rotational stiffness KR and cross-coupling stiffness KLR, of which the differences are discussed. The nonlinear pseudo three-dimensional finite element vertical slices model has been used to analyze the lateral behaviors of monopiles supporting the OWTs of different wind farm sites considered. Through the monopiles head movements (displacements and rotations), the values of KL, KR and KLR were obtained and substituted in the analytical expression of natural frequency for comparison. The comparison results between computed and measured natural frequencies showed an excellent agreement for most cases. This confirms the convenience of the finite element model used for the accurate estimation of the monopile head stiffness.

Mathematical Modeling of Thickness Dependent Physical Aging in Polymeric Membranes

The drawback of membrane process that reduces its competitive edge with the conventional separation technologies is ascribed to its decline separative performance over time due to the aging nature of polymeric material. The most widely accepted mechanism that has been thought of governing the volume relaxation process over the course of aging is the dual mode mechanism, whereby it is comprised of two components. The first is the “Lattice contraction” mechanism that describes the uniform collapse of free volume throughout the unrelaxed polymer matrix. The second is the “Diffusion of free volume” mechanism from the interior to the surface of the glassy polymer. Albeit acknowledgement of the dual mode mechanism as the contributing factor, previous aging model renders high implementation challenges to characterize the complicated nature of aging evolution, which requires adaptation of high end computational tools to solve the relatively complex differential equations. In this work, the dual mode mechanism governing the physical aging process has been modelled employing a simple one dimensional finite element numerical solution whereby the film has been divided into many finite slices with equal thickness along the depth of the membrane. The applicability of the mathematical model has been validated with experimental aging data, whereby a small deviation is observed between the two over a wide range of film thicknesses and reasonable intuitive explanation pertaining to the parameters is obtained.

Viscosity scaling of fingering instability in finite slices with Korteweg stress

We perform linear stability analyses and direct numerical simulations to investigate the influence of the dynamic viscosity on viscous fingering instability in miscible slices. Selecting the characteristic scales appropriately, the importance of the magnitude of the dynamic viscosity of individual fluids on viscous fingering in miscible slice has been shown in the context of the transient interfacial tension. Further, we have confirmed this result for immiscible fluids and shown the similarities between viscous fingering in immiscible and miscible slices with transient interfacial tension. In a more general setting, the findings of this letter will be very useful for different viscous flows, such as displacement of a buoyant miscible layers in a vertical Hele-Shaw cell, viscous fingering instability with viscosity-dependent dispersion, etc.

Effect of Korteweg stress on viscous fingering of solute plugs in a porous medium

In this work we first present a unified framework for the analysis of miscible and immiscible viscous fingering. To establish this we introduce the Korteweg stresses for miscible fluids which arise due to concentration gradients and are analogous to surface tension between two immiscible fluids. For the immiscible fingering we use the continuum representation of surface tension which treats surface tension as a body force. This analogy between the two types of fingering helps us obtain a better insight into the role of Korteweg stresses in miscible fluids and enables in resolving ambiguities in the role of these stresses in a dynamic system. Finally we examine the effect of Korteweg stresses to see how they can be a stabilizing influence for miscible viscous fingering of finite slices in a chromatography column and discuss if this can give an extra control option to improve the performance of the separation.

Influence of miscible viscous fingering of finite slices on an adsorbed solute dynamics

Viscous fingering (VF) between miscible fluids of different viscosities can affect the dispersion of finite width samples in porous media. We investigate here the influence of such VF due to a difference between the viscosity of the displacing fluid and that of the sample solvent on the spatiotemporal dynamics of the concentration of a passive solute initially dissolved in the injected sample and undergoing adsorption on the porous matrix. Such a three component system is modeled using Darcy’s law for the fluid velocity coupled to mass-balance equations for the sample solvent and solute concentrations. Depending on the conditions of adsorption, the spatial distribution of the solute concentration can either be deformed by VF of the sample solvent concentration profiles or disentangle from the fingering zone. In the case of deformation by fingering, a parametric study is performed to analyze the influence of parameters such as the log-mobility ratio, the ratio of dispersion coefficients, the sample length, and the adsorption retention parameter k′ on the widening of the solute concentration peak. The results highlight experimental evidences obtained recently in reversed-phase liquid chromatography.

Restricted interpolation property in superintuitionistic logics

The restricted interpolation property IPR in modal and superintuitionistic logics is investigated. It is proved that in superintuitionistic logics of finite slices and in finite-slice extensions of the Grzegorczyk logic, the property IPR is equivalent to the projective Beth property PB2.

Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio

When a sample of fluid of finite size is displaced in a porous medium by another miscible fluid, viscous fingering may occur when the two fluids have different viscosities. Depending whether the sample is more or less viscous than the carrier fluid, the log-mobility ratio R [defined as R=ln(mu_{2}mu_{1}) where mu_{2} and mu_{1} are the viscosities of the sample and of the carrier] is respectively positive or negative. In the case of a linear displacement of a finite slice of fluid, R>0 leads to fingering of the rear interface of the sample where the less viscous carrier invades the more viscous sample. If R<0 , it is on the contrary the frontal interface of the sample that develops fingers where the less viscous sample displaces the more viscous bulk solution. We investigate here numerically the differences in fingering dynamics between the positive and negative log-mobility ratio cases leading to the growth of fingers against or along the direction of the flow, respectively. To do so, we integrate Darcy's law coupled to a convection-diffusion equation for the concentration of a solute ruling the viscosity of the finite-size sample. The statistical moments of the solute's concentration distribution are analyzed as a function of dimensionless parameters of the problem such as the length of the slice l , the log-mobility ratio R , and the ratio between transverse and axial dispersion coefficients . We find that, on average, the mixing zones and the width of the sample broadening due to fingering are larger for negative R than for positive R . This is due to the fact that fingers travel quicker in the flow direction than against the flow. Relevance of our results are discussed for interpretation of experimental results obtained in chromatographic separation and for understanding conditions of enhanced spreading of contaminants in aquifers.

Viscous fingering of miscible slices

Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy’s law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem, i.e., the log-mobility ratio R, the length of the slice l, the Péclet number Pe, and the ratio between transverse and axial dispersion coefficients ε. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.

Finite element vertical slices model: Validation and application to an embedded square footing under combined loading

This paper describes an efficient formulation for the analysis of three-dimensional (3-D) soil/structure interaction problems. The technique which is called vertical slices model (VSM) subdivides the structure and the surrounding soil into vertical slices. It takes profit of finite element 2-D numerical solutions in plane stress for building approximate 3-D solutions by replacing the inter-slice interactions by fictitious body forces. The 2-D finite element and finite difference methods are combined in a relatively simple and compact procedure, and applied iteratively to each vertical slice. The 3-D aspect of the considered problem is kept by satisfying the continuity of shear stresses developed at the inter-slices. First, the theory of the vertical slices model is presented and then a Fortran computer program is elaborated. Next, the capabilities of this program are illustrated by applying the approach to the problems of both laterally and axially loaded piles founded in both homogeneous and non-homogeneous soils. A third problem of a rigid rectangular foundation resting on top of a homogeneous elastic stratum has also been investigated. Comparisons with other numerical solutions show good agreement and consequently they prove that the model is successfully able to capture the behavior of the three boundary value problems. Finally, in terms of stiffness factors the method is used to predict the behavior of an embedded square footing under combined loading, in a half-space where the stiffness exhibits a power-law variation with depth.

Finite foliations of open FRW universes and the point-like big bang

Every open FRW universe can be completely foliated by spacelike slices of finite volume, each intersecting every fundamental worldline. The volumes tend to zero in the past, suggesting a point-like big bang. Embedding diagrams confirm this. How finite slices can contain an infinite amount of matter is explained by time-reversed gravitational collapse.

Single kick approximations for beam-beam deflections

A six-dimensional symplectic beam-beam interaction map using finite discrete slices of a strong beam is extended to infinitesimal slices. The new map is calculated under the assumption of a longitudinal Gaussian distribution with approximations. A round Gaussian beam is simulated to demonstrate accuracies of the approximations.

Impurity atom diffusion into finite slices of semiconductor material

Impurity atom diffusion into finite slices of semiconductor material