Implicit Operator Research Articles

Influence of fluid properties on bubble formation, detachment, rising and collapse; Investigation using volume of fluid method

Numerical simulations have been carried out to investigate the formation and motion of single bubble in liquids using volume-of-fluid (VOF) method using the software platform of FLUENT 6.3. Transient conservation mass and momentum equations with considering the effects of surface tension and gravitational force were solved by the pressure implicit splitting operator (PISO) algorithm to simulate the behavior of gas-liquid interface movements in the VOF method. The simulation results of bubble formation and characteristics were in reasonable agreement with experimental observations and available literature results. Effects of fluid physical properties, operation conditions such as orifice diameter on bubble behavior, detachment time, bubble formation frequency and bubble diameter were numerically studied. The simulations showed that bubble size and bubble detachment times are linear functions of surface tension and decrease exponentially with the increase in liquid density. In contrast, only a small influence of the fluid viscosity on bubble size and detachment time was observed. Bubble collapse at a free surface simulation with VOF method was also investigated.

What do we know about implicit false-belief tracking?

There is now considerable evidence that neurotypical individuals track the internal cognitions of others, even in the absence of instructions to do so. This finding has prompted the suggestion that humans possess an implicit mental state tracking system (implicit Theory of Mind, ToM) that exists alongside a system that allows the deliberate and explicit analysis of the mental states of others (explicit ToM). Here we evaluate the evidence for this hypothesis and assess the extent to which implicit and explicit ToM operations are distinct. We review evidence showing that adults can indeed engage in ToM processing even without being conscious of doing so. However, at the same time, there is evidence that explicit and implicit ToM operations share some functional features, including drawing on executive resources. Based on the available evidence, we propose that implicit and explicit ToM operations overlap and should only be considered partially distinct.

Finite Difference Method: A Brief Study

This is a short article summarizing different finite difference schemes for the numerical solution of partial differential equation in application of pricing financial derivatives. The solution of partial difference equation (PDE) using finite difference method (FDM) with both uniform and non-uniform grids are presented here. This article mainly focuses on the solution of 1D and 2D PDE. The solution of 1D PDE using implicit, explicit and Crank-Nicolson scheme and 2D PDE using alternate direction implicit (ADI), alternate direction implicit operator splitting scheme (ADI-OS) and alternate direction explicit (ADE) is discussed here. There are various literature available for an extensive study of the finite difference methods. This article is intended to be written for a quick review of various finite difference schemes to solve a PDE.

Flow Behavior of Viscoelastic Polymer Solution in Porous Media

Polymer solution flowing in porous media is difficult to characterize and simulate due to the effect caused by the rheological behavior and physicochemical reaction. In this study, a mathematical model of viscoelastic polymer flooding for enhancing oil recovery is presented. The model combines a viscoelastic constitutive model, together with a modified permeability model and a new relative permeability model. The effect of the rheology of polymer solution in porous media, the parameters of pore throat, the residual resistance factor, and the residual oil saturation reduction related to polymer's viscoelasticity have all been taken into account in this new model. We use the implicit operator splitting method to handle the concentration equations, the conjugate gradient method to solve the implicit pressure equations, and the third-order total variation diminishing method to handle the upwind scheme for explicit coefficients. The model is verified with the experimental data. In addition, the numerical model is used to analyze the displacement characteristics of polymer solution flow in porous media influenced by the rheological behavior and porous characters. Also, a typical case of polymer flooding simulated by this new model is demonstrated.

ACCESS CONTROL FOR SHARED ONTOLOGIES

Entities and their relationships for various fields of specialization can be described by ontologies. For example, the classes, relationships, and methods for designing a virus may be put into a ProtAƒÂ©gAƒÂ© ontology. If that design is to be integrated with a missile design, it will require a standard way of sharing and cross-referencing both classes and objects of the ontologies. This should be done in a secure way which only allows access to specified researchers using specified classes, relations, methods, and documentation. In this paper, we introduce a framework for ontology sharing that enables ontologies to easily be deployed on the web. Kernel0 is the ontology of classes, relations, attributes, and objects. It describes its own typing constraints and meta-data in the same way as data. Objects can have relationships to objects of other ontologies. Kernel-1 authorization definitions in our framework are able to dynamically determine the permissions of each user or group for queried objects. Our authorization has the ability to perform inferences via IS-A inheritance and by evaluating implicit relations and operator definitions. All modifications of values in the knowledge base are checked for both appropriate authorization and satisfaction of all typing constraints. To cite this document: Daniel J. Buehrer and Tzu-Yang Wang, Access control for shared ontologies, International Journal of Electronic Commerce Studies, Vol.4, No.2, pp. 281-294, 2013. Permanent link to this document: http://dx.doi.org/10.7903/ijecs.1039

Some applications of infinitary logical languages in universal algebra

Some examples are given of applications of an innite logical language in universal algebra, in the algebraic geometry of universal algebras, in the theory of implicit operations on algebras, in the Galois theory between automorphisms of universal algebras and its subalgebras of xed points, in the theory of Hamiltonian closure of subalgebras and other areas.

A comparison study of ADI and operator splitting methods on option pricing models

In this paper we perform a comparison study of alternating direction implicit (ADI) and operator splitting (OS) methods on multi-dimensional Black–Scholes option pricing models. The ADI method is used extensively in mathematical finance for numerically solving multi-factor option pricing problems. However, numerical results from the ADI scheme show oscillatory solution behaviors with nonsmooth payoffs or discontinuous derivatives at the exercise price with large time steps. In the ADI scheme, there are source terms which include y-derivatives when we solve x-derivative involving equations. Then, due to the nonsmooth payoffs, source terms contain abrupt changes which are not in the range of implicit discrete operators and this leads to difficulty in solving the problem. On the other hand, the OS method does not contain the other variable’s derivatives in the source terms. We provide computational results showing the performance of the methods for two-asset option pricing problems. The results show that the OS method is very efficient and gives better accuracy and robustness than the ADI method with large time steps.

An interleaving semantics for UML 2 interactions using Petri nets

Weak sequencing is the implicit composition operator for interactions defined by the OMG specification. Accordingly, most semantics retain this operator to compose a CombinedFragment with the rest of the interactions. But all of them use only formalisms based on trace or interleaving semantics. True-concurrency-based formalisms ignore the standard interpretation and introduce synchronization on entering and exiting fragments. In this paper, we propose to revise the formal semantics of the CombinedFragments using a formalism that offers a high expressivity power to describe execution traces with regard to true concurrency as well as interleaving. We define an appropriate semantics, which is in accordance with the UML 2.4 specification regarding the event ordering over the operands and the constraints evaluation. For this purpose, we propose an approach to translate the CombinedFragments into Colored Petri Nets, or CPNs. The derived specification is value-oriented, composed of identified objects and events, thus allowing a more precise analysis of the model behavior. It is verified by model checking. A case study is given to illustrate the approach throughout the paper.

Linear-quadratic regulator with intermediate points for degenerate equations with unbounded operator

We study a linear-quadratic optimal control problem in a Hilbert space where the state equation is unsolvable with respect to the derivative and contains an unbounded operator. The performance index is the sum of the integral of a quadratic form with respect to the control and the state variable on a finite or infinite time interval and also quadratic forms with respect to the differences between the state variable values at fixed points and given values. The optimal control is presented in the feedback form using the implicit differential operator Riccati equation or the operator equation of the Riccati type under a special symmetry condition for the solution. The minimal value of the minimized functional is calculated. Some illustrative examples are also given.

Seismic cracking of concrete gravity dams by plastic–damage model using different damping mechanisms

Utilizing two different damping mechanisms, seismic cracking response of concrete gravity dams is examined by a plastic–damage model implemented in three-dimensional space. The material constitutive law employed herein is based on the one proposed by Lee and Fenves for the 2-D plane stress case. This plastic–damage model basically intended for cyclic or dynamic loading was founded on the combination of non-associated multi-hardening plasticity and isotropic damage theory to simulate the irreversible damages occurring in fracturing process of concrete. In this study, considering the HHT scheme as an implicit operator, the time integration procedure to iteratively solve the governing nonlinear equations is presented. Further, seismic fracture responses of gravity dams due to constant and damage-dependent damping mechanisms are compared. In order to assess the validity of the proposed model, several simple examples are solved and their results are presented first. Subsequently, Koyna gravity dam, which is a benchmark problem for the seismic fracture researches, is analyzed. It is concluded that employing the damage-dependent damping mechanism leads to more extensive damages and also predicts more reliable crack patterns in comparison with the constant damping mechanism in seismic analysis of concrete dams. Furthermore, including dam–water interaction intensifies the existing differences between the results of the two damping mechanisms.

Attentional bias for prescription opioid cues among opioid dependent chronic pain patients

Recurrent use of prescription opioid analgesics by chronic pain patients may result in opioid dependence, which involves implicit neurocognitive operations that organize and impel craving states and compulsive drug taking behavior. Prior studies have identified an attentional bias (AB) towards heroin among heroin dependent individuals. The aim of this study was to determine whether opioid-dependent chronic pain patients exhibit an AB towards prescription opioid-related cues. Opioid-dependent chronic pain patients (n=32) and a comparison group of non-dependent opioid users with chronic pain (n=33) completed a dot probe task designed to measure opioid AB. Participants also rated their opioid craving and self-reported arousal associated with opioid-related and neutral images, pain severity, and relief from pain treatments. Repeated-measures ANOVA revealed a significant group (opioid-dependent vs. non-dependent opioid user)×presentation duration (200. vs. 2,000ms.) interaction, such that opioid-dependent individuals evidenced a significant AB towards opioid cues presented for 200ms but not for cues presented for 2,000ms, whereas non-dependent opioid users did not exhibit a significant mean AB at either stimulus duration. Among opioid-dependent individuals, 200ms opioid AB was significantly associated with opioid craving, while among non-dependent opioid users, 200ms opioid AB was significantly associated with relief from pain treatments. Furthermore, dependent and non-dependent opioid users experienced opioid cues as significantly more arousing than neutral cues. Opioid dependence among chronic pain patients appears to involve an automatic AB towards opioid-related cues. When coupled with chronic pain, attentional fixation on opioid cues may promote compulsive drug use and addictive behavior.

Implicitly equivalent universal algebras

The concept of implicit operation on pseudovarieties of semigroups goes back to Eilenberg and Schutzenberger [1]. The author in [2–5] generalized this concept to other classes of algebras and established a connection between these operations and positively conditional termal functions in the case of uniform local finiteness of the algebras of the class in question. In this article we put forth the concept of an implicit operation for an arbitrary universal algebra, not necessarily locally finite, and establish a connection between these operations and infinite analogs of positively conditional terms, as well as ∞-quasi-identities arising in the algebraic geometry of universal algebras. We also consider conditions for implicit equivalence of algebras to lattices, semilattices, and Boolean algebras.

A Deformable Surface Model for Real-Time Water Drop Animation

A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.

Algebraic and logical geometries of universal algebras (a unified approach)

Using the congruences of free algebras as well as the concepts of a conditional term and an implicit operation, a unifying method for studying algebraic and logically definable subsets of universal algebras is suggested. An overview of the results of the author in this field of research is included.

An implicit finite-difference operator for the Helmholtz equation

We have developed an implicit finite-difference operator for the Laplacian and applied it to solving the Helmholtz equation for computing the seismic responses in the frequency domain. This implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost, compared with the corresponding conventional explicit finite-difference scheme. We achieved this by taking advantage of the inherently implicit nature of the Helmholtz equation and merging together the two linear systems: one from the implicit finite-difference discretization of the Laplacian and the other from the discretization of the Helmholtz equation itself. The end result of this simple yet important merging manipulation is a single linear system, similar to the one resulting from the conventional explicit finite-difference discretizations, without involving any differentiation matrix inversions. We analyzed grid dispersions of the discrete Helmholtz equation to show the accuracy of this implicit finite-difference operator and used two numerical examples to demonstrate its efficiency. Our method can be extended to solve other frequency domain wave simulation problems straightforwardly.

On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation

AbstractDifferential operators derived from the explicit or implicit solution of a diffusion equation are widely used for modelling background‐error correlations in geophysical applications of variational data assimilation. Key theoretical results underpinning the diffusion method are reviewed. Solutions to the isotropic diffusion problem on both the spherical space \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} and the d‐dimensional Euclidean space \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} are considered first. In \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} the correlation functions implied by explicit diffusion are approximately Gaussian, whereas those implied by implicit diffusion belong to the larger class of Matérn functions which contains the Gaussian function as a limiting case. The Daley length‐scale, defined as \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$D=\sqrt{-\! \left.d/\nabla^{2} c(r)\right|_{r=0}}$ \end{document} where ∇2 is the d‐dimensional Laplacian operator and r = |r| is Euclidean distance, is used as a standard parameter for comparing the different isotropic functions c(r). Diffusion on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} is shown to be well approximated by diffusion on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^2$ \end{document} for length‐scales of interest. As a result, fundamental parameters that define the correlation model on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb S}^2$ \end{document} can be specified using more convenient expressions available on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^2$ \end{document}.Anisotropic Gaussian or Matérn correlation functions on \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\mathbb R}^d$ \end{document} can be represented by a diffusion operator furnished with a symmetric and positive‐definite diffusion tensor. For anisotropic functions c(r), the tensor \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}${\bf D}=-\! \left( \nabla \nabla^{\rm T} c({\bf r}) |_{{\bf r}={\bf 0}} \right)^{-1}$ \end{document} where ∇ is the d‐dimensional gradient operator, is a natural generalization of the (square of) the Daley length‐scale for characterizing the spatial scales of the function. Relationships between this tensor, which we call the Daley tensor, and the diffusion tensor of the explicit and implicit diffusion operators are established. Methods to estimate the elements of the local Daley tensor from a sample of simulated background errors are presented and compared in an idealized experiment with spatially varying covariance parameters. Since the number of independent parameters needed to specify the local diffusion tensor is of the order of the total number of grid points N, sampling errors are inherently much smaller than those involved in the order N2 estimation problem of the full correlation function. While the correlation models presented in this paper are general, the discussion is slanted to their application to background‐error correlation modelling in ocean data assimilation. Copyright © 2012 Royal Meteorological Society

Awareness is awareness is awareness? Decomposing different aspects of awareness and their role in operant learning of pain sensitivity

Regarding awareness as a consistent concept has contributed to the controversy about implicit learning. The present study emphasized the importance of distinguishing aspects of awareness in order to determine whether learning is implicit. By decomposing awareness into awareness of contingencies, of the procedure being a learning task, and of the reinforcing stimuli, it was demonstrated that implicit operant learning modulated pain sensitivity. All of these aspects of awareness were demonstrated to not be necessary for learning. Additionally, discrimination of contingencies was not necessary on different levels of processing as demonstrated by a verbal and a behavioral method. It was demonstrated that explicit cognitive processes about one's own behavior, impaired learning, even though these cognitions were not immediately related to the learning process. The results of this study are of special interest in the context of pain, since implicit operant learning can explain the gradual development of hypersensitivity in chronic pain.

Implicit algebraic geometry on categories of universal algebras

Using the notion of an implicit operation on universal algebras, we redefine basic notions of the algebraic geometry of universal algebras. The results obtained for the implicit algebraic geometry imply (as special cases) the known results on the conditional geometric and algebraic geometric comparability of algebras.

Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Overlapping domain decomposition methods, otherwise known as overset grid or chimera methods, are useful for simplifying the discretization of partial differential equations in or around complex geometries. Though in wide use, such methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used, especially for higher-order methods. To address this shortcoming, high-order, provably energy stable, overlapping domain decomposition methods are derived for hyperbolic initial boundary value problems. The overlap is treated by splitting the domain into pieces and using generalized summation-by-parts derivative operators and polynomial interpolation. New implicit and explicit operators are derived that do not require regularization for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented, where it is found the explicit operators are preferred to the implicit ones.

Implicit finite-difference simulations of seismic wave propagation

We propose a new finite-difference modeling method, implicit both in space and in time, for the scalar wave equation. We use a three-level implicit splitting time integration method for the temporal derivative and implicit finite-difference operators of arbitrary order for the spatial derivatives. Both the implicit splitting time integration method and the implicit spatial finite-difference operators require solving systems of linear equations. We show that it is possible to merge these two sets of linear systems, one from implicit temporal discretizations and the other from implicit spatial discretizations, to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm. We give the complete derivations of the implicit splitting time integration method and the implicit spatial finite-difference operators, and present the resulting discretized formulas for the scalar wave equation. We conduct a thorough numerical analysis on grid dispersions of this new implicit modeling method. We show that implicit spatial finite-difference operators greatly improve the accuracy of the implicit splitting time integration simulation results with only a slight increase in computational time, compared with explicit spatial finite-difference operators. We further verify this conclusion by both 2D and 3D numerical examples.