Hybrid Difference Methods for PDEs

We propose the hybrid difference methods for partial differential equations (PDEs). The hybrid difference method is composed of two types of approximations: one is the finite difference approximation of PDEs within cells (cell FD) and the other is the interface finite difference (interface FD) on edges of cells. The interface finite difference is obtained from continuity of some physical quantities. The main advantages of this new approach are that the method can applied to non-uniform grids, retaining the optimal order of convergence and stability of the numerical method for the Stokes equations is obtained without introducing staggered grids.     

Dynamic Model Adaptation for Multiscale Simulation of Hyperbolic Systems with Relaxation

In numerous industrial CFD applications, it is usual to use two (or more) different codes to solve a physical phenomenon: where the flow is a priori assumed to have a simple behavior, a code based on a coarse model is applied, while a code based on a fine model is used elsewhere. This leads to a complex coupling problem with fixed interfaces. The aim of the present work is to provide a numerical indicator to optimize to position of these coupling interfaces. In other words, thanks to this numerical indicator, one could verify if the use of the coarser model and of the resulting coupling does not introduce spurious effects. In order to validate this indicator, we use it in a dynamical multiscale method with moving coupling interfaces. The principle of this method is to use as much as possible a coarse model instead of the fine model in the computational domain, in order to obtain an accuracy which is comparable with the one provided by the fine model. We focus here on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. Using a numerical Chapman–Enskog expansion and the distance to the equilibrium manifold, we construct the numerical indicator. Based on several works on the coupling of different hyperbolic models, an original numerical method of dynamic model adaptation is proposed. We prove that this multiscale method preserves invariant domains and that the entropy of the numerical solution decreases with respect to time. The reliability of the adaptation procedure is assessed on various 1D and 2D test cases coming from two-phase flow modeling.     

Towards Smooth Particle Methods Without Smoothing

In this article we present a new class of particle methods which aim at being accurate in the uniform norm with a minimal amount of smoothing. The crux of our approach is to compute local polynomial expansions of the characteristic flow to transport the particle shapes with improved accuracy. In the first order case the method consists of representing the transported density with linearly-transformed particles, the second order version transports quadratically-transformed particles, and so on. For practical purposes we provide discrete versions of the resulting LTP and QTP schemes that only involve pointwise evaluations of the forward characteristic flow, and we propose local indicators for the associated transport error. On a theoretical level we extend these particle schemes up to arbitrary polynomial orders and show by a rigorous analysis that for smooth flows the resulting methods converge in \(L^\infty \) without requiring remappings, extended overlapping or vanishing moments for the particles. Numerical tests using different passive transport problems demonstrate the accuracy of the proposed methods compared to basic particle schemes, and they establish their robustness with respect to the remapping period. In particular, it is shown that QTP particles can be transported without remappings on very long periods of time, without hampering the accuracy of the numerical solutions. Finally, a dynamic criterion is proposed to automatically select the time steps where the particles should be remapped. The strategy is a by-product of our error analysis, and it is validated by numerical experiments.     

An improved factor based approach to precedential constraint

In this article I argue for rule-based, non-monotonic theories of common law judicial reasoning and improve upon one such theory offered by Horty and Bench-Capon. The improvements reveal some of the interconnections between formal theories of judicial reasoning and traditional issues within jurisprudence regarding the notions of the ratio decidendi and obiter dicta. Though I do not purport to resolve the long-standing jurisprudential issues here, it is beneficial for theorists both of legal philosophy and formalizing legal reasoning to see where the two projects interact.     

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.     

Abstraction and approximation in fuzzy temporal logics and models

Recently, by defining suitable fuzzy temporal logics, temporal properties of dynamic systems are specified during model checking process, yet a few numbers of fuzzy temporal logics along with capable corresponding models are developed and used in system design phase, moreover in case of having a suitable model, it suffers from the lack of a capable model checking approach. Having to deal with uncertainty in model checking paradigm, this paper introduces a fuzzy Kripke model (FzKripke) and then provides a verification approach using a novel logic called Fuzzy Computation Tree Logic* (FzCTL*). Not only state space explosion is handled using well-known concepts like abstraction and bisimulation, but an approximation method is also devised as a novel technique to deal with this problem. Fuzzy program graph, a generalization of program graph and FzKripke, is also introduced in this paper in consideration of higher level abstraction in model construction. Eventually modeling, and verification of a multi-valued flip-flop is studied in order to demonstrate capabilities of the proposed models.     

Model checking dynamic pushdown networks

A dynamic pushdown network (DPN) is a set of pushdown systems (PDSs) where each process can dynamically create new instances of PDSs. DPNs are a natural model of multi-threaded programs with (possibly recursive) procedure calls and thread creation. Thus, it is important to have model checking algorithms for DPNs. We consider in this work model checking DPNs against single-indexed LTL and CTL properties of the form \({\bigwedge f_i}\) such that f _i is a LTL/CTL formula over the PDS i. We consider the model checking problems w.r.t. simple valuations (i.e., whether a configuration satisfies an atomic proposition depends only on its control location) and w.r.t. regular valuations (i.e., the set of the configurations satisfying an atomic proposition is a regular set of configurations). We show that these model checking problems are decidable. We propose automata-based approaches for computing the set of configurations of a DPN that satisfy the corresponding single-indexed LTL/CTL formula.     

A scalable hybrid decision system (HDS) for Roman word recognition using ANN SVM: study case on Malay word recognition

An off-line handwriting recognition (OFHR) system is a computerized system that is capable of intelligently converting human handwritten data extracted from scanned paper documents into an equivalent text format. This paper studies a proposed OFHR for Malaysian bank cheques written in the Malay language. The proposed system comprised of three components, namely a character recognition system (CRS), a hybrid decision system and lexical word classification system. Two types of feature extraction techniques have been used in the system, namely statistical and geometrical. Experiments show that the statistical feature is reliable, accessible and offers results that are more accurate. The CRS in this system was implemented using two individual classifiers, namely an adaptive multilayer feed-forward back-propagation neural network and support vector machine. The results of this study are very promising and could generalize to the entire Malay lexical dictionary in future work toward scaled-up applications.     

Design and implementation of novel thin film position-sensitive detectors (TFPSDs) based on photoconductive effect

In this paper, novel, very simple and low-cost thin film position sensitive detectors (TFPSDs) which employ indium tin oxide (ITO)-cadmium sulfide (CdS)-Au structures are presented. Different from the existed PSDs those based on lateral photovoltage effect, the proposed sensor is operated in principle of photoconductive effect. CdS film is chosen as the photosensitive layer since its excellent photoconductive property, low cost and suitable for depositing on different type substrates with large areas. In the present study, CdS films are deposited on silicon substrates by using rf magnetron sputtering at room temperature. After that, the prepared CdS films were annealed at different temperatures for 50 min in N₂ ambient and a rigorous analysis was presented on the surface topography, and photoconductive properties by scanning electron microscopy and semiconductor characteristics analyzer. The test results shows that the film annealed at 400 °C has the best photoconductive property. Moreover, the finite-element method was used to study the relationship between the Aluminium (Al) electrode shape and the linearity of PSD. Three different type PSDs (quadrilateral, rectangular-shaped and pillow-shaped) were designed and simulated. The simulation results indicate that the quadrilateral electrode is suitable for large-area PSDs, whereas the rectangular-shaped and pillow-shaped electrodes can be used to realize small-area PSDs. The measurement results shows that the non-linearities of three type PSDs with dimensions of 10 × 10 mm are respectively 2.106, 3.594, and 3.55 %, which verify the conclusion deduced from the simulation results.