Search results for "NUMBER"
showing 10 items of 3939 documents
Witt vectors and Fermat quotients
2008
Abstract We give a representation of any integer as a vector of the Witt ring W ( Z p ) and relate it to the Fermat quotient q ( n ) = ( n p − 1 − 1 ) / p . Logarithms are introduced in order to establish an isomorphism between the commutative unipotent groups 1 + p W ( Z p ) and W ( Z p ) .
Domain Specific Knowledge Representation for an Intelligent Tutoring System to Teach Algebraic Reasoning
2012
Translation of word problems into symbolic notation is one of the most challenging steps in learning the algebraic method. This paper describes a domain-specific knowledge representation mechanism to support Intelligent Tutoring Systems (ITS) which focus on this stage of the problem solving process. The description language proposed is based on the concept of a hypergraph and makes it possible to simultaneously a) represent all potential algebraic solutions to a given word problem; b) keep track of the student's actions; c) provide automatic remediation; and d) unequivocally determine the current state of the resolution process. An experimental evaluation with students at a public school su…
A comparative account of quantum dynamics of the H+ + H2 reaction at low temperature on two different potential energy surfaces
2014
Rotationally resolved reaction probabilities, integral cross sections, and rate constant for the H+ + H2 (v = 0, j = 0 or 1) → H2 (v′ = 0, j′) + H + reaction are calculated using a time-independent quantum mechanical method and the potential energy surface of Kamisaka et al. [J. Chem. Phys.116, 654 (2002)] (say KBNN PES). All partial wave contributions of the total angular momentum, J, are included to obtain converged cross sections at low collision energies and rate constants at low temperatures. In order to test the accuracy of the KBNN PES, the results obtained here are compared with those obtained in our earlier work [P. Honvault et al. , Phys. Rev. Lett.107, 023201 (2011)] using the ac…
Correlations for estimating the specific capital cost of multi-effect distillation plants considering the main design trends and operating conditions
2018
Abstract This work proposes a correlation for the specific capital cost of multi-effect distillation (MED) plants, considering their main design options and parameters, such as the number of effects, size/capacity, and heat source temperature. These parameters are varied within a large range to cover as many different cases as possible. The cost correlation decouples the evaporator cost and includes in the expression the ratio of the heat exchanger area to a reference one. This area is calculated using a validated MED numerical model, with the results then processed to produce fitted expressions. Two versions of this correlation with different levels of complexity are proposed, which provid…
Applications of mathematical modelling to the simulation of binary perfusion chromatography
1993
Abstract A mathematical model of binary (competitive adsorption involving two components) perfusion chromatography is used to simulate and study the behavior of a binary adsorption system. The dynamic behavior of column systems (frontal analysis) is examined for different particles sizes, column fluid superficial velocities, Vf, and intraparticle fluid velocities, νp. Column systems with perfusive (νp > 0) and purely diffusive (νp = 0) adsorbent particles are studied. The results obtained from the binary system studied in this work suggest that the times at which breakthrough begins for components 1 and 2, and the dynamic (unsteady state) relative separation between components 1 and 2 obtai…
R-Curve Modelling of Mode I Delamination in Multidirectional Carbon/Epoxy Composite Laminates
2014
In the present work, the mode I delamination behaviour of a quasi-isotropic quasi-homogeneous carbon/epoxy composite laminate with adjacent plies of 0o//45o is studied numerically. To describe the R-curve behaviour observed during crack propagation, a linear-exponential traction-separation law is proposed, where the fracture toughness and the increment in the fracture energy could be considered separately in the model. This model is then implemented in the finite element simulation of the delamination process in the composite laminate. Numerical results indicate that with the incorporation of the fibre bridging effect leads to a well-predicted force-displacement response of the composite la…
Process intensification in a photocatalytic membrane reactor: Analysis of the techniques to integrate reaction and separation
2017
Abstract Different methods to integrate reaction and separation in a membrane reactor are studied in the present work, with the aim being to highlight the pros and cons of the different alternatives and the effects of the intervening parameters. The coupling of the two processes can take place inside a single apparatus or using separate units. If a single apparatus is utilized, the coupling is more direct, but separate units offer higher degrees of freedom for the design with more opportunities to optimize the system without constraints. However, when using separate units, the integration of the two unit operations depends largely on the parameters intervening in the coupling procedure. The…
Application of cohesive-zone models to delamination behaviour of composite material
2012
International audience; The parameters of cohesive elements have to be chosen correctly in the simulation of composite delamination by finite element method: such as interface strength, interface stiffness and shape of cohesive law. The purpose of this work is to investigate their influence on the accuracy of the results obtained. A three-dimensional cohesive-zone model has been established using Ls-dyna to simulate Double-Cantilever-Beam mode I (DCB) and Edge-Notched-Flexure mode II (ENF) tests. The influence of these parameters of cohesive element on the maximum load and the slope of load-displacement curve have been discussed by comparing experimental and numerical results. Four traction…
Beyond ideal two-dimensional metals: Edges, vacancies, and polarizabilities
2018
Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously…
Physics based modelling of interface temperatures in machining with multilayer coated tools at moderate cutting speeds
2004
Abstract A new thermal model is presented for turning with tools with multilayer coatings. In the previous paper [Int. J. Mach. Tools Manuf. 43 (2003) 1311] devoted to the thermal problems in dry turning of steels with tools treated with multilayer coatings with an intermediate Al 2 O 3 layer new analytical models for estimating the heat partition to the chip and the average interface temperature were derived and the predictions were compared with experimental results. In this paper, a physics based modelling concept has been applied to both the individual layer and the composite layer approach to develop an estimate of the average and the maximum steady-state chip-tool interface temperatur…