D. Constales
Ghent University, Mathematical Analysis, Faculty Member
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The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to... more
The quaternionic operator calculus can be applied very elegantly to solve many important boundary value problems arising in fluid dynamics and electrodynamics in an analytic way. In order to set up fully explicit solutions. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one has to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. Recently the theory of quaternionic holomorphic multiperiodic functions and automorphic forms provided new impulses to set up explicit representation formulas for large classes of hyperbolic polyhedron type domains. These include block shaped domains, wedge shaped domains (with or without additional rectangular restrictions) and circular s...
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Abstract-Preconditioning for the simultaneous solution of non-filtered and filtered Eulerian-Eulerian gas-solid flow models is investigated. The impact of the gas-solid interaction source terms is shown. A possible approach for a new... more
Abstract-Preconditioning for the simultaneous solution of non-filtered and filtered Eulerian-Eulerian gas-solid flow models is investigated. The impact of the gas-solid interaction source terms is shown. A possible approach for a new preconditioner is proposed. The gas-solid interaction source terms are accounted for via the addition of a gas-solid interaction history force term to the preconditioner. Keywords: Preconditioning, Gas-solid flows, Mixture speed of sound, Gas-solid interactions, Filtering I. INTRODUCTION
A pointwise simultaneous solution algorithm based on dual time stepping was developed by De Wilde et al. (2002). With increasing grid aspect ratios, the efficiency of the point method quickly drops. Most realistic flow cases, however,... more
A pointwise simultaneous solution algorithm based on dual time stepping was developed by De Wilde et al. (2002). With increasing grid aspect ratios, the efficiency of the point method quickly drops. Most realistic flow cases, however, require high grid aspect ratio grids, with the highest grid spacing in the streamwise direction. In this direction, the stiffness is efficiently removed by applying preconditioning (Weiss and Smith, 1995). In the direction perpendicular to the stream wise direction, stiffness remains because of the viscous and the acoustic terms. To resolve this problem, a line method is presented. All nodes in a plane perpendicular to the stream wise direction, a so-called line, are solved simultaneously. This allows a fully implicit treatment of the fluxes in the line, removing the stiffness in the line wise directions. Calculations with different grid aspect ratios are presented to investigate the convergence behavior of the line method. The line method presented is...
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We study diffusion of active ingredients in coated textiles by a three-scale model. These scales consist of a fiber level representing the fiber with its polymer coating containing a n active ingredient, a yarn level, and the level of the... more
We study diffusion of active ingredients in coated textiles by a three-scale model. These scales consist of a fiber level representing the fiber with its polymer coating containing a n active ingredient, a yarn level, and the level of the room holding the textile. An analysis of the model is carried out using the characteristic times of the different levels. We investigate t he influence of the parameters in the model by solving several inverse problems.
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Arch. Math. 87 (2006) 468–477 0003–889X/06/050468–10 DOI 10.1007/s00013-006-1791-x © Birkhäuser Verlag, Basel, 2006 ... On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations ... Isabel Caç ˜ao1), Denis... more
Arch. Math. 87 (2006) 468–477 0003–889X/06/050468–10 DOI 10.1007/s00013-006-1791-x © Birkhäuser Verlag, Basel, 2006 ... On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations ... Isabel Caç ˜ao1), Denis Constales2) and Rolf S ören Krausshar ... Abstract. This paper exhibits an interesting relationship between arbitrary order Bessel functions and Dirac type equations. Let D := n∑ i=1 ∂ ∂xi ei be the Euclidean Dirac operator in the n-dimensional flat space Rn, ... 1. Introduction. Eigensolutions to higher dimensional ...
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The three-factor kinetic equation of catalyst deactivation was obtained in terms of apparent kinetic parameters. The three factors correspond to the main cycle with a linear, detailed mechanism regarding the catalytic intermediates, a... more
The three-factor kinetic equation of catalyst deactivation was obtained in terms of apparent kinetic parameters. The three factors correspond to the main cycle with a linear, detailed mechanism regarding the catalytic intermediates, a cycle of reversible deactivation, and a stage of irreversible deactivation (aging), respectively. The rate of the main cycle is obtained for the fresh catalyst under a quasi-steady-state assumption. The phenomena of reversible and irreversible deactivation are presented as special separate factors (hierarchical separation). In this case, the reversible deactivation factor is a function of the kinetic apparent parameters of the reversible deactivation and of those of the main cycle. The irreversible deactivation factor is a function of the apparent kinetic parameters of the main cycle, of the reversible deactivation, and of the irreversible deactivation. The conditions of such separability are found. The obtained equation is applied successfully to desc...
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Fundamental solutions of hyperbolic Dirac operators and hyperbolic versions of the Laplace operator are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out upper half-space of... more
Fundamental solutions of hyperbolic Dirac operators and hyperbolic versions of the Laplace operator are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out upper half-space of Rn by arithmetic subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincare ́ type series. As main goal we develop Cauchy and Green type integral formulas and describe Hardy space decompositions for spinor sections of the associated spinor bundles on these manifolds.
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We prove an integral representation and a power series expansion for the function $\det(A)^{-1}$ in a small neighborhood of the identity matrix. Both results are closely linked to the formula for the change of coordinates of the Dirac... more
We prove an integral representation and a power series expansion for the function $\det(A)^{-1}$ in a small neighborhood of the identity matrix. Both results are closely linked to the formula for the change of coordinates of the Dirac delta distribution in $\mathbb{R}^m$.
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In this paper we consider generalized Hardy spaces in the octonionic setting associated to arbitrary Lipschitz domains where the unit normal field exists almost everywhere. First we discuss some basic properties and explain structural... more
In this paper we consider generalized Hardy spaces in the octonionic setting associated to arbitrary Lipschitz domains where the unit normal field exists almost everywhere. First we discuss some basic properties and explain structural differences to the associative Clifford analysis setting. The non-associativity requires special attention in the definition of an appropriate inner product and hence in the definition of a generalized Szegö projection. Whenever we want to apply classical theorems from reproducing kernel Hilbert spaces we first need to switch to the consideration of real-valued inner products where the Riesz representation theorem holds. Then we introduce a generalization of the dual Cauchy transform for octonionic monogenic functions which represents the adjoint transform with respect to the real-valued inner product $$\langle \cdot , \cdot \rangle _0$$ ⟨ · , · ⟩ 0 together with an associated octonionic Kerzman–Stein operator and related kernel functions. Also in the ...
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The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen, J. Geom. Anal. 29 (2019), 2709-2737, we determine its reproducing kernel.... more
The monogenic Hua-Radon transform is defined as an orthogonal projection on holomorphic functions in the Lie sphere. Extending the work of Sabadini and Sommen, J. Geom. Anal. 29 (2019), 2709-2737, we determine its reproducing kernel. Integrating this kernel over the Stiefel manifold yields a linear combination of the zonal spherical monogenics. Using the reproducing properties of those monogenics we obtain an inversion for the monogenic Hua-Radon transform.
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New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using classical mechanisms, in particular the consecutive mechanism, as examples. We identify six different... more
New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using classical mechanisms, in particular the consecutive mechanism, as examples. We identify six different special points, and analyze and classify the 6 possible (out of 612 combinations) patterns of concentration peak and intersection times and values that distinguish the parameter subdomains and sometimes can eliminate the mechanism. This developed theory is tested on examples (multi-step ...
The MaCKiE-2002 conference discussed scientific problems that arise in applied chemistry, and for which advanced mathematical methods are known or are still under development. In this introduction to the special issue dedicated to the... more
The MaCKiE-2002 conference discussed scientific problems that arise in applied chemistry, and for which advanced mathematical methods are known or are still under development. In this introduction to the special issue dedicated to the conference, we discuss its background and give an overview of the contributions that were selected for publication.
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Different paradigms of multi-scale analysis and modeling in modern chemical engineering are described. First, the" sequential"(hierarchical) multi-scale mathematical modeling, which is... more
Different paradigms of multi-scale analysis and modeling in modern chemical engineering are described. First, the" sequential"(hierarchical) multi-scale mathematical modeling, which is based on the hidden assumption that the model on one level is independent of the model on the previous level; second, the multi-scale approach to a multi-objective task, in which experimental data on the different levels is obtained simultaneously, and the mathematical models are built up simultaneously as well. A new approach, the'multi-scale ...
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ABSTRACT Significance: it is shown, based on pulse-response experiments, that under special conditions the activity profile of a prepared catalytic system depends only on the total amount of admitted substance. This property, previously... more
ABSTRACT Significance: it is shown, based on pulse-response experiments, that under special conditions the activity profile of a prepared catalytic system depends only on the total amount of admitted substance. This property, previously found computationally, is here established mathematically for porous and nonporous catalyst in different pulse reactors This result can be used as a theoretical guidance for the design of systems or materials with optimal activity profile, in particular catalyst bed or catalyst particle. Consequently, it can be used for understanding and developing the different diffusion-reaction processes: wet impregnation, deactivation of active materials, etc. © 2014 American Institute of Chemical Engineers AIChE J, 2014
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In this paper we present some results on the asymptotic growth behavior of periodic paravector valued functions that satisfy the Dirac‐Hodge equation on upper half‐space. We set up a generalization of the classical Valiron inequality for... more
In this paper we present some results on the asymptotic growth behavior of periodic paravector valued functions that satisfy the Dirac‐Hodge equation on upper half‐space. We set up a generalization of the classical Valiron inequality for this class of functions and discuss some basic properties.
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Abstract In this paper, we present numerical modelling techniques supporting the determination of parameters for the contaminant transport by underground water flow. The parameter identification is based on measurements obtained by a... more
Abstract In this paper, we present numerical modelling techniques supporting the determination of parameters for the contaminant transport by underground water flow. The parameter identification is based on measurements obtained by a single injection–extraction well. The underground water flow is modelled using a Dupuit–Forchheimer approximation for the unsaturated–saturated aquifer.
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ABSTRACT Combustion optimization has been proved to be an effective way to reduce the NOx emissions and unburned carbon in fly ash by carefully setting the operational parameters of boilers. However, there is a trade-off relationship... more
ABSTRACT Combustion optimization has been proved to be an effective way to reduce the NOx emissions and unburned carbon in fly ash by carefully setting the operational parameters of boilers. However, there is a trade-off relationship between NOx emissions and the boiler economy, which could be expressed by Pareto solutions. The aim of this work is to achieve multi-objective optimization of the coal-fired boiler to obtain well distributed Pareto solutions. In this study, support vector regression (SVR) was employed to build NOx emissions and carbon burnout models. Thereafter, the improved Strength Pareto Evolutionary Algorithm (SPEA2), the new Multi-Objective Particle Swarm Optimizer (OMOPSO), the Archive-Based hYbrid Scatter Search method (AbYSS), and the cellular genetic algorithm for multi-objective optimization (MOCell) were used for this purpose. The results show that the hybrid algorithms by combining SVR can obtain well distributed Pareto solutions for multi-objective optimization of the boiler. Comparison of various algorithms shows MOCell overwhelms the others in terms of the quality of solutions and convergence rate.
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Abstract. In this paper the problem of taking the square root of bases of special monogenic polynomials is studied, thus leading to a number of results under some additional conditions of associated infinite matrices, related essentially... more
Abstract. In this paper the problem of taking the square root of bases of special monogenic polynomials is studied, thus leading to a number of results under some additional conditions of associated infinite matrices, related essentially to the so-called algebraicness of these matrices.
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Page 1. Laboratory for Chemical Technology, Ghent University http://www.lct.UGent.be TEMPORAL ANALYSIS OF PRODUCTS: PRESENT STATUS AND PERSPECTIVES Guy B. Marin Vladimir V. Galvita Denis Constales 1 ACS National Meeting,... more
Page 1. Laboratory for Chemical Technology, Ghent University http://www.lct.UGent.be TEMPORAL ANALYSIS OF PRODUCTS: PRESENT STATUS AND PERSPECTIVES Guy B. Marin Vladimir V. Galvita Denis Constales 1 ACS National Meeting, Anaheim,28/03/2011 Page 2. Overview 2 • Introduction • Case: total oxidation of volatile organic components • Mathematical analysis • Statistical analysis • Best practices • Conclusions ACS National Meeting, Anaheim,28/03/2011 Page 3. 3 Steady-state versus transient Kenzi Tamaru , Adv. ...
328 D. CONSTALES 3. Auxiliary results Lemma 1. Let г > 1 and let A and В be positive real numbers, then ,лл, A + cot2r ф (11) mm =— о<Ф<к/2 1 + Bsm~¿r ф is attained for a value ф = в where в is a solution in (0,7r/2) of the... more
328 D. CONSTALES 3. Auxiliary results Lemma 1. Let г > 1 and let A and В be positive real numbers, then ,лл, A + cot2r ф (11) mm =— о<Ф<к/2 1 + Bsm~¿r ф is attained for a value ф = в where в is a solution in (0,7r/2) of the equation (12) B{cos2r-'¿ в-A sin2"-' 0) + sin^-2 в cos37'-2 0 = 0, and the corresponding minimum value is A — cot2'"-2 в. Proof. The derivative of the function in (11) with respect to ф is ^ 2гашфсозф' ,B 2r_2 ^_Asin2r_2 + sin2),„2 фcog2r„2 , (S + sin2rV») whose value is small and negative near ф = 0 and small and ...
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Abstract. The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Gürlebeck, W. Sprößig and others. This study will be extended in this paper.... more
Abstract. The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Gürlebeck, W. Sprößig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the ...
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[2] Since more than a decade, contaminant transport with adsorption is a dynamical and difficult research area. Precise mathematical models are available, and a considerable effort has been made in developing effective mathematical tools... more
[2] Since more than a decade, contaminant transport with adsorption is a dynamical and difficult research area. Precise mathematical models are available, and a considerable effort has been made in developing effective mathematical tools to compute the desired solution. Realistic model data are crucial to get reliable numerical solutions; they can be obtained by calibration of the model with a real system. For this purpose, injection-extraction wells are used. In a simple injection-extraction well the flow model is unsteady and provides ...
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In this paper, we propose an efficient method for the identification of soil parameters in unsaturated porous media, using measurements from infiltration experiments. The infiltration is governed by Richard's nonlinear equation... more
In this paper, we propose an efficient method for the identification of soil parameters in unsaturated porous media, using measurements from infiltration experiments. The infiltration is governed by Richard's nonlinear equation expressed in terms of effective saturation. The soil retention and hydraulic permeability functions are expressed using the Van Genuchten-Mualem ansatz in terms of the soil parameters. The mathematical algorithm is based on a transformation of Richard's equation to a system of ordinary differential ...
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In this paper, we consider half-space domains (semi-infinite in one of the dimensions) and strip domains (finite in one of the dimensions) in real Euclidean spaces of dimension at least 2. The Szegö reproducing kernel for the space of... more
In this paper, we consider half-space domains (semi-infinite in one of the dimensions) and strip domains (finite in one of the dimensions) in real Euclidean spaces of dimension at least 2. The Szegö reproducing kernel for the space of monogenic and square integrable functions on a strip domain is obtained in closed form as a monogenic single-periodic function, viz a monogenic cosecant. The relationship between the Szegö and Bergman kernel for monogenic functions in a strip domain is explicitated in the transversally Fourier ...
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In this paper, we consider half-space domains (semi-infinite in one of the dimensions) and strip domains (finite in one of the dimensions) in real Euclidean spaces of dimension at least 2. The Szegö reproducing kernel for the space of... more
In this paper, we consider half-space domains (semi-infinite in one of the dimensions) and strip domains (finite in one of the dimensions) in real Euclidean spaces of dimension at least 2. The Szegö reproducing kernel for the space of monogenic and square integrable functions on a strip domain is obtained in closed form as a monogenic single-periodic function, viz a monogenic cosecant. The relationship between the Szegö and Bergman kernel for monogenic functions in a strip domain is explicitated in the transversally Fourier ...
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In this paper, it is shown that certain classes of special monogenic functions cannot be represented by the basic series in the whole space. New definitions for the order of basis of special monogenic polynomials are given together with... more
In this paper, it is shown that certain classes of special monogenic functions cannot be represented by the basic series in the whole space. New definitions for the order of basis of special monogenic polynomials are given together with theorems on representation of classes of special monogenic functions in certain balls and at a point.
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The notion of V angle, as introduced by Ramadanov and Skwarczynski in [11], can be summarized as follows. Let H be a Hilbert space over the field K, where K is fixed to be R or C, and let Nt, N2 be closed subspaces of H. Then the quantity... more
The notion of V angle, as introduced by Ramadanov and Skwarczynski in [11], can be summarized as follows. Let H be a Hilbert space over the field K, where K is fixed to be R or C, and let Nt, N2 be closed subspaces of H. Then the quantity &amp;#x27;Y(Nt, N2) E [0,11&amp;quot;/2], uniquely defined by the value of its cosine : ... • H is areal Hilbert space and both Nt and N2 are one-dimensional. Then if Nt f:. N2 , &amp;#x27;Y(Nt, N2 ) coincides with the ordinary angle defined between two lines. If Nt = N2, &amp;#x27;Y(Nt , N2) = 11&amp;quot;/2 instead of the value 0 which would make a continuous function of ...
The basic object type in this program is a vector: a linear combination of the three unit vectors el, e2, e3 that form an orthonormal right-handed basis. A vector takes the form: al*e(1) +a2*e(2) +a3*e(3) where the aj, j E {I, 2, 3} are... more
The basic object type in this program is a vector: a linear combination of the three unit vectors el, e2, e3 that form an orthonormal right-handed basis. A vector takes the form: al*e(1) +a2*e(2) +a3*e(3) where the aj, j E {I, 2, 3} are scalar expressions. The unit vectors e(j) are defined by means of an operator, e, which is declared noncommutative for reasons that will be explained soon: operator e; noncom e; Extracting a cartesian co-ordinate out of a vector can be done using camp: procedure comp (j, u); df (u, e (j)) ; Next to addition and scalar multiplication, the ...
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- 3:40 PM 139f. High Throughput of Non-Steady-State Catalytic Activity Characteristics Using Temporal Analysis of Products. Gregory S. Yablonsky 1 , John T. Gleaves 2 , Xiaolin Zheng 2 , Renato Feres 3 , and Denis Constales ...
ABSTRACT The chemical system of monomolecular reactions among n species, first analysed in the classical paper by Wei and Prater (1962) was revisited. It was shown that using symmetry relationships, based on all the equilibrium constants... more
ABSTRACT The chemical system of monomolecular reactions among n species, first analysed in the classical paper by Wei and Prater (1962) was revisited. It was shown that using symmetry relationships, based on all the equilibrium constants and known dependences, all remaining kinetic dependences can be calculated. A new method of closing the mass balance for such a complex chemical system was developed, using only measurements of one or a few species, and based on symmetry relations. A new method of testing completeness of a kinetic description was proposed, using the properties of the trace sum of components, i.e., the sum of all concentration dependences, each of which is started from maximal initial concentration.