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153. New Patterns in Steady-State Chemical Kinetics: Intersections, Coincidences, Map of Events (Two-Step Mechanism).

Author

Pinto, Daniel Branco, Yablonsky, Gregory, Marin, Guy B., and Constales, Denis

Subjects
PATTERNS (Mathematics), CHEMICAL kinetics, MAXIMA & minima, COINCIDENCE, ANALYTICAL mechanics, REACTION mechanisms (Chemistry)
Abstract

New patterns of steady-state chemical kinetics for continuously stirred-tank reactors (CSTR) have been found, i.e., intersections, maxima and coincidences, for twostep mechanism A↔B→C. There were found elegant analytical relationships for characteristics of these patterns (space times, values of concentrations and rates) allowing kinetic parameters to be easily determined. It was demonstrated that for the pair of species involved into the irreversible reaction (B and C), the space time of their corresponding concentration dependence intersection is invariant and does not depend on the initial conditions of the system. Maps of patterns are presented for visualization of their combinations and ranking in space time, and values of concentration and rates. [ABSTRACT FROM AUTHOR]

Published
2015
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154. When the final catalyst activity profile depends only on the total amount of admitted substance: Theoretical proof.

Author

Constales, Denis, Yablonsky, Gregory S., Phanawadee, Phungphai, Pongboutr, Nattapong, Limtrakul, Jumras, and Marin, Guy B.

Subjects
CATALYTIC activity, REACTION-diffusion equations, PARABOLIC differential equations, POROUS materials, MESOPOROUS materials
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 catalysts in different pulse reactors. This result can be used as a theoretical guidance for the design of systems or materials with an optimal activity profile, in particular a catalyst bed or a catalyst particle. Consequently, it can be used for understanding and developing the different diffusion-reaction processes, e.g., wet impregnation, deactivation of active materials, and so forth. © 2014 American Institute of Chemical Engineers AIChE J, 61: 31-34, 2015 [ABSTRACT FROM AUTHOR]

Published
2015
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158. OVALISATION MEASUREMENTS OF NEWLY BUILT CONCRETE TUNNELS BY MEANS OF TERRESTRIAL LASER SCANNING.

Author

Nuttens, Timothy, De Wulf, Alain, Stal, Cornelis, Constales, Denis, De Backer, Hans, and Schotte, Ken

Subjects
RAILROAD tunnels, TUNNEL design & construction, SCANNING systems, UNDERGROUND construction, WORKFLOW, RAILROAD design & construction
Abstract

This paper discusses the practical implementation of terrestrial laser scanning for ovalisation measurements of newly built concrete railway tunnels. Also an accuracy assessment is performed and then an overview of the measured deviations is given. This research is based on the ovalisation monitoring of concrete railway tunnels for the first projects of this kind in Belgium. These tunnels are measured with laser scanning during the first three months after construction. For all measurements, the concrete surface of the tunnel rings is scanned with a lateral resolution of 5 mm or higher with a phase-based Leica HDS6100 laser scanner. Based on the recorded point clouds of the tunnel rings, the deviations from ovalisation and the changes in ovalisation during the first three months after construction are determined. During this research, a workflow has been developed to determine the deviations from ovalisation and the changes during the first three months after placement. The differences that are observed between the control measurements at the different points in time show a stabilization of the construction after one or two weeks after construction. [ABSTRACT FROM AUTHOR]

Published
2011
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166. On generalized Helmholtz type equations in concentric annular domains in ℝ3

Author

Constales, Denis, Grob, Dennis, and Kraußhar, Rolf Sören

Abstract

In this paper we consider inhomogeneous generalized Helmholtz type equations (Δ+λ2)u=fin the annulus of an arbitrary ball in ℝ3with given boundary conditions, where we assume that λis an arbitrary complex number. Applying the hypercomplex operator calculus, one can express the solutions in terms of quaternionic integral operators. The quantitative entities to be determined in order to calculate these integral operators in practice are the Cauchy kernel and the Bergman kernel for eigensolutions to the Dirac operator in ℝ3. In contrast to the Cauchy kernel, which is universal for all domains in ℝ3, the Bergman kernel depends on the domain. In this paper, we give an explicit formula for the Bergman kernel of the annulus of a ball in ℝ3with arbitrary radii 0

Published
2010
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167. Reproducing kernel functions of solutions to polynomial Dirac equations in the annulus of the unit ball in Rn and applications to boundary value problems

Author

Constales, Denis, Grob, Dennis, and Krausshar, Rolf

Subjects
DOMAINS, Polynomial Dirac equations, CLIFFORD ANALYSIS, SPACES, Annular domains, Klein–Gordon equation, Reproducing kernels, Bergman and Hardy spaces, Harmonic analysis, Mathematics and Statistics, Klein-Gordon equation, Helmholtz equation, Clifford analysis
Abstract

Let D:=∑i=1n∂∂xiei be the Dirac operator in Rn and let P(X)=amXm+⋯+a1X1+a0 be a polynomial with complex coefficients. Differential equations of the form P(D)f=0 are called polynomial Dirac equations. In this paper we consider Hilbert spaces of Clifford algebra-valued functions that satisfy such a polynomial Dirac equation in annuli of the unit ball in Rn. We determine an explicit formula for the Bergman kernel for solutions of complex polynomial Dirac equations of any degree m in the annulus of radii μ and 1 where μ∈]0,1[. We further give formulas for the Szegö kernel for solutions to polynomial Dirac equations of degree m

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