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An example of the satisfiability problem in the continuous structure

Balcer Marek

Silesian Journal of Pure and Applied Mathematics

2020

vol. 10, iss. 1

121--131

The paper presents and demonstrates the theorem showing the equivalence of the problem of the verifiability test of a logical expression in the discrete model N of the logic with the search for the minimum value of a continuous function generated by this expression in the structure N, which is a simple extension of M. Theoretical considerations are illustrated by the example of a certain semi-heuristic algorithm seeking the minimum value of function ϕ with a short statistics of its.

Trendy w architekturze cyfrowej

Czernik E.

Przestrzeń i Forma

2011

nr 15

155-162

Architektura stoi u progu zupełnie nowej ery - ten etap to wręcz nowy paradygmat. Organiczne formy, wbrew szeroko panującej opinii, to nie trend formalny, lecz cyfrowo wygenerowana optymalizacja. Artykuł jest wstępem do rozważań związanych z architekturą cyfrową - traktuje o jej potencjale, możliwościach i ograniczeniach. Nowe cyfrowe technologie w architekturze to potężne narzędzie i olbrzymia odpowiedzialność.

Architecture is at the threshold of an entirely new era - this moment is indeed a new paradigm. Organic forms, contrary to a widely popular opinion, are not formal activities, but digitally generated optimization. This article is an introduction to new digital architecture - about its potential, possibilities and limitations.

Computational fluid dynamics modelling of buoyancy induced viscoelastic flow in a porous medium with magnetic field effects

Beg O. A., Takhar H. S., Kumari M., Nath G.

International Journal of Applied Mechanics and Engineering

2001

Vol. 6, no 1

187-210

A 2-dimensional computational fluid dynamics analysis of steady state thermal boundary layer flow of a second order non-Newtonian fluid past a horizontal wedge in a Brinkman-Darcy porous medium, in the presence of a transverse magnetic field, is presented. The governing equations are transformed from Cartesian coordinates (x,y) into a sixth order system of partial differential equations in a 'ksi'-n coordinate system. These complex equations are then reduced to a set of six first order equations which are solved using the robust Keller finite difference method, and a block tridiagonal iterative solver, SOLV6. It is shown that heat transfer magnitude is depressed by magnetic field parameter (Hartmann number, Ha) and also considerably reduced with increasing viscoelasticity parameter (K). Surface shear stresses are also reported to fall considerably with increase in viscoelasticity of the fluid. Effects of other hydrodynamic and thermal parameters on the flow are discussed in detail.