Using the machinery of Lie theory (groups and algebras) applied to the Navier-Stokes equations a number of exact solutions for the steady state are derived in (two) three dimensions. It is then shown how each of these generates an infinite number of time-dependent solutions via (three) four arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.
Catalytic fixed-bed reactors with a low tube-to-particle diameter ratio are widely used in industrial applications. The heterogeneous packing morphology in this reactor type causes local flow phenomena that significantly affect the reactor performance.Particle-resolved computational fluid dynamics has become a predictive numerical method to analyze the flow, temperature, and species field, as well as local reaction rates spatially and may, therefore, be used as a design tool to develop new improved catalyst shapes. Most validation studies which have been presented in the past were limited to simple particle shapes. More complex catalyst shapes are supposed to increase the reactor performance. A workflow for the simulation of fixed-bed reactors filled with various industrially relevant complex particle shapes is presented and validated against experimental data in terms of bed voidage and pressure drop. Industrially relevant loading strategies are numerically replicated and their impact on particle orientation and bed voidage is investigated.
K E Y W O R D Sbed voidage, fixed-bed reactor, numerical modeling, particle orientation, pressure drop
The present study, based on neurohistological techniques (Nissl-staining, Golgi-impregnation), focuses on the cytoarchitecture of the corticoid complex in the strawberry finch, Estrilda amandava. This complex in birds occupies the dorsolateral surface of the telencephalic pallium and remains subdivided into an intermediate corticoid area (CI) and a dorsolateral corticoid area (CDL). The CDL in the strawberry finch is a thin superficial part of the caudal pallium adjoining the medially situated hippocampal formation, whereas the CI is demarcated between the CDL and the parahippocampal area of telencephalon. Neurons of the corticoid complex are classified into three main cell groups: predominant projection neurons, local circuit neurons and stellate neurons. The spinous projection neurons send out distant projecting axons that typically extend several varicose collaterals. Most of these collaterals lie parallel to the ventricle. These neurons are subclassified into pyramidal neurons (localized only in the CI) and multipolar neurons (present in both the CI and CDL). The CDL also possesses small and medium-sized horizontal cells, which are bitufted or multipolar with smooth, moderately branching dendrites. The aspinous local circuit neurons extend short axons that ramify locally. Stellate neurons have sparse spinous dendrites and locally arborizing axons. The corticoid complex of birds corresponds to the lateral cerebral cortex of lizards and to the entorhinal cortex of mammals on the basis of neuronal morphology and bidirectional connections between adjacent areas.
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