FORCED CONVECTION TO LAMINAR FLOW OF LIQUID EGG YOLK IN CIRCULAR AND ANNULAR DUCTS

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

Dissociation of circadian and light inhibition of melatonin release through forced desynchronization in the rat

Pineal melatonin release exhibits a circadian rhythm with a tight nocturnal pattern. Melatonin synthesis is regulated by the master circadian clock within the hypothalamic suprachiasmatic nucleus (SCN) and is also directly inhibited by light. The SCN is necessary for both circadian regulation and light inhibition of melatonin synthesis and thus it has been difficult to isolate these two regulatory limbs to define the output pathways by which the SCN conveys circadian and light phase information to the pineal. A 22-h light-dark (LD) cycle forced desynchrony protocol leads to the stable dissociation of rhythmic clock gene expression within the ventrolateral SCN (vlSCN) and the dorsomedial SCN (dmSCN). In the present study, we have used this protocol to assess the pattern of melatonin release under forced desynchronization of these SCN subregions. In light of our reported patterns of clock gene expression in the forced desynchronized rat, we propose that the vlSCN oscillator entrains to the 22-h LD cycle whereas the dmSCN shows relative coordination to the light-entrained vlSCN, and that this dual-oscillator configuration accounts for the pattern of melatonin release. We present a simple mathematical model in which the relative coordination of a single oscillator within the dmSCN to a single light-entrained oscillator within the vlSCN faithfully portrays the circadian phase, duration and amplitude of melatonin release under forced desynchronization. Our results underscore the importance of the SCN`s subregional organization to both photic input processing and rhythmic output control.

SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.