Abstract: The spiral angle of the elementary cellulose fibril in
the wood cell wall, often called microfibril angle, (MFA). Microfibril
angle in hardwood is one of the key determinants of solid timber
performance due to its strong influence on the stiffness, strength,
shrinkage, swelling, thermal-dynamics mechanical properties and
dimensional stability of wood. Variation of MFA (degree) in the S2
layer of the cell walls among Acacia mangium trees was determined
using small-angle X-ray scattering (SAXS). The length and
orientation of the microfibrils of the cell walls in the irradiated
volume of the thin samples are measured using SAXS and optical
microscope for 3D surface measurement. The undetermined
parameters in the analysis are the MFA, (M) and the standard
deviation (σФ) of the intensity distribution arising from the wandering
of the fibril orientation about the mean value. Nine separate pairs of
values are determined for nine different values of the angle of the
incidence of the X-ray beam relative to the normal to the radial
direction in the sample. The results show good agreement. The
curve distribution of scattered intensity for the real cell wall structure
is compared with that calculated with that assembly of rectangular
cells with the same ratio of transverse to radial cell wall length. It is
demonstrated that for β = 45°, the peaks in the curve intensity
distribution for the real and the rectangular cells coincide. If this
peak position is Ф45, then the MFA can be determined from the
relation M = tan-1 (tan Ф45 / cos 45°), which is precise for rectangular
cells. It was found that 92.93% of the variation of MFA can be
attributed to the distance from pith to bark. Here we shall present our
results of the MFA in the cell wall with respect to its shape, structure
and the distance from pith to park as an important fast check and yet
accurate towards the quality of wood, its uses and application.
Abstract: Plasmodium vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.