Faculty of Science - Mahidol University
Faculty of Science - Mahidol University
Faculty of Science - Mahidol University
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Mahidol</strong> <strong>University</strong> Annual Research Abstracts, Vol. 33 297<br />
neuroendocrine ensemble exhibits prominent pulsatile secretory<br />
patterns governed by nonlinear and time-delayed feedforward and<br />
feedback signal interchanges. Formulation and subsequent<br />
bifurcation analysis <strong>of</strong> the model provide a qualitative and<br />
mathematical frame work for a better understanding <strong>of</strong> the delayed<br />
responsive mechanisms as well as the dynamic variations in different<br />
pathological situations.<br />
(Mathematical Medicine and Biology, 22(1)(2005) 15-33.)<br />
MATHEMATICAL MODELS FOR PRESSURE<br />
CONTROLLED VENTILATION OF OLEIC ACID-<br />
INJURED PIGS (NO. 777)<br />
Crooke P.S. 1 , Kongkul K. 2 , Lenbury Y. 2 , Adams A.B. 3 , Carter<br />
C.S. 3 , Marini J.J. 3 , Hotchkiss J.R. 3<br />
1 Department <strong>of</strong> Mathematics, Vanderbilt <strong>University</strong>, Nashville,<br />
TN 37240, USA. E-mail : pscrooke@math.vanderbilt.edu;<br />
2 Department <strong>of</strong> Mathematics, <strong>Faculty</strong> <strong>of</strong> <strong>Science</strong>, <strong>Mahidol</strong><br />
<strong>University</strong>, Bangkok 10400, Thailand. E-mail :<br />
konvika@tsu.ac.th, scylb@mahidol.ac.th; 3 Pulmonary and<br />
Critical Care Medicine, Regions Hospital and <strong>University</strong> <strong>of</strong><br />
Minnesota, St. Paul MN 55101 USA. E-mail :<br />
hotchkissjr@upmc.edu<br />
Key words : oleic acid injury, mathematical model, variable<br />
compliance<br />
One-compartment, mathematical models for pressure<br />
controlled ventilation, incorporating volume dependent<br />
compliances, linear and nonlinear resistances, are constructed and<br />
compared with data obtained from healthy and (oleic acid) lunginjured<br />
pigs. Experimental data are used to find parameters in the<br />
mathematical models and were collected in two forms. Firstly, the<br />
Pe-V curves for healthy and lung injured pigs were constructed;<br />
these dta are used to compute compliance functions for each animal.<br />
Secondly, dynamic data from pressure controlled ventilation for a<br />
variety <strong>of</strong> applied pressures are used to estimate resistance parameters<br />
in the models. The models were then compared against the collected<br />
dynamic data. The best mathematical models are ones with<br />
compliance functions <strong>of</strong> the form C(V) = a + bV where a and b are<br />
constants obtained from the Pe-V curves and the resistive pressures<br />
during inspiration change from a linear relation Pr = RQ to nonlinear<br />
relation Pr = RQ where Q is the flow into the one-compartment lung<br />
and is a positive number. The form <strong>of</strong> the resistance terms in the<br />
mathematical models indicate the possible presence <strong>of</strong> gas-liquid<br />
foams in the experimental data.<br />
(Mathematical Medicine and Biology 22 (2005) 99-112)<br />
DELAY EFFECT IN MODELS OF POPULATION<br />
GROWTH (NO. 778)<br />
Giang D.V. 1 , Lenbury Y. 2 , Seidman T.I. 3<br />
1 Hanoi Insititue <strong>of</strong> Mathematics, 18 Hoang Quoc Viet, 10307<br />
Hanoi, Vietnam, E-mai dvgiang@math.ac.vn ; 2 Department <strong>of</strong><br />
Mathematics, <strong>Faculty</strong> <strong>of</strong> <strong>Science</strong>, <strong>Mahidol</strong> <strong>University</strong>, Bangkok<br />
10400, Thailand. E-mail : scylb@mahidol.ac.th; 3 Department<br />
<strong>of</strong> Mathematics and Statistics, <strong>University</strong> <strong>of</strong> Maryland Baltimore<br />
County, Baltimore, MD 21250 USA. E-mail<br />
Seidman@math.umbc.edu<br />
Key words : Delay differential equations, Comparison theorem Oneparameter<br />
semi-group<br />
Frist we systematize earlier results on the global stability<br />
<strong>of</strong> the model x + μx = f(x(‘ – τ)) <strong>of</strong> population growth. Second, we<br />
investigate the effect <strong>of</strong> delay on the asymptotic behavior when the<br />
nonlinearity f is a unimodal function. Our results can be applied to<br />
several population models [Elements <strong>of</strong> Mathematical Ecology, 2001<br />
[7]; Appl. Anal. 43 (1992) 109-124; Math. Comput. Modelling, in<br />
press; Funkt. Boil. Med. 256 (1982) 156-164; Math. Comput.<br />
Modelling 35 (2002) 719-731; Mat. Stos. 6 (1976) 25-40] because<br />
the function f does not need to be monotone or differentiable.<br />
Specifically, our results generalize earlier result <strong>of</strong> [Delay Differential<br />
Equations with Applications in Population Dynamics 1993], since<br />
our function f may not be differentiable.<br />
(Journal <strong>of</strong> Mathematical Analysis and Applications 305 (2005)<br />
631-643.)<br />
THREE-DIMENSION MAGNETOTELLURIC<br />
INVASION : DATA SPACE METHOD (NO. 779)<br />
Siripunvaraporn W. 1 , Egbert G. 2 , Lenbury Y. 3 , Uyeshima M. 4<br />
1 Department <strong>of</strong> Physics, <strong>Faculty</strong> <strong>of</strong> <strong>Science</strong>, <strong>Mahidol</strong> <strong>University</strong>,<br />
Bangkok 10400, Thailand. E-mail : scwsp@mahidol.ac.th;<br />
2 College <strong>of</strong> Oceanic and Atmospheric <strong>Science</strong>s, Oregon State<br />
<strong>University</strong>, Corvallis OR 97331, USA; 3 Department <strong>of</strong><br />
Mathematics <strong>Faculty</strong> <strong>of</strong> <strong>Science</strong>, <strong>Mahidol</strong> <strong>University</strong>, Bangkok<br />
10400, Thailand. E-mail scylb@mahidol.ac.th; 4 Earthquake<br />
Research Insitute, <strong>University</strong> <strong>of</strong> Tokyo, 1-1-1 Yayoi, Bunkyoku,<br />
Tokyo 113-0032, Japan.<br />
Key words : Magnetotellurics, Data-space method, 3D inversion,<br />
Occam’s inversion<br />
A three-dimensional magnetotelluric (MT) minimum<br />
structure inversion algorithm has been developed based on a dataspace<br />
variant <strong>of</strong> the Occam approach. Computational costs associated<br />
with construction and inversion <strong>of</strong> model-space matrices make a<br />
model-space Occam approach to 3D MT inversion impractical. These<br />
difficulties are overcome with a data-space approach,where matrix<br />
dimensions depend on the size <strong>of</strong> the data set, rather than the number<br />
<strong>of</strong> model parameters. With the transformation to data space it<br />
becomes feasible to invert modest 3D MT data sets on a PC. To<br />
reduce computational time, a relaxed convergence criterion is used<br />
for the iterative forward modeling code used to compute the<br />
sensitivity matrix. This allows reduction in computational time by<br />
more than 70% without affecting the inversion results. Numerical<br />
experiments with synthetic data show that reasonable fits can be<br />
obtained within a small number <strong>of</strong> iterations, with a few additional<br />
iterations required to eliminate unnecessary structure and find the<br />
model with minimum norm.<br />
(Physics <strong>of</strong> the Earth and Planetary Interiors. 150 (2005) 3-14.)<br />
PDF created with FinePrint pdfFactory Pro trial version http://www.pdffactory.com