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Mathematical Study (mathematical + study)

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Engineering50%

Selected Abstracts

A study on the convergence of least-squares meshfree method under inaccurate integration

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003
Sang-Hoon Park
Abstract In the authors' previous work, it has been shown through numerical examples that the least-squares meshfree method (LSMFM) is highly robust to the integration errors while the Galerkin meshfree method is very sensitive to them. A mathematical study on the convergence of the solution of LSMFM under inaccurate integration is presented. New measures are introduced to take into account the integration errors in the error estimates. It is shown that, in LSMFM, solution errors are bounded by approximation errors even when integration is not accurate. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An experimental and mathematical study of efforts of a novel photovoltaic-Trombe wall on a test room

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 6 2008
Ji Jie
Abstract A novel photovoltaic-Trombe wall (PV-TW) is proposed and investigated experimentally and theoretically in this paper. The PV-TW was installed at the south-facing external wall of an environmental chamber that carried two identical test rooms. Both of the test rooms have a double window of the same size. One test room was installed with the PV-TW (known as the PV-TW room), and the other without PV-TW (known as the reference room). The influence of the PV-TW on the thermal environment of the test room was investigated under different operating conditions. The experimental results show the dual benefits of the PV-TW system: improving the room thermal condition and at the same time generating electricity. Compared with the reference room, the maximum indoor temperature was found to be 5,7°C higher in winter, and the daily electrical output reached about 0.3,kWh with a PV cell area of 0.72,m2. Also, a detailed model is given to evaluate the performance of PV-TW theoretically, and the PV-TW room is simulated under one certain operating condition. The simulated and measured air temperatures of PV-TW room are found to be in good agreement. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Experimental and mathematical study of the influence of growth factors on the growth kinetics of adult human articular chondrocytes,

JOURNAL OF CELLULAR PHYSIOLOGY, Issue 3 2005
Andrea Barbero
This study aimed at determining how kinetic parameters of adult human articular chondrocytes (AHAC) growth are modulated by the growth factor combination TGF,1, FGF-2, and PDGF BB (TFP), recently shown to stimulate AHAC proliferation. AHAC, isolated from cartilage biopsies of three individuals, were cultured in medium without (CTR) or with TFP. For growth curves, AHAC were seeded at 1,000 cells/cm2 and cultured for 12 days, with cell numbers measured fluorimetrically in the same wells every 12 h. For microcolony tests, AHAC were seeded at 2.5 cells/cm2 and cultured for 6 days, with cell numbers determined for each microcolony by phase contrast microscopy every 8 h. A mathematical model combining delay and logistic equations was developed to capture the growth kinetic parameters and to enable the description of the complete growth process of the cell culture. As compared to CTR medium, the presence of TFP increased the number of cells/well starting from the fifth day of culture, and a four-fold larger cell number was reached at confluency. For single microcolonies, TFP reduced the time for the first cell division by 26.6%, the time for subsequent cell divisions (generation time) by 16.8%, and the percentage of quiescent cells (Qc) by 42.5%. The mathematical model fitted well the experimental data of the growth kinetic. Finally, using both microcolony tests and the mathematical model, we determined that prolonged cell expansion induces an enrichment of AHAC with shorter first division time, but not of those with shorter generation time. © 2005 Wiley-Liss, Inc. [source]

The Andersen thermostat in molecular dynamics

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 1 2008
Weinan E
We carry out a mathematical study of the Andersen thermostat [1], which is a frequently used tool in molecular dynamics. After reformulating the continuous- and discrete-time Andersen dynamics, we prove that in both cases the Andersen dynamics is uniformly ergodic. A detailed numerical analysis is presented, establishing the rate of convergence of most commonly used numerical algorithms for the Andersen thermostat. Transport properties such as the diffusion constant are also investigated. It is proved for the Lorentz gas model where there is intrinsic diffusion that the diffusion coefficient calculated using the Andersen thermostat converges to the true diffusion coefficient in the limit of vanishing collision frequency in the Andersen thermostat. © 2007 Wiley Periodicals, Inc. [source]