Direct methods for the solution of systems of linear equations with sparse coefficient matrix and related topics Final report, 1 Dec. 1967 - 31 Aug. 1970

Deriving algorithms for computations involving sparse matrice

Sorting and ordering sparse linear systems

Transformations of sparse linear systems by row-column permutations are considered and various algorithms are constructed to transform arbitrary symmetric positive definite sparse matrices, as well as matrices in band form, doubly bordered band form, and doubly bordered block diagonal form

Product form of inverses of sparse matrices Progress report

Product form of inverses of sparse matrices - matrix algebra and linear programming code

Solution of a generalized diffusion equation by difference methods

Thesis (Ph.D.)--Boston Universit

The effect of temperature and ventilation condition on the toxic product yields from burning polymers

A major cause of death or permanent injury in fires is inhalation of toxic gases. Moreover, every fire is unique, and the range of products, highly dependant on fire conditions, produces a wide variety of toxic and irritant species responsible for the most fire fatalities. Therefore, to fully understand each contribution to the toxicity it is necessary to quantify the decomposition products of the material under the test. Fires can be divided into a number of stages from smouldering combustion to early well-ventilated flaming through to fully developed under-ventilated flaming. These stages can be replicated by certain bench-scale physical fire models using different fuel-to-oxygen ratios, controlled by the primary air flow, and expressed in terms of the equivalence ratio (the actual fuel/air ratio divided by the stoichiometric fuel/air ratio). This work presents combustion product yields generated using a small-scale fire model. The Purser Furnace apparatus (BS7990 and ISO TS 19700) enables different fire stages to be created. Identification and quantification of combustion gases and particularly their toxic components from different fire scenarios were undertaken by continuous Fourier transform infrared spectroscopy. The relationship between type of the fire particularly the temperature and ventilation conditions and the toxic product yields for four bulk polymers, low-density polyethylene, polystyrene (PS), Nylon 6.6 and polyvinyl chloride (PVC) is reported. For all the polymers tested, except PVC, there is a dramatic increase in the yield of products of incomplete combustion (CO and hydrocarbons) with increase in equivalence ratio, as might be expected. For PVC there is a consistently high level of products of incomplete combustion arising both from flame inhibition by HCl and oxygen depletion. There is a low sensitivity to furnace temperature over the range 650–850°C, except that at 650°C PS shows an unexpectedly high yield of CO under well-ventilated conditions and PVC shows a slightly higher hydrocarbon yield. This demonstrates the dependence of toxic product yields on the equivalence ratio, and the lack of dependence on furnace temperature, within this range

Computational techniques for inverse problems in kidney modeling

AbstractIn order to understand the concentrating mechanism of the mammalian kidneys, it is necessary to study the relationship between the parameter vector h (permeabilities of water and solutes) and the corresponding vector of concentration profiles V. We consider the inverse problem: determine h from a given V. This problem is ill-posed. Therefore, the regularization methods must be used to circumvent the ill-conditioning. We show how the Levenberg-Tikhonov-Marquard method with the Sobolev norm can be used to handle the inverse problem

The convergence of quasi-Gauss-Newton methods for nonlinear problems

AbstractQuasi-Gauss-Newton methods for nonlinear equations are investigated. A Quasi-Gauss-Newton method is proposed. In this method, the Jacobian is modified by a convex combination of Broyden's update and a weighted update. The convergence of the method described by Wang and Tewarson in [1] and the proposed method is proved. Computational evidence is given in support of the relative efficiency of the proposed method

Effects of the generic nature of polymers on their fire behavior

International audienceFire behavior of four aliphatic and two aromatic C, H, O, N, S, and Cl atom containing polymers has been examined. Experiments were performed in three ASTM E 2058 Fire Propagation Apparatuses. The differences in the ignition behavior of polymers were found to be mainly due to differences in the ignition temperature. Chemical effects appear to contribute about 25 % towards the ignition resistance of the polymers. For thermoplastics, formation of polymer melt and its burning as a pool fire was found to increase the fire intensity by factors of two to four. The combustion efficiency and generation efficiency of CO2 were found to decrease and the generation efficiencies of CO and smoke were found to increase by changes in the generic nature of the polymers (aliphatic to aromatic to halogenated). About four times as much carbon atoms in the polymers converted to smoke than converted to CO. Large-scale fire propagation behavior of polymers was characterized by a Fire Propagation Index (FPI). The FPI values of melting type thermoplastics (showing rapid-fire propagation behavior) were high, whereas they were low for the engineered charring type and halogenated polymers (showing either slow or decelerating fire propagation behavior)