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Full-Text Articles in Physical Sciences and Mathematics
A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models - A Trend Towards Simplicity, John A. Adam, John A. Sokolowski, Catherine M. Banks
A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models - A Trend Towards Simplicity, John A. Adam, John A. Sokolowski, Catherine M. Banks
Mathematics & Statistics Faculty Publications
A sequence of analytic mathematical models has been developed in the context of the "low-level insurgency" in Colombia, from 1993 to the present. They are based on generalizations of the two-population "predator-prey" model commonly applied in ecological modeling, and interestingly, the less sophisticated models yield more insight into the problem than the more complicated ones, but the formalism is available to adapt the model "upwards" in the event that more data becomes available, or as the situation increases in complexity. Specifically, so-called "forcing terms" were included initially in the coupled differential equations to represent the effects of government policies towards …
A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam
A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam
Mathematics & Statistics Faculty Publications
Recently, a one-dimensional model was developed which gives a reasonable explanation for the existence of a Critical Size Defect (CSD) in certain animals [1]. In this paper, we examine the more realistic two-dimensional model of a circular wound of uniform depth to see what modifications are to be found, as compared with the one-dimensional model, in studying the CSD phenomenon. It transpires that the range of CSD sizes for a reasonable estimate of parameter values is 1 mm-1 cm. More realistic estimates await the appropriate experimental data.
A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam
A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam
Mathematics & Statistics Faculty Publications
This paper is an attempt to construct a simple mathematical model of wound healing/tissue regeneration which reproduces some of the known qualitative features of those phenomena. It does not address the time development of the wound in any way, but does examine conditions (e.g., wound size) under which such healing may occur. Two related one-dimensional models are examined here. The first, and simpler of the two corresponds to a "swath" of tissue (or more realistically in this case, bone) removed from an infinite plane of tissue in which only a thin band of tissue at the wound edges takes part …
Antiplane Shear Of A Strip Containing A Staggered Array Of Rigid Line Inclusions, G. Kerr, G. Melrose, J. Tweed
Antiplane Shear Of A Strip Containing A Staggered Array Of Rigid Line Inclusions, G. Kerr, G. Melrose, J. Tweed
Mathematics & Statistics Faculty Publications
Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. it should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite …
Data Compression Based On The Cubic B-Spline Wavelet With Uniform Two-Scale Relation, S. K. Yang, C. H. Cooke
Data Compression Based On The Cubic B-Spline Wavelet With Uniform Two-Scale Relation, S. K. Yang, C. H. Cooke
Mathematics & Statistics Faculty Publications
The aim of this paper is to investigate the potential artificial compression which can be achieved using an interval multiresolution analysis based on a semiorthogonal cubic B-spline wavelet. The Chui-Quak [1] spline multiresolution analysis for the finite interval has been modified [2] so as to be characterized by natural spline projection and uniform two-scale relation. Strengths and weaknesses of the semiorthogonal wavelet as regards artificial compression and data smoothing by the method of thresholding wavelet coefficients are indicated.
Temporal Model Of An Optically Pumped Co-Doped Solid State Laser, T. G. Wangler, J. J. Swetits, A. M. Buoncristiani
Temporal Model Of An Optically Pumped Co-Doped Solid State Laser, T. G. Wangler, J. J. Swetits, A. M. Buoncristiani
Mathematics & Statistics Faculty Publications
Currently, research is being conducted on the optical properties of materials associated with the development of solid-state lasers in the 2 micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are obtained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.