Frederic Wan - Academia.edu (original) (raw)
Papers by Frederic Wan
Studies in Applied Mathematics, Mar 1, 1973
SIAM journal on scientific and statistical computing, Mar 1, 1980
An efficient method is developed for the accurate numerical solution of the nonlinear boundary va... more An efficient method is developed for the accurate numerical solution of the nonlinear boundary value problem (BVP) governing the optimal economic growth with a finite multi-grade deposit of nonrenewable and nonaugmentable essential resource under R. M. Solow's maximum sustainable per head consumption level criterion. Unusual computational features of the BVP include: (1) the semi-infinite (time) domain of the problem is divided into a number of subintervals of unknown (and unequal) lengths with a different set of differential equations for each subinterval and with the subinterval lengths to be determined in the solution process; (2) some solution components are known to be unbounded at infinity while others decay very slowly,and (3) in a certain range of parameter values, a previously used solution method is known to be sensitive to boundary data. The new method is used to generate new accurate numerical solutions for single-grade resource problems with a high unit extraction cost and more accurate results for two-grade deposit problems previously investigated. As well, it enables us to investigate for the first time problems with more than two grades of deposits. The implications of these new results are analyzed.
AIAA Journal, Mar 1, 1968
Royal Society Open Science, Feb 1, 2016
This paper is concerned with the elastodynamics of embryonic epidermal wound closing. Underlying ... more This paper is concerned with the elastodynamics of embryonic epidermal wound closing. Underlying the recovery process for this type of wounds is a mechanism of wound recognition through directed cell-to-cell signaling. The observed actin filament realignment induced by the biological signals leads to a purse-string effect and the resulting (unknown) “active stresses. ” The circumferential contraction of the epidermis surrounding the wound is then determined by the laws of mechanics and propagation properties of the relevant cell–cell signaling that decays with distance. With the wound known to retract for a short period immediately after infliction, the quasi-equilibrium configuration reached during this initial phase serves as the initial condition for the dynamic wound closing phase. A small strain variation of the Murray–Sherratt model of the quasi-equilibrium problem will be formulated for speedy computation of this initial state at the inception of the wound closure phase, with...
Our research focuses on the study of HIV cell dynamics in healthy bodies and the immune response.... more Our research focuses on the study of HIV cell dynamics in healthy bodies and the immune response. Our goal is to create a mathematical system that models the dynamics between the immune system’s CTL cells and HIV with the complications of time delay between infection and response. The expansion of the model allows our method to reflect a more realistic biological system. Varying the parameters in the simulations within the system will help us understand and predict the behavior of the CTL response and the potential viral long-term nonprogression.
SIAM Journal on Scientific and Statistical Computing, 1980
An efficient method is developed for the accurate numerical solution of the nonlinear boundary va... more An efficient method is developed for the accurate numerical solution of the nonlinear boundary value problem (BVP) governing the optimal economic growth with a finite multi-grade deposit of nonrenewable and nonaugmentable essential resource under R. M. Solow's maximum sustainable per head consumption level criterion. Unusual computational features of the BVP include: (1) the semi-infinite (time) domain of the problem is divided into a number of subintervals of unknown (and unequal) lengths with a different set of differential equations for each subinterval and with the subinterval lengths to be determined in the solution process; (2) some solution components are known to be unbounded at infinity while others decay very slowly,and (3) in a certain range of parameter values, a previously used solution method is known to be sensitive to boundary data. The new method is used to generate new accurate numerical solutions for single-grade resource problems with a high unit extraction cost and more accurate results for two-grade deposit problems previously investigated. As well, it enables us to investigate for the first time problems with more than two grades of deposits. The implications of these new results are analyzed.
![Research paper thumbnail of Author’s response to Comment by Yang Gao and Min-Zhong Wang on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123]](https://attachments.academia-assets.com/119576135/thumbnails/1.jpg)
](International Journal of Solids and Structures, 2006
Royal Society Open Science, 2016
Studies in Applied Mathematics, 1993
The method of decaying residual solution is applied to obtain an approximate interior solution fo... more The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.
Zeitschrift für angewandte Mathematik und Physik ZAMP, 1966
Zusammenfassung Es wird gezeigt, wie man gewisse bekannte Elastizitätsgleichungen der linearen Sc... more Zusammenfassung Es wird gezeigt, wie man gewisse bekannte Elastizitätsgleichungen der linearen Schalentheorie [2] umschreiben kann mit Hilfe von verallgemeinerten Dehnungskomponenten und verallgemeinerten Energiefunktionen, welche von dem erstgenannten Verfasser [3] eingeführt worden sind.
Zeitschrift für angewandte Mathematik und Physik ZAMP, 1971
ZusammenfassungDie Klasse von Problemen der linearen Theorie für schraubenförmige Schalen mit Spa... more ZusammenfassungDie Klasse von Problemen der linearen Theorie für schraubenförmige Schalen mit Spannungen und Verzerrungen von der Formeiθf(r) wird auf ein Randwertproblem für ein System von zwei gewöhnlichen Differentialgleichungen dritter Ordnung reduziert. Für Schalen unter dem Einfluß von Endbiegemomenten werden Lösungen mit Hilfe von Störungsrechnung sowie asymptotische Lösungen bestimmt.
Journal of Engineering Materials and Technology, 2007
To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, st... more To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, stress and strain must be determined experimentally for the same configurations. Such experiments are hindered by the inherent theoretical complexity of continuum mechanics, and by the technical difficulties of effecting external stress loads or body forces on the tissue without invasion, especially on a small scale. An understanding of appropriate mechanical problems and their solutions can help the experimentalist overcome these difficulties to a certain extent. Based on recent work on fiber-reinforced material, we formulate a constitutive theory for the root of different angiosperm species and suggest a set of loading conditions to determine the parameter values in a specific tissue sample. The loading conditions are formulated with a view toward experimental realization in vivo or with minimal invasion. For each loading condition, we formulate the corresponding mechanical problem and s...
Mathematical Biosciences and Engineering, 2008
Journal of Mechanics of Materials and Structures, 2011
Dedicated to Charles and Marie-Louise Steele for their years of outstanding management of IJSS an... more Dedicated to Charles and Marie-Louise Steele for their years of outstanding management of IJSS and JoMMS, and for their more than forty years of warm friendship with the last author.
Journal of Applied Mechanics, Sep 1, 1988
Necessary conditions have been established recently for the prescribed data alon the cylindrical ... more Necessary conditions have been established recently for the prescribed data alon the cylindrical edge(s) of an elastic flat plate to induce only an exponentially deca ing elastostatic state. The present paper describes how these conditions may be use to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary condition for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first tim how the stretching action in the plate interior induced by transverse loads can b
Bulletin of Mathematical Biology, Feb 17, 2021
Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch... more Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch from a dividing form (reticulate body or RB) to an infectious form (elementary body or EB). RBs replicate by binary fission within an infected host cell, but there is a delay before RBs convert into EBs for spread to a new host cell. We developed stochastic optimal control models of the Chlamydia developmental cycle to examine factors that control the number of EBs produced. These factors included the probability and timing of conversion, and the duration of the developmental cycle before the host cell lyses. Our mathematical analysis shows that the observed delay in RB-to-EB conversion is important for maximizing EB production by the end of the intracellular infection.
In this paper, the effects of a conventional form of negative feedback on receptor synthesis rate... more In this paper, the effects of a conventional form of negative feedback on receptor synthesis rate as a mechanism to induce robustness of biological development of the Drosophila wing imaginal disc is analyzed through the initial-boundary value problem in a basic partial differential equation model for the extracellular biological development activities. The existence, uniqueness, linear stability and monotonicity of the steady state signaling gradient are established rigorously. Solutions are then obtained for a special case of the steady state problem to show explicitly the effects of the chosen form of negative feedback. It is evident from the results that the principal effect of such a feedback mechanism is to render the signaling bound morphogen gradient more uniformly distributed except for a narrow layer adjacent to the edge of the posterior compartment of the wing disc. While the change in the magnitude of the maximum signaling morphogen concentration near the ligand source may be kept at an acceptable level, the leveling and flattening of the gradient render it less differential in space (except in the boundary layer) and hence more deviating from the desired gradient for the target biological pattern. The conclusion is then shown to apply to the general case with the help of the theoretical results on monotonicity. These results suggest that negative feedback on the receptor synthesis rate of the chosen form is not effective for promoting robustness. In fact, it drives the system somewhat in the opposite direction, a conclusion supported by the simulation results. The findings in turn suggest more useful forms of the negative feedback for mediating receptor synthesis to offset a higher ligand synthesis rate for our types of systems.
Recent data collected on the Chlamydia Trachomatis life cycle show an initial period of no RB-to-... more Recent data collected on the Chlamydia Trachomatis life cycle show an initial period of no RB-to-EB conversion. This and other features of the observed bacterial life cycle are postulated to be consequences of the bacteria's drive for Darwinian survival. Stochastic optimal control models formulated herein in fact lead to an initial conversion holiday that support this proposition.
Studies in Applied Mathematics, Mar 1, 1973
SIAM journal on scientific and statistical computing, Mar 1, 1980
An efficient method is developed for the accurate numerical solution of the nonlinear boundary va... more An efficient method is developed for the accurate numerical solution of the nonlinear boundary value problem (BVP) governing the optimal economic growth with a finite multi-grade deposit of nonrenewable and nonaugmentable essential resource under R. M. Solow's maximum sustainable per head consumption level criterion. Unusual computational features of the BVP include: (1) the semi-infinite (time) domain of the problem is divided into a number of subintervals of unknown (and unequal) lengths with a different set of differential equations for each subinterval and with the subinterval lengths to be determined in the solution process; (2) some solution components are known to be unbounded at infinity while others decay very slowly,and (3) in a certain range of parameter values, a previously used solution method is known to be sensitive to boundary data. The new method is used to generate new accurate numerical solutions for single-grade resource problems with a high unit extraction cost and more accurate results for two-grade deposit problems previously investigated. As well, it enables us to investigate for the first time problems with more than two grades of deposits. The implications of these new results are analyzed.
AIAA Journal, Mar 1, 1968
Royal Society Open Science, Feb 1, 2016
This paper is concerned with the elastodynamics of embryonic epidermal wound closing. Underlying ... more This paper is concerned with the elastodynamics of embryonic epidermal wound closing. Underlying the recovery process for this type of wounds is a mechanism of wound recognition through directed cell-to-cell signaling. The observed actin filament realignment induced by the biological signals leads to a purse-string effect and the resulting (unknown) “active stresses. ” The circumferential contraction of the epidermis surrounding the wound is then determined by the laws of mechanics and propagation properties of the relevant cell–cell signaling that decays with distance. With the wound known to retract for a short period immediately after infliction, the quasi-equilibrium configuration reached during this initial phase serves as the initial condition for the dynamic wound closing phase. A small strain variation of the Murray–Sherratt model of the quasi-equilibrium problem will be formulated for speedy computation of this initial state at the inception of the wound closure phase, with...
Our research focuses on the study of HIV cell dynamics in healthy bodies and the immune response.... more Our research focuses on the study of HIV cell dynamics in healthy bodies and the immune response. Our goal is to create a mathematical system that models the dynamics between the immune system’s CTL cells and HIV with the complications of time delay between infection and response. The expansion of the model allows our method to reflect a more realistic biological system. Varying the parameters in the simulations within the system will help us understand and predict the behavior of the CTL response and the potential viral long-term nonprogression.
SIAM Journal on Scientific and Statistical Computing, 1980
An efficient method is developed for the accurate numerical solution of the nonlinear boundary va... more An efficient method is developed for the accurate numerical solution of the nonlinear boundary value problem (BVP) governing the optimal economic growth with a finite multi-grade deposit of nonrenewable and nonaugmentable essential resource under R. M. Solow's maximum sustainable per head consumption level criterion. Unusual computational features of the BVP include: (1) the semi-infinite (time) domain of the problem is divided into a number of subintervals of unknown (and unequal) lengths with a different set of differential equations for each subinterval and with the subinterval lengths to be determined in the solution process; (2) some solution components are known to be unbounded at infinity while others decay very slowly,and (3) in a certain range of parameter values, a previously used solution method is known to be sensitive to boundary data. The new method is used to generate new accurate numerical solutions for single-grade resource problems with a high unit extraction cost and more accurate results for two-grade deposit problems previously investigated. As well, it enables us to investigate for the first time problems with more than two grades of deposits. The implications of these new results are analyzed.
International Journal of Solids and Structures, 2006
Royal Society Open Science, 2016
Studies in Applied Mathematics, 1993
The method of decaying residual solution is applied to obtain an approximate interior solution fo... more The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.
Zeitschrift für angewandte Mathematik und Physik ZAMP, 1966
Zusammenfassung Es wird gezeigt, wie man gewisse bekannte Elastizitätsgleichungen der linearen Sc... more Zusammenfassung Es wird gezeigt, wie man gewisse bekannte Elastizitätsgleichungen der linearen Schalentheorie [2] umschreiben kann mit Hilfe von verallgemeinerten Dehnungskomponenten und verallgemeinerten Energiefunktionen, welche von dem erstgenannten Verfasser [3] eingeführt worden sind.
Zeitschrift für angewandte Mathematik und Physik ZAMP, 1971
ZusammenfassungDie Klasse von Problemen der linearen Theorie für schraubenförmige Schalen mit Spa... more ZusammenfassungDie Klasse von Problemen der linearen Theorie für schraubenförmige Schalen mit Spannungen und Verzerrungen von der Formeiθf(r) wird auf ein Randwertproblem für ein System von zwei gewöhnlichen Differentialgleichungen dritter Ordnung reduziert. Für Schalen unter dem Einfluß von Endbiegemomenten werden Lösungen mit Hilfe von Störungsrechnung sowie asymptotische Lösungen bestimmt.
Journal of Engineering Materials and Technology, 2007
To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, st... more To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, stress and strain must be determined experimentally for the same configurations. Such experiments are hindered by the inherent theoretical complexity of continuum mechanics, and by the technical difficulties of effecting external stress loads or body forces on the tissue without invasion, especially on a small scale. An understanding of appropriate mechanical problems and their solutions can help the experimentalist overcome these difficulties to a certain extent. Based on recent work on fiber-reinforced material, we formulate a constitutive theory for the root of different angiosperm species and suggest a set of loading conditions to determine the parameter values in a specific tissue sample. The loading conditions are formulated with a view toward experimental realization in vivo or with minimal invasion. For each loading condition, we formulate the corresponding mechanical problem and s...
Mathematical Biosciences and Engineering, 2008
Journal of Mechanics of Materials and Structures, 2011
Dedicated to Charles and Marie-Louise Steele for their years of outstanding management of IJSS an... more Dedicated to Charles and Marie-Louise Steele for their years of outstanding management of IJSS and JoMMS, and for their more than forty years of warm friendship with the last author.
Journal of Applied Mechanics, Sep 1, 1988
Necessary conditions have been established recently for the prescribed data alon the cylindrical ... more Necessary conditions have been established recently for the prescribed data alon the cylindrical edge(s) of an elastic flat plate to induce only an exponentially deca ing elastostatic state. The present paper describes how these conditions may be use to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary condition for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first tim how the stretching action in the plate interior induced by transverse loads can b
Bulletin of Mathematical Biology, Feb 17, 2021
Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch... more Chlamydia trachomatis is an important bacterial pathogen that has an unusual developmental switch from a dividing form (reticulate body or RB) to an infectious form (elementary body or EB). RBs replicate by binary fission within an infected host cell, but there is a delay before RBs convert into EBs for spread to a new host cell. We developed stochastic optimal control models of the Chlamydia developmental cycle to examine factors that control the number of EBs produced. These factors included the probability and timing of conversion, and the duration of the developmental cycle before the host cell lyses. Our mathematical analysis shows that the observed delay in RB-to-EB conversion is important for maximizing EB production by the end of the intracellular infection.
In this paper, the effects of a conventional form of negative feedback on receptor synthesis rate... more In this paper, the effects of a conventional form of negative feedback on receptor synthesis rate as a mechanism to induce robustness of biological development of the Drosophila wing imaginal disc is analyzed through the initial-boundary value problem in a basic partial differential equation model for the extracellular biological development activities. The existence, uniqueness, linear stability and monotonicity of the steady state signaling gradient are established rigorously. Solutions are then obtained for a special case of the steady state problem to show explicitly the effects of the chosen form of negative feedback. It is evident from the results that the principal effect of such a feedback mechanism is to render the signaling bound morphogen gradient more uniformly distributed except for a narrow layer adjacent to the edge of the posterior compartment of the wing disc. While the change in the magnitude of the maximum signaling morphogen concentration near the ligand source may be kept at an acceptable level, the leveling and flattening of the gradient render it less differential in space (except in the boundary layer) and hence more deviating from the desired gradient for the target biological pattern. The conclusion is then shown to apply to the general case with the help of the theoretical results on monotonicity. These results suggest that negative feedback on the receptor synthesis rate of the chosen form is not effective for promoting robustness. In fact, it drives the system somewhat in the opposite direction, a conclusion supported by the simulation results. The findings in turn suggest more useful forms of the negative feedback for mediating receptor synthesis to offset a higher ligand synthesis rate for our types of systems.
Recent data collected on the Chlamydia Trachomatis life cycle show an initial period of no RB-to-... more Recent data collected on the Chlamydia Trachomatis life cycle show an initial period of no RB-to-EB conversion. This and other features of the observed bacterial life cycle are postulated to be consequences of the bacteria's drive for Darwinian survival. Stochastic optimal control models formulated herein in fact lead to an initial conversion holiday that support this proposition.