The Kermack-McKendrick (KM) (1927) epidemiological equations are used to analyse different pandem... more The Kermack-McKendrick (KM) (1927) epidemiological equations are used to analyse different pandemic scenarios. The infection rate constant and the withdrawal rate constant of infected individuals for the Spanish influenza pandemic (1918 Á 1920) are found by curve fitting the solution of the KM equations to the historical data for the number of dead and the number of infected individuals during the pandemic. Hypothetically assuming the very same parameters for hypervirulent strains of H5N1 influenza virus (with 50% lethality), our simulations reveal that the latter (without vigorous countermeasures) can infect the total world population during a period of 20 Á30 days, with a mortality of 50% of the total world population. The short time it takes before the pandemic is over precludes the use of new vaccines that are developed only after a pandemic has started. We examine a logistically more feasible method of achieving rapid immunization after a pandemic has started (and if prefabricated vaccines cannot be used either because they are not effective or for logistic reasons): the influence of a counter-pandemic running ahead and immunizing the population before the hypervirulent H5N1 virus attacks. We find that the counter-pandemic can significantly reduce the total death toll during a pandemic with a hypervirulent strain of H5N1 influenza virus, provided that its infectivity at a population level is much larger than for the hypervirulent virus. This can be achieved if everything possible is done to hinder geographic dispersal of the hypervirulent virus (e.g. immediate cessation of all international passenger traffic, immediate cessation of all ordinary road traffic, house quarantine) at the same time as dispersal of the 'vaccine virus' is deliberately facilitated by sending it around in a similar way as for a vaccine, but seeding it only in every local population and not in every person as for ordinary vaccine. From a logistic point of view this might be the only feasible method of achieving immunization of a significant proportion of the population in poor countries with poor infrastructure during the very short time interval available before the superpathogen itself normally would be expected to arrive. However, mortality caused by a counter-pandemic virus will probably be higher than during an ordinary influenza epidemic, especially among elderly and malnourished persons. Vaccination, using vaccines that have been prefabricated and stored before the start of an eventual pandemic, should therefore be the preferred method of achieving immunization whenever logistically feasible.
Complex numbers extend the concept of the 1 dimensional numbers to 2 dimensions. Quaternions exte... more Complex numbers extend the concept of the 1 dimensional numbers to 2 dimensions. Quaternions extend numbers to 4 dimensions. Octonions and sedenions are extensions to 8 and 16 dimensions respectively. We study a general form of complex numbers, various axiomatic structures of 3 dimensional numbers, and finally N dimensional numbers, 2 k N , k=0,1,2,.... Quaternions, octonions and sedenions are special cases. Two different structures for addition are studied.
The potential impregnation of Al(0) nanoparticles in the pores of three different metal-organic f... more The potential impregnation of Al(0) nanoparticles in the pores of three different metal-organic frameworks (MOFs), MIL-53-Al, HKUST-1, and UiO-67, was investigated through the suspension of the MOFs in AlH 3 •NMe 2 Et (1), followed by filtration, toluene wash, and heating to 150 °C under vacuum. Calculations based on the ratios of molecular and pore volumes provided idealized, benchmark impregnation capacities. Three successive impregnation cycles were performed to provide maximum incorporation of Al in the pores, and the materials were characterized after each impregnation cycle by ICP elemental analysis, BET surface area, and pore volume measurements. For MIL-53-Al, about half of the calculated amount of Al was incorporated into the MIL-53 pore structure, and PXRD data indicated a loss of crystallinity after the third incorporation cycle. Little Al incorporation was observed with HKUST-1, and the large decrease in surface area and pore volume, without significant change in the PXRD pattern, is attributed to pore blockage. Reaction of a large excess of 1 with UiO-67 was highly exothermic and evolved gas, likely from reaction with the µ 3-OH groups in the UiO-67 structure. The resulting material was amorphous apart from metallic Al(0) crystals approximately 30 nm in size and larger than the UiO-67 pores, as determined by PXRD and 27 Al MAS NMR spectroscopy. This material exhibited no apparent reaction with air or water and exposure to air gave little change in the 27 Al MAS NMR spectrum. The Al(0) crystals thus appear to be protected from oxidation, presumably by the remaining UiO-67 framework.
3 degrees of freedom (DOF) exterior ballistic computer models are used in fragment studies to cal... more 3 degrees of freedom (DOF) exterior ballistic computer models are used in fragment studies to calculate individual trajectories of each fragment based on drag coefficient and the projected (presented) area in the direction of velocity of center of mass. The expectation of a randomly distributed projected area is commonly used for fragments that tumble (random rotation) during flight. We forecast a model where the expected drag coefficient is dependent of shape and Mach number. Rotation or tumbling only affects the expected projected area. Models of projected areas during tumbling and rotation are presented. An examination of the data by McCleskey (1988) indicates that the volume of the fragment to the power of 2/3 is a better parameter to characterize the drag coefficient of the fragments than the maximum projected area. Hydrocode simulations are used to verify results and to study projected area and drag coefficient of fragments.
Moxnes, John Fredrik; Hansen, Finn Knut; Jensen, Tomas Lunde; Sele, Marta Lill; Unneberg, Erik. A... more Moxnes, John Fredrik; Hansen, Finn Knut; Jensen, Tomas Lunde; Sele, Marta Lill; Unneberg, Erik. A computational study of density of some high energy molecules. Propellants, explosives, pyrotechnics 2016
In this work we study different energetic measures such as calorimetric energy of explosion, work... more In this work we study different energetic measures such as calorimetric energy of explosion, work of explosion, work of Carnot, enthalpy of explosion and free energy of explosion of aluminized explosives. For highly aluminized explosives with around 50 % aluminum and 50 % RDX we find that the work of Carnot is of the same size as the work of explosion. In general, we find that due to irreversible processes, none of the commonly used energy concepts in the literature are good measures of effectiveness. Mathematical relations that can be used to calculate the mechanical work, the work of explosion and the work of Carnot are presented.
During plastic flow, hydrostatic pressure and plastic strain control the size of the yield surfac... more During plastic flow, hydrostatic pressure and plastic strain control the size of the yield surface while the Lode angle is responsible for its shape. The von Mises yield condition shows no dependency of the Lode angle while the Tresca condition shows. It has been concluded that the deviation from the von Mises criterion is real and could not be explained on the basis of lack of experimental accuracy and isotropy. What is notable is that from an engineering viewpoint the accuracy of the von Mises yielding is amply sufficient. However, it has been forecast that Lode dependency must be included to describe ductility. It has been shown that internal necking down of ligaments between voids that have become significantly enlarged in size dominates at high triaxiality, while internal shear localization of plastic strain between voids of limited growth dominates at low stress triaxiality. The Lode angle has been used to account for these effects. In this paper, various mathematical relations are examined that may be useful for further studies of the Lode angle and its relation to fracture and ductility.
Central European Journal of Energetic Materials, 2016
Nitrated derivatives of 5-amino-3-nitro-1,2,4-triazole (ANTA) and 3-nitro-1,2,4-triazol-5-one (NT... more Nitrated derivatives of 5-amino-3-nitro-1,2,4-triazole (ANTA) and 3-nitro-1,2,4-triazol-5-one (NTO) were theoretically characterized with respect to their performance as high explosives and rocket propellants. The detonation velocity and the detonation pressure of the derivatives, calculated with EXPLO5 software, were at the same level or slightly above the performance of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX). The results showed that compositions of 1,3,4-trinitro-1,2,4-triazol-5-one and glycidyl azide polymer (GAP) could give specific impulses just above 2600 m/s in rocket propellants. The sensitivities of the derivatives were evaluated using their heats of detonation, CHNO-ratios, free space in the crystal lattice and N−NO2 bond dissociation energy. The stability and sensitivity of several of the derivatives could be poor due to the low N−NO2 bond dissociation energies. The N−NO2 bond dissociation energies in the derivatives were calculated to be between 41 and 296 kJ/mol when the M06-2X/6-311+G(2d,p) functional was used. Synthetic routes for the most stable derivatives were proposed. In addition, preliminary studies of the chloride-assisted nitrolysis of NTO were performed. The infrared spectrum of the NTO derivative indicated that N−NO2 bonds were formed.
The crystal density of neutral and ionic molecular crystals is remarkably well approximated by th... more The crystal density of neutral and ionic molecular crystals is remarkably well approximated by the enclosed volume of molecular surfaces, where these surfaces are defined as regions of constant and small electron density. Several workers have proposed that estimates may be improved if one includes quantities extracted from the electrostatic potential on the surface of the molecule. The variation of the potential and the imbalance of positive and negative values have been considered to be of importance. In this study we demonstrate that whereas variation is important for improving crystal density predictions, imbalance is not. We present a density functional theory study on a set of 44 neutral molecular crystals. Tenfold cross-validations were performed on models that incorporate variation, imbalance and combinations of both. Geometries were optimised using B3LYP and basis sets of type 6-31G(d). Electron densities and electrostatic potentials were computed with B3LYP and M05. Regardless of functional, models that correct for variation yield a relative decrease of 15%-18% in root-mean-square error of prediction. This correction appears to sharpen the error distribution about zero. Models based on imbalance yield no improvement, and we argue that it plays an insignificant role.
This paper provides a mathematical description based on the theory of differential equations, for... more This paper provides a mathematical description based on the theory of differential equations, for the dynamics of lactate production and removal. Analytical and numerical results for training/exercise of endurance of athletes are presented based on the common concept of training impulse (Trimp). The relationships between activity, production rate, and removal strategies of lactate are studied. Parameters are estimated from published data. A model for optimum removal of lactate after exercise is developed. The model provides realistic predictions when compared with experimental results. We show some specific examples for the usefulness of the mathematical model by studying some recent problems discussed in the literature. (a) Is interval exercise more beneficial than steady-state exercise? (b) What is the optimum aerobic power during recovery? We discuss whether steady-state exercise gives higher Trimp than interval exercise, when imposing an upper boundary for the lactate concentrat...
The article presents a dynamic model of exchange, production, and consumption. In a dynamic world... more The article presents a dynamic model of exchange, production, and consumption. In a dynamic world, complicated predictions often have to be made. Thus, in this article, the classical exchange model is expanded with a dynamic model specifying the intermediate states toward a static equilibrium, which may or may not be reached. A price mechanism was necessary to develop in order to describe these changes over time. The model is illustrated with two examples of the emergence of division of labor. The robustness of the dynamic model is tested with sensitivity analysis.
This article analyzes crime development which is one of the largest threats in today's world,... more This article analyzes crime development which is one of the largest threats in today's world, frequently referred to as the war on crime. The criminal commits crimes in his free time (when not in jail) according to a non-stationary Poisson process which accounts for fluctuations. Expected values and variances for crime development are determined. The deterrent effect of imprisonment follows from the amount of time in imprisonment. Each criminal maximizes expected utility defined as expected benefit (from crime) minus expected cost (imprisonment). A first-order differential equation of the criminal's utility-maximizing response to the given punishment policy is then developed. The analysis shows that if imprisonment is absent, criminal activity grows substantially. All else being equal, any equilibrium is unstable (labile), implying growth of criminal activity, unless imprisonment increases sufficiently as a function of criminal activity. This dynamic approach or perspective ...
International Journal of Energetic Materials and Chemical Propulsion, 2010
The ignition threshold and combustion characteristics of two pyrotechnic powders (A and B) initia... more The ignition threshold and combustion characteristics of two pyrotechnic powders (A and B) initiated by mechanical stimulation were examined. A piston-driven compaction (PDC) experiment was used to compare the two powders. The two powders differ in their oxidizer type and initial particle size distribution. It was found that Pyrotechnic A, formulated with potassium perchlorate, had a lower ignition threshold (~80 m/s) than Pyrotechnic B (~120 m/s), which was formulated with a blend of ammonium nitrate and barium nitrate. Compaction wave front velocities through the sample were a function of piston velocity and were comparable for the two samples; however, the characteristics of a "sustained" combustion front differed between the two samples. Powder models were developed for the two materials and used to simulate the PDC experiments.
Natural fragmentation of warheads that detonates causes the casing of the warhead to split into v... more Natural fragmentation of warheads that detonates causes the casing of the warhead to split into various sized fragments through shear or radial fractures depending on the toughness, density, and grain size of the material. The best known formula for the prediction of the size distribution is the Mott formulae, which is further examined by Grady and Kipp by investigating more carefully the statistical most random way of portioning a given area into a number of entities. We examine the fragmentation behavior of radially expanding steel rings cut from a 25 mm warhead by using an in house smooth particle hydrodynamic (SPH) simulation code called REGULUS. Experimental results were compared with numerical results applying varying particle size and stochastic fracture strain. The numerically obtained number of fragments was consistent with experimental results. Increasing expansion velocity of the rings increases the number of fragments. Statistical variation of the material parameters influences the fragment characteristics, especially for low expansion velocities. A least square regression fit to the cumulative number of fragments by applying a generalized Mott distribution shows that the shape parameter is around 4 for the rings, which is in contrast to the Mott distribution with a shape parameter of ½. For initially polar distributed particles, we see signs of a bimodal cumulative fragment distribution. Adding statistical variation in material parameters of the fracture model causes the velocity numerical solutions to become less sensitive to changes in resolution for Cartesian distributed particles.
ABSTRACT In all living species at most, two parents are needed in order to make an offspring. In ... more ABSTRACT In all living species at most, two parents are needed in order to make an offspring. In this paper, we assume that N parents are needed, and we calculate the optimum N in terms of fitness using a simple probabilistic approach. The probability of finding an attractive partner is set to P. The probability that this partner gives increased fitness is set to 1−R. We show that the best number of partners is N = 2 for any value of R as long as 1/2 P P N = 1 partner. As P increases, there exists an optimum number of partners N > 2.
Theoretical biology & medical modelling, Jan 13, 2012
Based on a literature review, the current study aimed to construct mathematical models of lactate... more Based on a literature review, the current study aimed to construct mathematical models of lactate production and removal in both muscles and blood during steady state and at varying intensities during whole-body exercise. In order to experimentally test the models in dynamic situations, a cross-country skier performed laboratory tests while treadmill roller skiing, from where work rate, aerobic power and blood lactate concentration were measured. A two-compartment simulation model for blood lactate production and removal was constructed. The simulated and experimental data differed less than 0.5 mmol/L both during steady state and varying sub-maximal intensities. However, the simulation model for lactate removal after high exercise intensities seems to require further examination. Overall, the simulation models of lactate production and removal provide useful insight into the parameters that affect blood lactate response, and specifically how blood lactate concentration during pract...
Mathematical and Computer Modelling of Dynamical Systems, 2008
We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the... more We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the two well-known principles ‘train to failure’ and ‘use it or lose it’. The anabolic and catabolic processes are modelled with differential equations. Fitness is defined as muscle fitness. We model the work power of any muscle or set of muscles, and the muscle's maximum work power. Parameters are estimated and we present analytical and numerical results. The relationships between performance, fitness and fatigue are demonstrated for various activity scenarios. For example, the model quantifies the exact manner in which the optimal rest period can be determined to maximize the performance on a given day. The model provides realistic predictions, and constitutes a powerful tool which describes the processes by which performance, fitness and fatigue can be regulated and controlled.
The Kermack-McKendrick (KM) (1927) epidemiological equations are used to analyse different pandem... more The Kermack-McKendrick (KM) (1927) epidemiological equations are used to analyse different pandemic scenarios. The infection rate constant and the withdrawal rate constant of infected individuals for the Spanish influenza pandemic (1918 Á 1920) are found by curve fitting the solution of the KM equations to the historical data for the number of dead and the number of infected individuals during the pandemic. Hypothetically assuming the very same parameters for hypervirulent strains of H5N1 influenza virus (with 50% lethality), our simulations reveal that the latter (without vigorous countermeasures) can infect the total world population during a period of 20 Á30 days, with a mortality of 50% of the total world population. The short time it takes before the pandemic is over precludes the use of new vaccines that are developed only after a pandemic has started. We examine a logistically more feasible method of achieving rapid immunization after a pandemic has started (and if prefabricated vaccines cannot be used either because they are not effective or for logistic reasons): the influence of a counter-pandemic running ahead and immunizing the population before the hypervirulent H5N1 virus attacks. We find that the counter-pandemic can significantly reduce the total death toll during a pandemic with a hypervirulent strain of H5N1 influenza virus, provided that its infectivity at a population level is much larger than for the hypervirulent virus. This can be achieved if everything possible is done to hinder geographic dispersal of the hypervirulent virus (e.g. immediate cessation of all international passenger traffic, immediate cessation of all ordinary road traffic, house quarantine) at the same time as dispersal of the 'vaccine virus' is deliberately facilitated by sending it around in a similar way as for a vaccine, but seeding it only in every local population and not in every person as for ordinary vaccine. From a logistic point of view this might be the only feasible method of achieving immunization of a significant proportion of the population in poor countries with poor infrastructure during the very short time interval available before the superpathogen itself normally would be expected to arrive. However, mortality caused by a counter-pandemic virus will probably be higher than during an ordinary influenza epidemic, especially among elderly and malnourished persons. Vaccination, using vaccines that have been prefabricated and stored before the start of an eventual pandemic, should therefore be the preferred method of achieving immunization whenever logistically feasible.
Complex numbers extend the concept of the 1 dimensional numbers to 2 dimensions. Quaternions exte... more Complex numbers extend the concept of the 1 dimensional numbers to 2 dimensions. Quaternions extend numbers to 4 dimensions. Octonions and sedenions are extensions to 8 and 16 dimensions respectively. We study a general form of complex numbers, various axiomatic structures of 3 dimensional numbers, and finally N dimensional numbers, 2 k N , k=0,1,2,.... Quaternions, octonions and sedenions are special cases. Two different structures for addition are studied.
The potential impregnation of Al(0) nanoparticles in the pores of three different metal-organic f... more The potential impregnation of Al(0) nanoparticles in the pores of three different metal-organic frameworks (MOFs), MIL-53-Al, HKUST-1, and UiO-67, was investigated through the suspension of the MOFs in AlH 3 •NMe 2 Et (1), followed by filtration, toluene wash, and heating to 150 °C under vacuum. Calculations based on the ratios of molecular and pore volumes provided idealized, benchmark impregnation capacities. Three successive impregnation cycles were performed to provide maximum incorporation of Al in the pores, and the materials were characterized after each impregnation cycle by ICP elemental analysis, BET surface area, and pore volume measurements. For MIL-53-Al, about half of the calculated amount of Al was incorporated into the MIL-53 pore structure, and PXRD data indicated a loss of crystallinity after the third incorporation cycle. Little Al incorporation was observed with HKUST-1, and the large decrease in surface area and pore volume, without significant change in the PXRD pattern, is attributed to pore blockage. Reaction of a large excess of 1 with UiO-67 was highly exothermic and evolved gas, likely from reaction with the µ 3-OH groups in the UiO-67 structure. The resulting material was amorphous apart from metallic Al(0) crystals approximately 30 nm in size and larger than the UiO-67 pores, as determined by PXRD and 27 Al MAS NMR spectroscopy. This material exhibited no apparent reaction with air or water and exposure to air gave little change in the 27 Al MAS NMR spectrum. The Al(0) crystals thus appear to be protected from oxidation, presumably by the remaining UiO-67 framework.
3 degrees of freedom (DOF) exterior ballistic computer models are used in fragment studies to cal... more 3 degrees of freedom (DOF) exterior ballistic computer models are used in fragment studies to calculate individual trajectories of each fragment based on drag coefficient and the projected (presented) area in the direction of velocity of center of mass. The expectation of a randomly distributed projected area is commonly used for fragments that tumble (random rotation) during flight. We forecast a model where the expected drag coefficient is dependent of shape and Mach number. Rotation or tumbling only affects the expected projected area. Models of projected areas during tumbling and rotation are presented. An examination of the data by McCleskey (1988) indicates that the volume of the fragment to the power of 2/3 is a better parameter to characterize the drag coefficient of the fragments than the maximum projected area. Hydrocode simulations are used to verify results and to study projected area and drag coefficient of fragments.
Moxnes, John Fredrik; Hansen, Finn Knut; Jensen, Tomas Lunde; Sele, Marta Lill; Unneberg, Erik. A... more Moxnes, John Fredrik; Hansen, Finn Knut; Jensen, Tomas Lunde; Sele, Marta Lill; Unneberg, Erik. A computational study of density of some high energy molecules. Propellants, explosives, pyrotechnics 2016
In this work we study different energetic measures such as calorimetric energy of explosion, work... more In this work we study different energetic measures such as calorimetric energy of explosion, work of explosion, work of Carnot, enthalpy of explosion and free energy of explosion of aluminized explosives. For highly aluminized explosives with around 50 % aluminum and 50 % RDX we find that the work of Carnot is of the same size as the work of explosion. In general, we find that due to irreversible processes, none of the commonly used energy concepts in the literature are good measures of effectiveness. Mathematical relations that can be used to calculate the mechanical work, the work of explosion and the work of Carnot are presented.
During plastic flow, hydrostatic pressure and plastic strain control the size of the yield surfac... more During plastic flow, hydrostatic pressure and plastic strain control the size of the yield surface while the Lode angle is responsible for its shape. The von Mises yield condition shows no dependency of the Lode angle while the Tresca condition shows. It has been concluded that the deviation from the von Mises criterion is real and could not be explained on the basis of lack of experimental accuracy and isotropy. What is notable is that from an engineering viewpoint the accuracy of the von Mises yielding is amply sufficient. However, it has been forecast that Lode dependency must be included to describe ductility. It has been shown that internal necking down of ligaments between voids that have become significantly enlarged in size dominates at high triaxiality, while internal shear localization of plastic strain between voids of limited growth dominates at low stress triaxiality. The Lode angle has been used to account for these effects. In this paper, various mathematical relations are examined that may be useful for further studies of the Lode angle and its relation to fracture and ductility.
Central European Journal of Energetic Materials, 2016
Nitrated derivatives of 5-amino-3-nitro-1,2,4-triazole (ANTA) and 3-nitro-1,2,4-triazol-5-one (NT... more Nitrated derivatives of 5-amino-3-nitro-1,2,4-triazole (ANTA) and 3-nitro-1,2,4-triazol-5-one (NTO) were theoretically characterized with respect to their performance as high explosives and rocket propellants. The detonation velocity and the detonation pressure of the derivatives, calculated with EXPLO5 software, were at the same level or slightly above the performance of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX). The results showed that compositions of 1,3,4-trinitro-1,2,4-triazol-5-one and glycidyl azide polymer (GAP) could give specific impulses just above 2600 m/s in rocket propellants. The sensitivities of the derivatives were evaluated using their heats of detonation, CHNO-ratios, free space in the crystal lattice and N−NO2 bond dissociation energy. The stability and sensitivity of several of the derivatives could be poor due to the low N−NO2 bond dissociation energies. The N−NO2 bond dissociation energies in the derivatives were calculated to be between 41 and 296 kJ/mol when the M06-2X/6-311+G(2d,p) functional was used. Synthetic routes for the most stable derivatives were proposed. In addition, preliminary studies of the chloride-assisted nitrolysis of NTO were performed. The infrared spectrum of the NTO derivative indicated that N−NO2 bonds were formed.
The crystal density of neutral and ionic molecular crystals is remarkably well approximated by th... more The crystal density of neutral and ionic molecular crystals is remarkably well approximated by the enclosed volume of molecular surfaces, where these surfaces are defined as regions of constant and small electron density. Several workers have proposed that estimates may be improved if one includes quantities extracted from the electrostatic potential on the surface of the molecule. The variation of the potential and the imbalance of positive and negative values have been considered to be of importance. In this study we demonstrate that whereas variation is important for improving crystal density predictions, imbalance is not. We present a density functional theory study on a set of 44 neutral molecular crystals. Tenfold cross-validations were performed on models that incorporate variation, imbalance and combinations of both. Geometries were optimised using B3LYP and basis sets of type 6-31G(d). Electron densities and electrostatic potentials were computed with B3LYP and M05. Regardless of functional, models that correct for variation yield a relative decrease of 15%-18% in root-mean-square error of prediction. This correction appears to sharpen the error distribution about zero. Models based on imbalance yield no improvement, and we argue that it plays an insignificant role.
This paper provides a mathematical description based on the theory of differential equations, for... more This paper provides a mathematical description based on the theory of differential equations, for the dynamics of lactate production and removal. Analytical and numerical results for training/exercise of endurance of athletes are presented based on the common concept of training impulse (Trimp). The relationships between activity, production rate, and removal strategies of lactate are studied. Parameters are estimated from published data. A model for optimum removal of lactate after exercise is developed. The model provides realistic predictions when compared with experimental results. We show some specific examples for the usefulness of the mathematical model by studying some recent problems discussed in the literature. (a) Is interval exercise more beneficial than steady-state exercise? (b) What is the optimum aerobic power during recovery? We discuss whether steady-state exercise gives higher Trimp than interval exercise, when imposing an upper boundary for the lactate concentrat...
The article presents a dynamic model of exchange, production, and consumption. In a dynamic world... more The article presents a dynamic model of exchange, production, and consumption. In a dynamic world, complicated predictions often have to be made. Thus, in this article, the classical exchange model is expanded with a dynamic model specifying the intermediate states toward a static equilibrium, which may or may not be reached. A price mechanism was necessary to develop in order to describe these changes over time. The model is illustrated with two examples of the emergence of division of labor. The robustness of the dynamic model is tested with sensitivity analysis.
This article analyzes crime development which is one of the largest threats in today's world,... more This article analyzes crime development which is one of the largest threats in today's world, frequently referred to as the war on crime. The criminal commits crimes in his free time (when not in jail) according to a non-stationary Poisson process which accounts for fluctuations. Expected values and variances for crime development are determined. The deterrent effect of imprisonment follows from the amount of time in imprisonment. Each criminal maximizes expected utility defined as expected benefit (from crime) minus expected cost (imprisonment). A first-order differential equation of the criminal's utility-maximizing response to the given punishment policy is then developed. The analysis shows that if imprisonment is absent, criminal activity grows substantially. All else being equal, any equilibrium is unstable (labile), implying growth of criminal activity, unless imprisonment increases sufficiently as a function of criminal activity. This dynamic approach or perspective ...
International Journal of Energetic Materials and Chemical Propulsion, 2010
The ignition threshold and combustion characteristics of two pyrotechnic powders (A and B) initia... more The ignition threshold and combustion characteristics of two pyrotechnic powders (A and B) initiated by mechanical stimulation were examined. A piston-driven compaction (PDC) experiment was used to compare the two powders. The two powders differ in their oxidizer type and initial particle size distribution. It was found that Pyrotechnic A, formulated with potassium perchlorate, had a lower ignition threshold (~80 m/s) than Pyrotechnic B (~120 m/s), which was formulated with a blend of ammonium nitrate and barium nitrate. Compaction wave front velocities through the sample were a function of piston velocity and were comparable for the two samples; however, the characteristics of a "sustained" combustion front differed between the two samples. Powder models were developed for the two materials and used to simulate the PDC experiments.
Natural fragmentation of warheads that detonates causes the casing of the warhead to split into v... more Natural fragmentation of warheads that detonates causes the casing of the warhead to split into various sized fragments through shear or radial fractures depending on the toughness, density, and grain size of the material. The best known formula for the prediction of the size distribution is the Mott formulae, which is further examined by Grady and Kipp by investigating more carefully the statistical most random way of portioning a given area into a number of entities. We examine the fragmentation behavior of radially expanding steel rings cut from a 25 mm warhead by using an in house smooth particle hydrodynamic (SPH) simulation code called REGULUS. Experimental results were compared with numerical results applying varying particle size and stochastic fracture strain. The numerically obtained number of fragments was consistent with experimental results. Increasing expansion velocity of the rings increases the number of fragments. Statistical variation of the material parameters influences the fragment characteristics, especially for low expansion velocities. A least square regression fit to the cumulative number of fragments by applying a generalized Mott distribution shows that the shape parameter is around 4 for the rings, which is in contrast to the Mott distribution with a shape parameter of ½. For initially polar distributed particles, we see signs of a bimodal cumulative fragment distribution. Adding statistical variation in material parameters of the fracture model causes the velocity numerical solutions to become less sensitive to changes in resolution for Cartesian distributed particles.
ABSTRACT In all living species at most, two parents are needed in order to make an offspring. In ... more ABSTRACT In all living species at most, two parents are needed in order to make an offspring. In this paper, we assume that N parents are needed, and we calculate the optimum N in terms of fitness using a simple probabilistic approach. The probability of finding an attractive partner is set to P. The probability that this partner gives increased fitness is set to 1−R. We show that the best number of partners is N = 2 for any value of R as long as 1/2 P P N = 1 partner. As P increases, there exists an optimum number of partners N > 2.
Theoretical biology & medical modelling, Jan 13, 2012
Based on a literature review, the current study aimed to construct mathematical models of lactate... more Based on a literature review, the current study aimed to construct mathematical models of lactate production and removal in both muscles and blood during steady state and at varying intensities during whole-body exercise. In order to experimentally test the models in dynamic situations, a cross-country skier performed laboratory tests while treadmill roller skiing, from where work rate, aerobic power and blood lactate concentration were measured. A two-compartment simulation model for blood lactate production and removal was constructed. The simulated and experimental data differed less than 0.5 mmol/L both during steady state and varying sub-maximal intensities. However, the simulation model for lactate removal after high exercise intensities seems to require further examination. Overall, the simulation models of lactate production and removal provide useful insight into the parameters that affect blood lactate response, and specifically how blood lactate concentration during pract...
Mathematical and Computer Modelling of Dynamical Systems, 2008
We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the... more We provide a mathematical dynamic model of athletic performance, fitness and fatigue based on the two well-known principles ‘train to failure’ and ‘use it or lose it’. The anabolic and catabolic processes are modelled with differential equations. Fitness is defined as muscle fitness. We model the work power of any muscle or set of muscles, and the muscle's maximum work power. Parameters are estimated and we present analytical and numerical results. The relationships between performance, fitness and fatigue are demonstrated for various activity scenarios. For example, the model quantifies the exact manner in which the optimal rest period can be determined to maximize the performance on a given day. The model provides realistic predictions, and constitutes a powerful tool which describes the processes by which performance, fitness and fatigue can be regulated and controlled.
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Papers by John Moxnes