Models for predicting impact sensitivity of energetic materials based on the trigger linkage hypothesis and Arrhenius kinetics.

In order to predict the impact sensitivity of high explosives, we designed and evaluated several models based on the trigger linkage hypothesis and the Arrhenius equation. To this effect, we calculated the heat of detonation, temperature of detonation, and bond dissociation energy for 70 energetic molecules. The bond dissociation energy divided by the temperature of detonation proved to be a good predictor of the impact sensitivity of nitroaromatics, with a coefficient of determination (R2) of 0.81. A separate Bayesian analysis gave similar results, taking model complexity into account. For nitramines, there was no relationship between the impact sensitivity and the bond dissociation energy. None of the models studied gave good predictions for the impact sensitivity of liquid nitrate esters. For solid nitrate esters, the bond dissociation energy divided by the temperature of detonation showed promising results (R2 = 0.85), but since this regression was based on only a few data points, it was discredited when model complexity was accounted for by our Bayesian analysis. Since the temperature of detonation correlated with the impact sensitivity for nitroaromatics, nitramines, and nitrate esters, we consider it to be one of the leading predictive factors of impact sensitivity for energetic materials.

The crystal density of nitrogen cubane and other polynitrogen species.

The elusive Nn species remain hypothetical at the time of writing. However, they have long captured the imaginations of researchers in the field of energetic materials due to their high detonation velocity and detonation pressure. Solid nitrogen cubane N8 is one candidate material that has been much studied theoretically. We question the reported crystal density of this hypothetical solid (2.65 g/cm3). Here quantum mechanical volume estimates indicate that its density might be as low as 1.89 g/cm3. The predicted detonation pressure and velocities may thus be grossly overestimated of their true values.

A computational study of ANTA and NTO derivatives.

This work is a study of 5-amino-3-nitro-1,2,4-triazole (ANTA), 3-nitro-1,2,4-triazol-5-one (NTO), and nitrated derivatives of ANTA and NTO. RDX and TNT were studied for comparison. ANTA and NTO are low-sensitive high explosives with detonation properties comparable to 2,4,6-trinitrotoluene (TNT) and 1,3,5-trinitroperhydro-1,3,5-triazine (RDX). We showed previously that nitrated NTO and ANTA compounds, when used in a glycidyl azide polymer (GAP) matrix in rocket propellants, could give impulses above 2600 m/s and that the oxygen balance is positive. If used in aluminized explosives, the heat of detonation may be increased to a practical level significantly above RDX/aluminum compositions. Here, we use two different methods for sensitivity and two density functional theory functionals, B3LYP and M06-2X with the 6-31G(d) basis set, together with the complete basis set method CBS-4M. Calculations indicate that most of the nitrated derivatives have nearly equal sensitivity to RDX. Significantly different bond dissociation energies in the nitrimino functional group are predicted, although most models give much the same result.

Studying the time trend of Methicillin-resistant Staphylococcus aureus (MRSA) in Norway by use of non-stationary γ-Poisson distributions.

OBJECTIVES: Study the time development of methicillin-resistant Staphylococcus aureus (MRSA) and forecast future behaviour. The major question: Is the number of MRSA isolates in Norway increasing and will it continue to increase? DESIGN: Time trend analysis using non-stationary γ-Poisson distributions. SETTING: Two data sets were analysed. The first data set (data set I) consists of all MRSA isolates collected in Oslo County from 1997 to 2010; the study area includes the Norwegian capital of Oslo and nearby surrounding areas, covering approximately 11% of the Norwegian population. The second data set (data set II) consists of all MRSA isolates collected in Health Region East from 2002 to 2011. Health Region East consists of Oslo County and four neighbouring counties, and is the most populated area of Norway. PARTICIPANTS: Both data sets I and II consist of all persons in the area and time period described in the Settings, from whom MRSA have been isolated. PRIMARY AND SECONDARY OUTCOME MEASURES: MRSA infections have been mandatory notifiable in Norway since 1995, and MRSA colonisation since 2004. In the time period studied, all bacterial samples in Norway have been sent to a medical microbiological laboratory at the regional hospital for testing. In collaboration with the regional hospitals in five counties, we have collected all MRSA findings in the South-Eastern part of Norway over long time periods. RESULTS: On an average, a linear or exponential increase in MRSA numbers was observed in the data sets. A Poisson process with increasing intensity did not capture the dispersion of the time series, but a γ-Poisson process showed good agreement and captured the overdispersion. The numerical model showed numerical internal consistency. CONCLUSIONS: In the present study, we find that the number of MRSA isolates is increasing in the most populated area of Norway during the time period studied. We also forecast a continuous increase until the year 2017.

Using the power balance model to simulate cross-country skiing on varying terrain.

The current study adapts the power balance model to simulate cross-country skiing on varying terrain. We assumed that the skier's locomotive power at a self-chosen pace is a function of speed, which is impacted by friction, incline, air drag, and mass. An elite male skier's position along the track during ski skating was simulated and compared with his experimental data. As input values in the model, air drag and friction were estimated from the literature based on the skier's mass, snow conditions, and speed. We regard the fit as good, since the difference in racing time between simulations and measurements was 2 seconds of the 815 seconds racing time, with acceptable fit both in uphill and downhill terrain. Using this model, we estimated the influence of changes in various factors such as air drag, friction, and body mass on performance. In conclusion, the power balance model with locomotive power as a function of speed was found to be a valid tool for analyzing performance in cross-country skiing.

Mathematical simulation of energy expenditure and recovery during sprint cross-country skiing.

PURPOSE: A cross-country sprint competition relies on maximal effort durations of 3-4 minutes. Significant anaerobic energy contribution is expected. Anaerobic energy contribution has been estimated in different sports to date from the accumulated O2 deficit. However, the O2-deficit model can be questioned. We investigate anaerobic energy contribution by applying other methods than the O2 deficit. METHODS: Theoretical model development. RESULTS: For sprint cross-country competitions, the anaerobic energy contribution was 20%-25% independent of the employed mathematical model. Recovery times of a minimum 20 minutes were found to be required after sprint races to be sure that the performance in subsequent heats was not influenced. CONCLUSION: The O2-deficit model gave anaerobic energy results in agreement with other models from the literature. Recovery times of a minimum 20 minutes were found to be required after sprint races to be sure that the performance in subsequent heats was not influenced.

Methicillin-resistant Staphylococcus aureus (MRSA) is increasing in Norway: a time series analysis of reported MRSA and methicillin-sensitive S. aureus cases, 1997-2010.

BACKGROUND: Accurate estimates of the incidence and prevalence of methicillin-resistant Staphylococcus aureus (MRSA) infections are needed to inform public health policies. In Norway, where both MRSA infection and carriage are notifiable conditions, the reported incidence of MRSA is slowly increasing. However, the proportion of MRSA in relation to all S. aureus isolates is unknown, making it difficult to determine if the rising incidence is real or an artifact of an increasing number of tests performed. AIM: To characterize recent trends in MRSA infections and obtain a more complete understanding of the MRSA level in Norway. METHODS: All reported cases of MRSA and methicillin-sensitive S. aureus (MSSA) from Oslo County (1997-2010) and Health Region East (2008-2008), representing approximately 11% and 36% of the Norwegian population, respectively, were analyzed using a stochastic time series analysis to characterize trends. RESULTS: In Oslo County, the proportion of methicillin-resistant cases increased from 0.73% to 3.78% during the study period and was well modeled by an exponential growth with a doubling constant of 5.7 years (95% CI 4.5-7.4 years). In Health Region East, the proportion of MRSA cases increased from 0.4% to 2.1% from 2002 to 2008, with a best-fitting linear increase of 0.26% (95% CI 0.21-0.30%) per year. In both cases, the choice of a linear or exponential model for the time trend produced only marginally different model fits. We found no significant changes due to revised national MRSA guidelines published in June 2009. Significant variations in the increasing time trend were observed in the five hospitals within the region. The yearly reported incidence of MSSA was relatively stable in both study areas although we found seasonal patterns with peaks in August. CONCLUSION: The level of MRSA is increasing in Norway, and the proportion of methicillin resistance in all S. aureus isolates are higher than the reported proportion of MRSA in invasive infections.

A simulation of cross-country skiing on varying terrain by using a mathematical power balance model.

The current study simulated cross-country skiing on varying terrain by using a power balance model. By applying the hypothetical inductive deductive method, we compared the simulated position along the track with actual skiing on snow, and calculated the theoretical effect of friction and air drag on skiing performance. As input values in the model, air drag and friction were estimated from the literature, whereas the model included relationships between heart rate, metabolic rate, and work rate based on the treadmill roller-ski testing of an elite cross-country skier. We verified this procedure by testing four models of metabolic rate against experimental data on the treadmill. The experimental data corresponded well with the simulations, with the best fit when work rate was increased on uphill and decreased on downhill terrain. The simulations predicted that skiing time increases by 3%-4% when either friction or air drag increases by 10%. In conclusion, the power balance model was found to be a useful tool for predicting how various factors influence racing performance in cross-country skiing.

On the kinetics of anaerobic power.

BACKGROUND: This study investigated two different mathematical models for the kinetics of anaerobic power. Model 1 assumes that the work power is linear with the work rate, while Model 2 assumes a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power. In order to test these models, a cross country skier ran with poles on a treadmill at different exercise intensities. The aerobic power, based on the measured oxygen uptake, was used as input to the models, whereas the simulated blood lactate concentration was compared with experimental results. Thereafter, the metabolic rate from phosphocreatine break down was calculated theoretically. Finally, the models were used to compare phosphocreatine break down during continuous and interval exercises. RESULTS: Good similarity was found between experimental and simulated blood lactate concentration during steady state exercise intensities. The measured blood lactate concentrations were lower than simulated for intensities above the lactate threshold, but higher than simulated during recovery after high intensity exercise when the simulated lactate concentration was averaged over the whole lactate space. This fit was improved when the simulated lactate concentration was separated into two compartments; muscles + internal organs and blood. Model 2 gave a better behavior of alactic energy than Model 1 when compared against invasive measurements presented in the literature. During continuous exercise, Model 2 showed that the alactic energy storage decreased with time, whereas Model 1 showed a minimum value when steady state aerobic conditions were achieved. During interval exercise the two models showed similar patterns of alactic energy. CONCLUSIONS: The current study provides useful insight on the kinetics of anaerobic power. Overall, our data indicate that blood lactate levels can be accurately modeled during steady state, and suggests a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power.

The kinetics of lactate production and removal during whole-body exercise.

BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: 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 practical training and testing in dynamical situations should be interpreted.

Systematization of a set of closure techniques.

Approximations in population dynamics are gaining popularity since stochastic models in large populations are time consuming even on a computer. Stochastic modeling causes an infinite set of ordinary differential equations for the moments. Closure models are useful since they recast this infinite set into a finite set of ordinary differential equations. This paper systematizes a set of closure approximations. We develop a system, which we call a power p closure of n moments, where 0≤p≤n. Keeling's (2000a,b) approximation with third order moments is shown to be an instantiation of this system which we call a power 3 closure of 3 moments. We present an epidemiological example and evaluate the system for third and fourth moments compared with Monte Carlo simulations.

A dynamic model of Nordic diagonal stride skiing, with a literature review of cross country skiing.

The forces during the kicking phase in Nordic diagonal stride skiing are described by differential equations and the results are compared with experiments. The difference between static and dynamic friction, interacting with characteristics of the skier such as weight, velocity and the kicking force's angle with the terrain, are essential for high-velocity diagonal striding. Analytical results for relationships between glide length, friction and kicking force are shown. Aerodynamic drag and gravity are accounted for. A propulsion force based on the Hill (1970) equation for muscle contraction velocity and activation is constructed. The model shows a feasible tool for studying the effects of ski stiffness, the kicking force and the amount of waxing during diagonal stride skiing.

A mathematical model for the proliferation of bacteria in the urinary bladder due to enlarged prostate.

Urinary retention due to enlargement of the prostate (prostate hypertrophy) leads to increased proliferation of bacteria in the bladder. This in turn increases the infection rate. The reason is that the enlarged prostate presses on the urine channel and tends to close it. Thus the out flux of the bladder consists of repeatedly small amounts of fluid during a day. A mathematical dynamic model with differential equations is developed for the proliferation of bacteria in the urinary bladder (vesica urinary). The model accounts for how this proliferation is associated with varying amounts of mass of urine within the bladder. Parameters are estimated from published data and analytical and numerical results are presented. The relationships between the proliferation of bacteria within the bladder and the type of urinal out flux from the bladder are examined. The proliferation is shown to depend on the amount of mass of urine and the out flux of urine from the bladder. In the normal situation the bladder is drained successfully which also drains the bacteria. In the abnormal situation the bladder drains only partly. Despite frequent urination, substantial urine mass in the bladder on the average allows bacteria to proliferate and increase in number through time. The simulations depend on the numerical values of the parameters which again depend on the prostate condition of each male adult under scrutiny. By determining the parameters for each male, the dynamic model can be used as a powerful tool by which the proliferation of bacteria in the bladder can be studied and controlled by different means. Three clinical advices are provided. First, try to achieve that the proliferation rate of bacteria in the bladder is as small as possible, e.g. through altering the pH or chemical composition within the bladder. Second, try to achieve that the out flux of urine from the bladder is substantial, through sufficient drinking. Third, try to achieve that the mass of urine in the bladder is as small as possible, through sufficient urination. The intrinsic parameters for each male can be used to pinpoint the actual out flux during a day necessary to keep the number of bacteria in the bladder low. Suggestions for how to test the model are briefly presented.

The dynamics of cell proliferation.

The article provides a mathematical description based on the theory of differential equations, for the proliferation of malignant cells (cancer). A model is developed which enables us to describe and predict the dynamics of cell proliferation much better than by using ordinary curve fitting procedures. By using differential equations the ability to foresee the dynamics of cell proliferation is in general much better than by using polynomial extrapolations. Complex time relations can be revealed. The mass of each living cell and the number of living cells are described as functions of time, accounting for each living cell's age since cell-birth. The linkage between micro-dynamics and the population dynamics is furnished by coupling the mass increase of each living cell up against the mitosis rate. A comparison is made by in vitro experiments with cancer cells exposed to digitoxin, a new promising anti-cancer drug. Theoretical results for the total number of cells (living or dead) is found to be in good agreement with experiments for the cell line considered, assuming different concentrations of digitoxin. It is shown that for the chosen cell line, the proliferation is halted by an increased time from birth to mitosis of the cells. The delay is probably connected with changes in the Ca concentration inside the cell. The enhanced time between the birth and mitosis of a cell leads effectively to smaller mitosis rates and thereby smaller proliferation rates. This mechanism is different from the earlier results on digitoxin for different cell lines where an increased rate of apoptosis was reported. But we find it reasonable that cell lines can react differently to digitoxin. A development from enhanced time between birth and mitosis to apoptosis can be furnished, dependent of the sensitivity of the cell lines. This mechanism is in general very different from the mechanism appealed to by standard chemotherapy and radiotherapy where the death ratios of the cells are mainly affected. Thus the analysis supports the view that a quite different mechanism is invoked when using digitoxin. This is important, since by appealing to different types of mechanism in parallel during cancer treatment, more selectivity in the targeting of benign versus malignant cells can be invoked. This increases the probability of successful treatment. The critical digitoxin level concentration, i.e. the concentration level where the number of living cells is not increasing, is approximately 50 ng/ml for the cell line we investigated in this article. Therapeutic plasma concentration of digitoxin when treating cardiac congestion is about 15-33 ng/ml, but individual tolerances are large. The effect of digitoxin during cancer treatment is therefore very promising. The dynamic model constitutes a new powerful tool, supported by empirics, describing the mechanism or process by which the number of malignant cells during anti-cancer treatment can be studied and reduced.

Predicting the concentration level of an anti-cancer drug during treatment of a living organism.

For many drugs used in chemotherapy the difference between the therapeutic concentration and the toxic concentration is small. During treatment of a living organism from cancer by using chemotherapy, it is therefore important to foresee the therapeutic concentration in the organism as a function of the injected therapeutic drug dose. This article provides a mathematical dynamic description of the interaction between the organism and the drug, and analyses the dynamics by using ordinary differential equations. The model is tested in a clinical situation where digitoxin is used as the therapeutic drug. The agreement with this experiment is good.

Behaviorist stochastic modeling of instrumental learning.

A mathematical model is presented descriptive of instrumental learning, i.e. operant conditioning. An agent learns to commit a certain number of acts per time unit, distributed as a non-stationary Poisson process. The derivative of the agent's expected utility per time unit, where utility is expected benefit minus expected cost, is interpreted as his drive to reach a local maximum of his expected utility. This drive multiplied with his act intensity are proportional to the change of the agent's act intensity per time unit, which is an ordinary first order differential equation for instrumental learning.