Interaction Potential between the Ground States of H and Hˉ

An investigation of the interaction potential for H and H- in both ungerade and gerade modes is carried out by a semiempirical method in which the recently observed isotope effect in dissociative attachment of electrons to hydrogen molecules is used. The interaction obtained is complex, and the imaginary parts of the interaction account for electron emissions during the course of the interaction. A comparison of the present result with other calculations is presented. The isotope effect in dissociative attachment is also discussed. It is shown that the ratios of the survival probabilities alone do not provide an adequate approximation for the isotope effect

Survival Probability in Dissociative Attachment

The survival probability in dissociative attachment is investigated with special attention to the (e, H2 ) system. It is shown that the simple expression for the dissociative-attachment cross section, as given by the product of a capture cross section and a survival probability, is equivalent to the s -wave approximation for the g → g dissociative attachment. This expression, however, does not constitute an approximation for the g → u dissociative attachment, since the parity of the initial rotational states of H2 is always opposite to that of the relative angular momentum states of H and H- and the capture cross section appearing in the simple expression is identically zero. According to the Kronig selection rules and the symmetry requirements, only odd partial waves of the incident electron may contribute to the g → u dissociative attachment in the (e, H2 ) system. Consequently, the lowest contributing partial wave is not the s wave but the p wave of the incident electron. This, then, destroys the simple proportional dependence of the cross section on the survival probability. However, one may still express the cross section as a sum of products of a capture cross section and a survival probability for the various contributing angular momentum states of the constituent nuclei. The dependence of the survival probability on the angular momentum states of the constituent nuclei is also investigated for the (e, H2) system. It is observed that for the g → u dissociative attachment the survival probability depends strongly on the angular momentum states. This arises because the g → u dissociative attachment occurs at such a low energy that variations in the centrifugal barrier become comparable with the breakup energy of the constituent atoms. This then suggests a strong temperature dependence for the g → u dissociative attachment in the (e, H2) system. For the g → g dissociative attachment, such dependence is much weaker since here the process significant at a somewhat higher energy and the variation in centrifugal energy is overshadowed by the larger break-up energy of the constituent atoms. The validity of the commonly adopted approximation for survival probability (involving the auto-ionization width and relative velocity of the nuclei) is also examined

Associative Detachment: H+Hˉ→₂\u3csup\u3e*\u3c/sup\u3e+e

The process of associative detachment in the (H,H-) collision system is investigated at energies below 12 eV. In this energy region, the interaction potential between H and H- has recently been determined. The energy dependence of the cross section is calculated with explicit allowance for the production of hot hydrogen molecules. It is observed that associative detachment provides a possible mechanism for generating an inverted population of the residual molecule such as H2

A mathematical model of the growth of uterine myomas

Uterine myomas or fibroids are common, benign smooth muscle tumours that can grow to 10 cm or more in diameter and are routinely removed surgically. They are typically slow- growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material, based on a linear stress–strain relationship, and Darcy’s law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of nonlinear partial differential equations with two moving boundaries. Numerical solutions of the model successfully reproduce qualitatively the clinically observed three-phase “fast–slow–fast” growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch-like cell growth response to stress. Analysis of large-time solutions reveal that while there is a functioning vasculature throughout the myoma, exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is also presented, and in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model

A mathematical model for the human menstrual cycle

A simple mathematical model framework is developed to describe the hormonal interactions of the human menstrual cycle along the hypothalamus–pituitary–ovaries axis. The framework is designed so that it can be readily extended to model processes that disrupt the normal functioning cycle. The model in its most basic formulation exhibits multiple periodic solutions, one of which shows the key characteristics of a menstrual cycle, while the others indicate possible abnormalities sometimes observed in women of reproductive age. The basic model is extended to encompass receptor down-regulation as a mechanism to describe the desensitization of the pituitary to continuous stimulation of hypothalamic hormone, a hormonal therapy that is commonly prescribed prior to the surgical procedure for the removal of uterine myomas. Though the mechanisms for desensitization are likely to be more complex, the model results are in good qualitative agreement with physiological observations

THE EFFECT OF DIFFERENT PLYOMETRIC-SQUAT TRAINING ON TAEKWONDO POWER DEVELOPMENT IN THE LOWER EXTREMITY

The purpose of this study was to investigate the effect on three different training methods by combining the typical plyometric training method (drop jump) and traditional weight training (112squat). The subjects were fifteen male high school athletes. The training duration for all subjects was eight weeks, and the frequency was twice a week. One Kistler force plate was used to record the power abilities of the subjects performing counter-movement jump (CMJ) and one PEAK camera (120 Hz) was also used to record the Axe-kicking movement time. Based on the results of this study, combining the vertical drop jump and horizontal drop jump with weight training could improve the maximum power and Axe-kick movement time. Therefore, it is important to consider the movement specific character when the muscular strength training of Taekwondo athletes

Modelling the outbreak of infectious disease following mutation from a non-transmissible strain

In-host mutation of a cross-species infectious disease to a form that is transmissible between humans has resulted with devastating global pandemics in the past. We use simple mathematical models to describe this process with the aim to better understand the emergence of an epidemic resulting from such a mutation and the extent of measures that are needed to control it. The feared outbreak of a human–human transmissible form of avian influenza leading to a global epidemic is the paradigm for this study. We extend the SIR approach to derive a deterministic and a stochastic formulation to describe the evolution of two classes of susceptible and infected states and a removed state, leading to a system of ordinary differential equations and a stochastic equivalent based on a Markov process. For the deterministic model, the contrasting timescale of the mutation process and disease infectiousness is exploited in two limits using asymptotic analysis in order to determine, in terms of the model parameters, necessary conditions for an epidemic to take place and timescales for the onset of the epidemic, the size and duration of the epidemic and the maximum level of the infected individuals at one time. Furthermore, the basic reproduction number is determined from asymptotic analysis of a distinguished limit. Comparisons between the deterministic and stochastic model demonstrate that stochasticity has little effect on most aspects of an epidemic, but does have significant impact on its onset particularly for smaller populations and lower mutation rates for representatively large populations. The deterministic model is extended to investigate a range of quarantine and vaccination programmes, whereby in the two asymptotic limits analysed, quantitative estimates on the outcomes and effectiveness of these control measures are established

Multimedia Object Modelling and Storage Allocation Strategies for Heterogeneous Parallel Access Storage Devices in Real Time Multimedia Computing Systems

The improvements in disk speeds have not kept up with improvements in processor and memory speeds. Conventional storage techniques, in the face of multimedia data, are inefficient and/or inadequate. Here, an efficient multimedia object allocation strategy is presented. We describe a multimedia object model, the object and storage device characteristics, and the fragmentation strategy. A bipartite graph approach is used for mapping fragments to storage devices and a cost function is used to determine an efficient allocation of an object and to balance the loads on the devices

ANALYSIS OF THE PRESSURE DISTRIBUTION PATTERN AND THE CONTROLLING BALANCE DURING KICK MOVEMENT OF TAI-CHI CHUAN

The purpose of this study was to compare the pressure distribution patterns of the stable kick and unstable kick from the kick movement of a Tai-Chi Chuan athlete. A national elite female Tai-Chi Chuan athlete was the subject for this study. The Tekscan HR Mat Pressure Measurement System was used to collect the vertical ground reaction force and the pressure history of the standing foot in right kicking movement and left kicking movement. All the data of the standing foot were divided into metatarsals, tarsals and phalanges to calculate the partial force and partial pressure. The pressure-time diagram of the phalanges, metatarsals and tarsals indicated that the pressure histories trended to be stable in each time as the lefl kick completed, and the phalanges produced 'snatchy' and larger pressures acting on the ground