The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

Statistical analysis of microscale gas flows and stock price changes

First, recent studies on the information preservation (IP) method, a particle approach for low-speed micro-scale gas flows, are reviewed. The IP method was validated for benchmark issues such as Couette, Poiseuille and Rayleigh flows, compared well with measured data for typical internal flows through micro-channels and external flows past micro flat plates, and combined with the Navier-Stokes equations to be a hybrid scheme for subsonic, rarefied gas flows. Second, the focus is moved to the microscopic characteristic of China stock market, particularly the price correlation between stock deals. A very interesting phenomenon was found that showed a reverse transition behaviour between two neighbouring price changes. This behaviour significantly differs from the transition rules for atomic and molecular energy levels, and it is very helpful to understand the essential difference between stock markets and nature.

Changes in landing mechanics in patients following anterior cruciate ligament reconstruction when wearing an extension constraint knee brace.

BACKGROUND: Anterior cruciate ligament (ACL) reconstruction is associated with a high incidence of second tears (graft tears and contralateral ACL tears). These secondary tears have been attributed to asymmetrical lower extremity mechanics. Knee bracing is one potential intervention that can be used during rehabilitation that has the potential to normalize lower extremity asymmetry; however, little is known about the effect of bracing on movement asymmetry in patients following ACL reconstruction. HYPOTHESIS: Wearing a knee brace would increase knee joint flexion and joint symmetry. It was also expected that the joint mechanics would become more symmetrical in the braced condition. OBJECTIVE: To examine how knee bracing affects knee joint function and symmetry over the course of rehabilitation in patients 6 months following ACL reconstruction. STUDY DESIGN: Controlled laboratory study. LEVEL OF EVIDENCE: Level 3. METHODS: Twenty-three adolescent patients rehabilitating from ACL reconstruction surgery were recruited for the study. The subjects all underwent a motion analysis assessment during a stop-jump activity with and without a functional knee brace on the surgical side that resisted extension for 6 months following the ACL reconstruction surgery. Statistical analysis utilized a 2 × 2 (limb × brace) analysis of variance with a significant alpha level of 0.05. RESULTS: Subjects had increased knee flexion on the surgical side when they were braced. The brace condition increased knee flexion velocity, decreased the initial knee flexion angle, and increased the ground reaction force and knee extension moment on both limbs. Side-to-side asymmetry was present across conditions for the vertical ground reaction force and knee extension moment. CONCLUSION: Wearing a knee brace appears to increase lower extremity compliance and promotes normalized loading on the surgical side. CLINICAL RELEVANCE: Knee extension constraint bracing in postoperative ACL patients may improve symmetry of lower extremity mechanics, which is potentially beneficial in progressing rehabilitation and reducing the incidence of second ACL tears.

Fracture Mechanics Analysis of the Dentine-Luting Cement Interface.

The objectives of this study were to determine the fracture toughness of adhesive interfaces between dentine and clinically relevant, thin layers of dental luting cements. Cements tested included a conventional glass-ionomer, F (Fuji I), a resin-modified glass-ionomer, FP (Fuji Plus) and a compomer cement, D (DyractCem). Ten miniature short-bar chevron notch specimens were manufactured for each cement, each comprising a 40 µm thick chevron of lute, between two 1.5 mm thick blocks of bovine dentine, encased in resin composite. The interfacial KIC results (MN/m3/2) were median (range): F; 0.152 (0.14-0.16), FP; 0.306 (0.27-0.37), D; 0.351 (0.31-0.37). Non-parametric statistical analysis showed that the fracture toughness of F was significantly lower (p

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Improving on- and off-campus student performance in structural mechanics

This paper investigates the performance of 329 (173 on- and 186  off-campus) students enrolled in two structural mechanics units at Deakin University, a leader in engineering distance-education in Australia. The two units experience unacceptably high rates of failure. An analysis of the assignment, laboratory and examination marks is presented. Consideration is also given to the total marks. The results show that on-campus students perform better in structural mechanics than their off-campus counterparts. Plots of the student performance distributions for the three assessment methods are provided (for each unit) and high failure rates are linked to low examination marks. Students tend to perform best in assignments and worst in examinations. Parametric statistical tests show a correlation between the continuous assessment and examination marks. To motivate students to fully participate in continuous assessment tasks the authors therefore propose several changes to the assessment criteria and marking schemes.

Delivery and assessment strategies to improve on- and off-campus student performance in structural mechanics

This paper considers the delivery and assessment strategies used in two structural mechanics units at Deakin University, a leader in distance education in Australia. The two units have had unacceptably high rates of student failure. Student perceptions of the delivery method were analysed and an investigation was carried out of the performance of 329 (173 on- and 156 off-campus) students enrolled in the two units. An analysis of the assignment, laboratory and examination marks is presented. Consideration is also given to the total marks. The results show that on-campus students performed better in structural mechanics than their off-campus counterparts. Plots of the distributions of student performance for the three assessment methods are provided (for each unit) and high failure rates are linked to low examination marks. Students tended to perform best in assignments and worst in examinations. Parametric statistical tests show a correlation between the marks obtained in continuous assessment and in examinations, and it is therefore proposed that, in order to improve performance, the students must be encouraged to participate fully in all aspects of the course. Many students were unenthusiastic about laboratory practical sessions and did not think they aided their understanding of the theoretical material. Motivation to participate is often dependent on the perceived relevance of a given task and its contribution to the total mark and, thus, to help motivate students to participate fully in the continuous assessment tasks, the authors propose several changes to the delivery methods, as well as to assessment criteria and marking schemes.

Transcriptional insights on the regenerative mechanics of axotomized neurons in vitro

Axotomized neurons have the innate ability to undergo regenerative sprouting but this is often impeded by the inhibitory central nervous system environment. To gain mechanistic insights into the key molecular determinates that specifically underlie neuronal regeneration at a transcriptomic level, we have undertaken a DNA microarray study on mature cortical neuronal clusters maintained in vitro at 8, 15, 24 and 48 hrs following complete axonal severance. A total of 305 genes, each with a minimum fold change of ±1.5 for at least one out of the four time points and which achieved statistical significance (one-way ANOVA, P < 0.05), were identified by DAVID and classified into 14 different functional clusters according to Gene Ontology. From our data, we conclude that post-injury regenerative sprouting is an intricate process that requires two distinct pathways. Firstly, it involves restructuring of the neurite cytoskeleton, determined by compound actin and microtubule dynamics, protein trafficking and concomitant modulation of both guidance cues and neurotrophic factors. Secondly, it elicits a cell survival response whereby genes are regulated to protect against oxidative stress, inflammation and cellular ion imbalance. Our data reveal that neurons have the capability to fight insults by elevating biological antioxidants, regulating secondary messengers, suppressing apoptotic genes, controlling ion-associated processes and by expressing cell cycle proteins that, in the context of neuronal injury, could potentially have functions outside their normal role in cell division. Overall, vigilant control of cell survival responses against pernicious secondary processes is vital to avoid cell death and ensure successful neurite regeneration.

Improved systolic ventricular function with normal myocardial mechanics in compensated cardiac hypertrophy

There still controversy about the relation between changes in myocardial contractile function and global left ventricular (LV) performance during stable concentric hypertrophy. To clarify this, we analyzed LV function in vivo and myocardial mechanics in vitro in rats with pressure overload-induced cardiac hypertrophy. Male Wistar rats (70 g) underwent ascending aorta stenosis for 8 weeks (group AAS, n=9). LV performance was assessed by transthoracic echocardiography under light anesthesia. Myocardial function was studied in isolated papillary muscle preparation during isometric contraction. The data were compared with age- and sex-matched sham-operated rats (group C, n=9). LV weight-to-body weight ratio (C: 2.0 ± 0.5 mg/g; AAS: 3.3 ± 0.7 mg/g), LV relative wall thickness (C: 0.19 ± 0.02; AAS; 0.34 ± 0.10), and LV fractional shortening (C: 54 ± 5%; AAS: 70 ± 8%) were increased in the group AAS (p<0.05). Echocardiographic analysis also indicated a significant association (r=0.74; p<0.001) between percent fractional shortening and LV relative wall thickness. The performance of AAS isolated muscle revealed that active tension (C: 6.6 ± 1.7 g/mm 2; AAS: 6.5 ± 1.5 g/mm 2) and maximum rate of tension development (C: 69 ± 21 g/mm 2/s; AAS: 69 ± 18 g/mm 2) were not significantly different from group C (p>0.05). In conclusion: 1) Compensated pressure-overload myocardial hypertrophy is associated with preserved myocardial function and increased ventricular performance; 2) The improved LV function might be due to the ventricular remodeling characterized by an increased relative wall thickness. Copyright © 2002 By PJD Publications Limited.

Assessment of the mechanics of a tissue-engineered rat trachea in an image-processing environment

OBJECTIVES: Despite the recent success regarding the transplantation of tissue-engineered airways, the mechanical properties of these grafts are not well understood. Mechanical assessment of a tissue-engineered airway graft before implantation may be used in the future as a predictor of function. The aim of this preliminary work was to develop a noninvasive image-processing environment for the assessment of airway mechanics.METHOD: Decellularized, recellularized and normal tracheas (groups DECEL, RECEL, and CONTROL, respectively) immersed in Krebs-Henseleit solution were ventilated by a small-animal ventilator connected to a Fleisch pneumotachograph and two pressure transducers (differential and gauge). A camera connected to a stereomicroscope captured images of the pulsation of the trachea before instillation of saline solution and after instillation of Krebs-Henseleit solution, followed by instillation with Krebs-Henseleit with methacholine 0.1 M (protocols A, K and KMCh, respectively). The data were post-processed with computer software and statistical comparisons between groups and protocols were performed.RESULTS: There were statistically significant variations in the image measurements of the medial region of the trachea between the groups (two-way analysis of variance [ANOVA], p<0.01) and of the proximal region between the groups and protocols (two-way ANOVA, p<0.01).CONCLUSIONS: The technique developed in this study is an innovative method for performing a mechanical assessment of engineered tracheal grafts that will enable evaluation of the viscoelastic properties of neo-tracheas prior to transplantation.

Statistical and dynamical properties of a dissipative kicked rotator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Relationships between running economy and mechanics in middle-distance runners

Running economy (RE), i.e. the oxygen consumption at a given submaximal speed, is an important determinant of endurance running performance. So far, investigators have widely attempted to individuate the factors affecting RE in competitive athletes, focusing mainly on the relationships between RE and running biomechanics. However, the current results are inconsistent and a clear mechanical profile of an economic runner has not been yet established. The present work aimed to better understand how the running technique influences RE in sub-elite middle-distance runners by investigating the biomechanical parameters acting on RE and the underlying mechanisms. Special emphasis was given to accounting for intra-individual variability in RE at different speeds and to assessing track running rather than treadmill running. In Study One, a factor analysis was used to reduce the 30 considered mechanical parameters to few global descriptors of the running mechanics. Then, a biomechanical comparison between economic and non economic runners and a multiple regression analysis (with RE as criterion variable and mechanical indices as independent variables) were performed. It was found that a better RE was associated to higher knee and ankle flexion in the support phase, and that the combination of seven individuated mechanical measures explains ∼72% of the variability in RE. In Study Two, a mathematical model predicting RE a priori from the rate of force production, originally developed and used in the field of comparative biology, was adapted and tested in competitive athletes. The model showed a very good fit (R2=0.86). In conclusion, the results of this dissertation suggest that the very complex interrelationships among the mechanical parameters affecting RE may be successfully dealt with through multivariate statistical analyses and the application of theoretical mathematical models. Thanks to these results, coaches are provided with useful tools to assess the biomechanical profile of their athletes. Thus, individual weaknesses in the running technique may be identified and removed, with the ultimate goal to improve RE.

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations.

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.