Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.

A Bayesian latent class safety performance function for identifying motor vehicle crash blackspots

The current state of the practice in Blackspot Identification (BSI) utilizes safety performance functions based on total crash counts to identify transport system sites with potentially high crash risk. This paper postulates that total crash count variation over a transport network is a result of multiple distinct crash generating processes including geometric characteristics of the road, spatial features of the surrounding environment, and driver behaviour factors. However, these multiple sources are ignored in current modelling methodologies in both trying to explain or predict crash frequencies across sites. Instead, current practice employs models that imply that a single underlying crash generating process exists. The model mis-specification may lead to correlating crashes with the incorrect sources of contributing factors (e.g. concluding a crash is predominately caused by a geometric feature when it is a behavioural issue), which may ultimately lead to inefficient use of public funds and misidentification of true blackspots. This study aims to propose a latent class model consistent with a multiple crash process theory, and to investigate the influence this model has on correctly identifying crash blackspots. We first present the theoretical and corresponding methodological approach in which a Bayesian Latent Class (BLC) model is estimated assuming that crashes arise from two distinct risk generating processes including engineering and unobserved spatial factors. The Bayesian model is used to incorporate prior information about the contribution of each underlying process to the total crash count. The methodology is applied to the state-controlled roads in Queensland, Australia and the results are compared to an Empirical Bayesian Negative Binomial (EB-NB) model. A comparison of goodness of fit measures illustrates significantly improved performance of the proposed model compared to the NB model. The detection of blackspots was also improved when compared to the EB-NB model. In addition, modelling crashes as the result of two fundamentally separate underlying processes reveals more detailed information about unobserved crash causes.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

A generalized mathematical theory and experimental verification of proportional notches

A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.

Ring loading of a long, thin, circular cylindrical shell enclosing a soft, solid core: A recalculation by the love function method of elasticity.

The problem is solved using the Love function and Flügge shell theory. Numerical work has been done with a computer for various values of shell geometry parameters and elastic constants.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

The Evolving Roles of the Human Resource Function: Understanding Role Changes in the Context of Large-Scale Mergers

The human resource (HR) function is under pressure both to change roles and to play a large variety of roles. Questions of change and development in the HR function become particularly interesting in the context of mergers and acquisitions when two corporations are integrated. The purpose of the thesis is to examine the roles played by the HR function in the context of large-scale mergers and thus to understand what happens to the HR function in such change environments, and to shed light on the underlying factors that influence changes in the HR function. To achieve this goal, the study seeks first to identify the roles played by the HR function before and after the merger, and second, to identify the factors that affect the roles played by the HR function. It adopts a qualitative case study approach including ten focal case organisations (mergers) and four matching cases (non-mergers). The sample consists of large corporations originating from either Finland or Sweden. HR directors and members of the top management teams within the case organisations were interviewed. The study suggests that changes occur within the HR function, and that the trend is for the HR function to become increasingly strategic. However, the HR function was found to play strategic roles only when the HR administration ran smoothly. The study also suggests that the HR function has become more versatile. An HR function that was perceived to be mainly administrative before the merger is likely after the merger to perform some strategically important activities in addition to the administrative ones. Significant changes in the roles played by the HR function were observed in some of the case corporations. This finding suggests that the merger integration process is a window of opportunity for the HR function. HR functions that take a proactive and leading role during the integration process might expand the number of roles played and move from being an administrator before the merger to also being a business partner after integration. The majority of the HR functions studied remained mainly reactive during the organisational change process and although the evidence showed that they moved towards strategic tasks, the intra-functional changes remained comparatively small in these organisations. The study presents a new model that illustrates the impact of the relationship between the top management team and the HR function on the role of the HR function. The expectations held by the top management team for the HR function and the performance of the HR function were found to interact. On a dimension reaching from tactical to strategic, HR performance is likely to correspond to the expectations held by top management.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Molecular hydrodynamic theory of non‐Markovian collective orientational relaxation in dense dipolar liquids

A microscopic study of the non‐Markovian (or memory) effects on the collective orientational relaxation in a dense dipolar liquid is carried out by using an extended hydrodynamic approach which provides a reliable description of the dynamical processes occuring at the molecular length scales. Detailed calculations of the wave‐vector dependent orientational correlation functions are presented. The memory effects are found to play an important role; the non‐Markovian results differ considerably from that of the Markovian theory. In particular, a slow long‐time decay of the longitudinal orientational correlation function is observed for dense liquids which becomes weaker in the presence of a sizeable translational contribution to the collective orientational relaxation. This slow decay can be attributed to the intermolecular correlations at the molecular length scales. The longitudinal component of the orientational correlation function becomes oscillatory in the underdamped limit of momenta relaxations and the frequency dependence of the friction reduce the frictional resistance on the collective excitations (commonly known as dipolarons) to make them long lived. The theory predicts that these dipolarons can, therefore, be important in chemical relaxation processes, in contradiction to the claims of some earlier theoretical studies.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.