Transition probabilities for diffusion equations by means of path integrals.

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leading to analytical expressions for the transition probabilities and for the maximum probability paths. A second part consists of the derivation of an analytical approximation for the transition probability, which is useful in case the path integral is too complex to be calculated. The approximation we present is based on a convex combination of a new analytical upper and lower bound for the transition probabilities. The fact that the approximation is analytical has some important advantages, e.g. for the investigation of Asian options. Finally, we demonstrate the accuracy of the approximation by means of a few graphical illustrationsAdvantages; Comonotonicity; Diffusion processes; Models; Option; Path integral;

Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.Comment: Published; withdrawn since ordering in archive gives misleading impression of new publicatio

Viscosity of Colloidal Suspensions

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $\phi$ and frequency $\omega$ over the entire fluid range, i.e., for volume fractions $0 < \phi < 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $\eta (\phi,\omega) = \eta_{\infty}(\phi) + \eta_{cd}(\phi,\omega)$, where $\eta_{\infty}(\phi) = \eta_0 \chi(\phi)$ is the infinite frequency (or very short time) viscosity, with $\eta_0$ the solvent viscosity, $\chi(\phi)$ the equilibrium hard sphere radial distribution function at contact, and $\eta_{cd}(\phi,\omega)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'{e}clet time scale $\tau_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $\eta_N(\phi) = \eta(\phi,\omega = 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $\omega$ is of the form $\eta_{\infty}(\phi) + A(\phi)(\omega \tau_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(\phi)$ differs by a constant factor $2/\chi(\phi)$ from the exact coefficient, computed from the Green-Kubo formula for $\eta(\phi,\omega)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.Comment: 51 page

A straightforward analytical calculation of the distribution of an annuity certain with stochastic interest rate.

Starting from the moment generating function of the annuity certain with stochastic interest rate written by means of a time discretization of the Wiener process as an n-fold integral, a straightforward evaluation of the corresponding distribution function is obtained letting n tend to infinity. The advantage of the present method consists in the direct calculation technique of the n-fold integral, instead of using moment calculation or differential equations, and in the possible applicability of the present method to varying annuities which could be applied to IBNR results, as well as to pension fund calculations, etc.Distribution; Annuities; Processes; Evaluation;

Dynamic structure factors of a dense mixture

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal packing of the two species. In contrast, a few small particles diffuse easily in the background of a dense fluid of large particles. We expect our results to describe neutron scattering from a dense mixture

Improved simulation of phase change processes in applications where conduction is the dominant heat transfer mode

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierThis paper reports on the development, experimental validation and application of a semi-empirical model for the simulation of the phase change process in phase change materials (PCM). PCMs are now increasingly being used in various building materials such as plasterboard, concrete or panels to improve thermal control in buildings and accurate modelling of their behaviour is important to effectively capture the effects of storage on indoor thermal conditions. Unlike many commercial simulation packages that assume very similar melting and freezing behaviour for the PCM and no hysteresis, the methodology employed treats the melting and freezing processes separately and this allows the inclusion of the effect of hysteresis in the modelling. As demonstrated by the results in this paper, this approach provides a more accurate prediction of the temperature and heat flow in the material, which is of particular importance in providing accurate representation of indoor thermal conditions during thermal cycling. The difference in the prediction accuracy of the two methods is a function of the properties of the PCM. The smaller the hysteresis of the PCM, the lower will be the prediction error of the conventional approach, and solution time will become the determining factor in selecting the simulation approach in practical applications.This work is funded from the Engineering and Physical Sciences Research Council (EPSRC) of the UK, Grant No: EP/H004181/1

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

The role of area level social deprivation on childhood and adolescent consultation rate in primary care:a population based, cohort study

BACKGROUND: Studies show that children and adolescents in the most socially deprived areas (SDA) consult their general practitioner (GP) more often than those in the least socially deprived areas (Non-SDA). Given that GPs see a wide range of diseases, it is important to know which clinical diagnoses are shaped by socioeconomic factors. The primary objective was to determine the association between area level social deprivation and consultation rates in a pediatric population. The secondary objective was to explore this association across a wide range of clinical diagnoses. METHODS: A cohort study using the Rijnmond Primary Care Database (RPCD) was conducted. Between 2013 and 2020, a total of 69,861 patients aged 0 to 17 years registered with a GP were analysed. A consultation was defined as patient contact and entry of a diagnosis using the International Classification of Primary Care (ICPC-1) code. Associations between consultation rates, ICPC-1 codes and area level social deprivation were explored using a Poisson regression model. The incidence risk ratio (IRR) and 95% confidence interval (CI) were reported. RESULTS: Over the 7-year study period the consultation rate of the study population was 3.8 per person-years. The top 5 reasons for children and adolescents to consult their GP was related to skin, respiratory, general unspecified, musculoskeletal and digestive symptoms or diagnoses. Consultation rate was higher in SDA group compared to Non-SDA group (IRR 1.20, 95% CI 1.19–1.20). Consultation rate for ICPC-1 code related to pregnancy and family planning was significantly lower in SDA group compared to Non-SDA group. Upon further exploration of this code, SDA group were less likely to consult for oral contraception and more likely to contact a GP for induced termination of pregnancy compared to Non-SDA group (IRR 0.36; 95% CI 0.33–0.44 and IRR 2.94; 95% CI 1.58–5.46 respectively). CONCLUSIONS: Overall, SDA group had higher GP consultation rates for the majority of clinical diagnoses except for pregnancy and family planning. In this latter category, adolescent females in SDA consulted less frequently for oral contraception. This study illustrates the need to understand the underlying health seeking behaviors of children and adolescents at different development phases of their lives. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12875-022-01873-x

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur