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Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

We analyze biased ensembles of trajectories for a two-dimensional system of particles, evolving by Langevin dynamics in a channel geometry. This bias controls the degree of particle clustering. On biasing to large clustering, we observe a dynamical phase transition where the particles break symmetry and accumulate at one of the walls. We analyze the mechanical properties of this symmetry-broken state using the Irving-Kirkwood stress tensor. The biased ensemble is characterized by body forces that originate in random thermal noises, but they have finite averages in the presence of the bias. We discuss the connection of these forces to Doob's transform and optimal control theory.

We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. We focus on the probabilities of rare events (large deviations). First, we discuss a PT (parity-time) symmetry that appears in ensembles of trajectories where a current is constrained to have a large (non-typical) value. We analyse the heat flow in such ensembles, and compare it with non-equilibrium steady states. Second, we consider pathwise large deviations that are defined by considering many copies of a system. We show how the probability currents in such systems can be decomposed into orthogonal contributions that are related to convergence to equilibrium and to dissipation. We discuss the implications of these results for modelling non-equilibrium steady states.

Abstract Leakage currents accelerate surface degradation of metal contacts via small scale arcing across lubricating films, but recent observations suggest that metallic nanoparticle additives in lubricants may be useful to improve contact performance. These findings prompted a study that examined electrically induced surface pitting of steel contacts in the presence of several lubricating greases including some containing nanometer-sized colloidal silver (Ag) particles. Reciprocating rolling sphere-on-disk experiments were conducted under electro-tribological loads employing polyurea greases derived from mineral and synthetic base oils with and without additives. Friction forces and electrical resistance were monitored continuously during the tests; surface changes were characterized by means of optical spectroscopy, stylus profilometry, and scanning electron microscopy (SEM) including compositional analysis using energy dispersive spectroscopy (EDS). The observations demonstrate that surface pitting induced by arcing occurs mainly at the points were the rolling motion changes direction and that eroded metal is deposited along the wear grove. Micron-sized pits are formed which contain carbon and oxygen indicating that arcing causes decomposition of the hydrocarbon lubricants. Numerous findings indicate a significant inhibition of pitting is induced by the Ag nanoparticles; some greases containing other additives exhibit a similar, although less pronounced, effect.

As public attention is increasingly drawn toward more sustainable transportation methods, the popularity of electric vehicles (EVs) as part of the solution is rapidly expanding. Operating conditions within EVs can be severe compared to standard combustion powertrains, and the risk of electrical arcing across mechanical surfaces from electric leakage currents incites additional concern. This study employed a series of electro-tribological tests utilizing various moving patterns to improve understanding of the driving conditions for electrically induced bearing damage (EIBD). Rolling ball-on-disk tests were performed with different polyurea-thickened greases. Rotational tests were initially run at various speeds and test durations, but electrical damage was limited. However, electrical damage was unmistakable when a reciprocating motion was used at different track lengths and speeds. These results suggest that the conditions associated with the track length, such as the number of directional changes and speed-dependent film thickness, play a considerable role in forming electrical damage. This work provides critical insights into the mechanisms of EIBD in EVs and other electrical systems. It highlights the importance of understanding the operational conditions that contribute to EIBD, which can lead to improved designs and maintenance practices, ultimately enhancing the efficiency and lifespan of these systems.

Abstract In the numerical study of rough surfaces in contact problem, the flexible body beneath the roughness is commonly assumed as a half-space or a half-plane. The surface displacement on the boundary, the displacement components and state of stress inside the half-space can be determined through the convolution of the traction and the corresponding influence function in a closed-form. The influence function is often represented by the Boussinesq-Cerruti solution and the Flamant solution for three-dimensional elasticity and plane strain/stress, respectively. In this study, we rigorously show that any numerical model using the above mentioned half-space solution is a special form of the boundary element method (BEM). The boundary integral equations (BIEs) in the BEM is simplified to the Flamant solution when the domain is strictly a half-plane for the plane strain/stress condition. Similarly, the BIE is degraded to the Boussinesq-Cerruti solution if the domain is strictly a half-space. Therefore, the numerical models utilizing these closed-form influence functions are the special BEM where the domain is a half-space (or a half-plane). This analytical work sheds some light on how to accurately simulate the non-half-space contact problem using the BEM.

Electrical contacts, although critically important for a wide range of applications, are susceptible to degradation due to fretting corrosion, especially when sliding and vibrations occur. To overcome fretting corrosion and sliding wear, lubricants are often used. However, the use of lubricants can cause other detrimental issues. Lubricants usually consist of non-conductive fluids such as hydrocarbons and fluorocarbons. Due to fluid dynamics, when sliding, vibration or other excitation occurs, these fluids can cause prolonged gaps between the conducting metal surfaces. Practically, this has been observed in data centers where vibrations due to technician maintenance or even earthquakes can occur. Depending on the viscosity and roughness of the surfaces, the time it takes these connector surfaces to return to solid conductive contact can be many seconds or longer. This work uses a novel theoretical model of the coupled fluid and solid mechanics between the rough metallic surfaces to evaluate these intermittent breaks in contact due to sliding. The influence of variation in lubricant properties, roughness, contact radius and contact force are considered by the model.

The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.

This study investigates the predictions of the real contact area for perfectly elastic rough surfaces using a boundary element method (BEM). Sample surface measurements were used in the BEM to predict the real contact area as a function of load. The surfaces were normalized by the root-mean-square (RMS) slope to evaluate if contact area measurements would collapse onto one master curve. If so, this would confirm that the contact areas of manufactured, real measured surfaces are directly proportional to the root mean square slope and the applied load, which is predicted by fractal diffusion-based rough surface contact theory. The data predicts a complex response that deviates from this behavior. The variation in the RMS slope and the spectrum of the system related to the features in contact are further evaluated to illuminate why this property is seen in some types of surfaces and not others.

In many machines and mechanical components, there is a need for new bearing technologies to reduce friction and wear, and provide precision control of motion when the load is varied. This can be provided by electronically controlled actuators and sensors on the surfaces, but then the system reliability can be an issue. In contrast, biomimetic surfaces can be created that adapt mechanically to variations in load. This work uses numerical methods to research the use of self-adapting surfaces for bearings that are based on the deformable nature of biological materials such as articular cartilage. These surfaces are designed to change their profiles to achieve a desired behavior, without any external control. The surfaces change their profile to control the film height and tilt of the bearing to a near constant value for different loads. If the surfaces are tilted, the grooved self-adapting surfaces will also react with a larger restoring moment than a conventional grooved surface. These surfaces could be beneficial to applications where electrical systems and controls are not feasible.

This article explores the congruence between poetry therapy and the strengths perspective of social work. It demonstrates the ways in which poetry therapy is consistent with the strengths perspective and discusses methods for its utilization in direct practice settings. Case examples are provided to help the practitioner learn how to utilize poetry therapy with clients from diverse backgrounds. As a tool in strengths-based practice, poetry and poetry therapy can help empower clients and help to focus practitioners on clients’ capacities and resilencies. This article seeks to expand upon the growing literature of strengths-based social work, addressing how the theory can be applied to clinical practice situations.

We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhibits tricritical behavior. Self-propulsion has a non-perturbative effect on the phase diagram, yielding novel phase behaviors depending on the type of aligning interactions. For aligning interaction that increase monotonically with the density, the tricritical point diverges to infinite density reproducing the standard scenario of a discontinuous flocking transition accompanied by traveling bands. In contrast, for models where the aligning interaction is non-monotonic in density, the system can exhibit either (the nonequilibrium counterpart of) an azeotropic point, associated with a continuous flocking transition, or a state with counterpropagating bands.

We apply Bayesian inference methods to a suite of distinct compartmental models of generalised SEIR type, in which diagnosis and quarantine are included via extra compartments. We investigate the evidence for a change in lethality of COVID-19 in late autumn 2020 in the UK, using age-structured, weekly national aggregate data for cases and mortalities. Models that allow a (step-like or graded) change in infection fatality rate (IFR) have consistently higher model evidence than those without. Moreover, they all infer a close to two-fold increase in IFR. This value lies well above most previously available estimates. However, the same models consistently infer that, most probably, the increase in IFR preceded the time window during which variant B.1.1.7 (alpha) became the dominant strain in the UK. Therefore, according to our models, the caseload and mortality data do not offer unequivocal evidence for higher lethality of a new variant. We compare these results for the UK with similar models for Germany and France, which also show increases in inferred IFR during the same period, despite the even later arrival of new variants in those countries. We argue that while the new variant(s) may be one contributing cause of a large increase in IFR in the UK in autumn 2020, other factors, such as seasonality, or pressure on health services, are likely to also have contributed.