Dynamical density functional theory: phase separation in a cavity and the influence of symmetry

Consider a fluid composed of two species of particles, where the interparticle pair potentials $u_{11} = u_{22} \neq u_{12}$. On confining an equal number of particles from each species in a cavity, one finds that the average one body density profiles of each species are constrained to be exactly the same due to the symmetry, when both external cavity potentials are the same. For a binary fluid of Brownian particles interacting via repulsive Gaussian pair potentials that exhibits phase separation, we study the dynamics of the fluid one body density profiles on breaking the symmetry of the external potentials, using the dynamical density functional theory of Marconi and Tarazona [{\it J. Chem. Phys.}, {\bf 110}, 8032 (1999)]. On breaking the symmetry we see that the fluid one body density profiles can then show the phase separation that is present.Comment: 7 pages, 4 figures. Accepted for the proceedings of the Liquid Matter conference 2005, to be publication in J. Phys.: Condens. Matte

The Experience of Burnout in Counselling Psychology Trainees: An Interpretative Phenomenological Analysis

Counselling psychology training consists of many professional, academic and personal demands. Poor management of these demands could lead to burnout and drop out from training (Cornér et al, 2017). The current quantitative literature places emphasis on three-dimensional conceptual frameworks of burnout using measures such as the Maslach Burnout Inventory (MBI) (Maslach & Jackson, 1981) and the Copenhagen Burnout Inventory (CBI) (Kristensen et al, 2005). The qualitative literature outlined only stressors of counselling psychology training and burnout in qualified counselling psychologists. To address a research gap in how trainees experience burnout, this study was designed to explore burnout as part of a wider context. Eight third-year trainee counselling psychologists were recruited from six universities across London. Data was collected using semi-structured interviews. Interpretative Phenomenological Analysis (IPA) was used to analyse the data. Three superordinate themes emerged: A perfect storm: the demands of counselling psychology training, Treading on shaky foundations, and Impact of training on self and others. Participants described the training as an extremely demanding endeavour which led to a disconcerting loss of agency and resentment towards the process. Participants often could not gauge their own progress, and they perceived the training environment as hostile towards difficulties and failure. To disguise their feelings of self-doubt, the participants appeared to foster a form of artificial confidence to give the illusion of self-assurance. Other effects of burnout included upheaval in significant relationships, as well as physical and health-related changes. Burnout was characterised as perseverance through unaddressed difficulties, rather than inability to function. However, participants reported developing greater resilience and self-monitoring to prevent burnout occurring in the future. Recommendations include normalisation of difficulties and burnout by trainers, and development of literature and workshops for prospective trainees to fully understand the training before embarking on the process. Other areas for future research are also discussed

Dynamical density functional theory and its application to spinodal decomposition

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multi-body interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our non-linear theory is equivalent to the (generalised) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wavenumber larger than that of the main peak.Comment: 23 pages, 3 figure

Microscopic theory of solvent mediated long range forces: influence of wetting

We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of strong adsorption (wetting) and of critical fluctuations in the solvent. We illustrate the approach for the Gaussian core model, a simple model of a polymer mixture in solution and find extremely attractive, long ranged solvent mediated potentials between the big particles for state points lying close to the binodal, on the side where the solvent is poor in the species which is favoured by the big particles.Comment: 7 pages, 3 figures, submitted to Europhysics Letter

Mean-field dynamical density functional theory

We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini Bettolo Marconi and Tarazona [J. Chem. Phys. {\bf 110}, 8032 (1999)], supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian Dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed.Comment: 8 pagers, 4 figure

Investigating Primary Source Literacy

Primary source research requires students to acquire specialized research skills. This paper presents results from a user study testing the effectiveness of a Web guide designed to convey the concepts behind “primary source literacy”. The study also evaluated students’ strengths and weaknesses when conducting primary source research