Dynamics of Shock Probes in Driven Diffusive Systems

We study the dynamics of shock-tracking probe particles in driven diffusive systems and also in equilibrium systems. In a driven system, they induce a diverging timescale that marks the crossover between a passive scalar regime at early times and a diffusive regime at late times; a scaling form characterises this crossover. Introduction of probes into an equilibrium system gives rise to a system-wide density gradient, and the presence of even a single probe can be felt across the entire system.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

The critical Ising model via Kac-Ward matrices

The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. First of all, they satisfy some generalized Kramers-Wannier duality: there is an explicit equality relating the determinants associated to a graph and to its dual graph. Also, they are proportional to the determinants of the discrete critical Laplacians on the graph G, exactly when the genus g is zero or one. Finally, they share several formal properties with the Ray-Singer \bar\partial-torsions of the Riemann surface in which G embeds.Comment: 30 pages, 10 figures; added section 4.4 in version

Fluctuations and skewness of the current in the partially asymmetric exclusion process

We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant) and obtain an explicit finite size formula for the third cumulant. The expression for the third cumulant takes a simple integral form in the limit where the asymmetry scales as the inverse of the square root of the size of the system, which corresponds to a natural separation between weak and strong asymmetry.Comment: 21 pages, 3 figure

Non equilibrium steady states: fluctuations and large deviations of the density and of the current

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.Comment: 35 pages, 9 figure

The near-critical planar FK-Ising model

We study the near-critical FK-Ising model. First, a determination of the correlation length defined via crossing probabilities is provided. Second, a phenomenon about the near-critical behavior of FK-Ising is highlighted, which is completely missing from the case of standard percolation: in any monotone coupling of FK configurations $\omega_p$ (e.g., in the one introduced in [Gri95]), as one raises $p$ near $p_c$, the new edges arrive in a self-organized way, so that the correlation length is not governed anymore by the number of pivotal edges at criticality.Comment: 34 pages, 8 figures. This is a streamlined version; the previous one contains more explanations and additional material on exceptional times in FK models with general $q$. Furthermore, the statement and proof of Theorem 1.2 have slightly change

Recovery practice in community mental health teams: national survey

Background There is consensus about the importance of ‘recovery’ in mental health services, but the link between recovery orientation of mental health teams and personal recovery of individuals has been underresearched. Aims To investigate differences in team leader, clinician and service user perspectives of recovery orientation of community adult mental health teams in England. Method In six English mental health National Health Service (NHS) trusts, randomly chosen community adult mental health teams were surveyed. A random sample of ten patients, one team leader and a convenience sample of five clinicians were surveyed from each team. All respondents rated the recovery orientation of their team using parallel versions of the Recovery Self Assessment (RSA). In addition, service users also rated their own personal recovery using the Questionnaire about Processes of Recovery (QPR). Results Team leaders (n = 22) rated recovery orientation higher than clinicians (n = 109) or patients (n = 120) (Wald(2) = 7.0, P = 0.03), and both NHS trust and team type influenced RSA ratings. Patient-rated recovery orientation was a predictor of personal recovery (b = 0.58, 95% CI 0.31–0.85, P50.001). Team leaders and clinicians with experience of mental illness (39%) or supporting a family member or friend with mental illness (76%) did not differ in their RSA ratings from other team leaders or clinicians. Conclusions Compared with team leaders, frontline clinicians and service users have less positive views on recovery orientation. Increasing recovery orientation may support personal recovery

Bond percolation on isoradial graphs: criticality and universality

In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the sense that the one-arm and 2j-alternating-arm critical exponents (and therefore also the connectivity and volume exponents) are constant across the family of such percolation processes. The isoradial graphs in question are those that satisfy certain weak conditions on their embedding and on their track system. This class of graphs includes, for example, isoradial embeddings of periodic graphs, and graphs derived from rhombic Penrose tilings.Comment: In v2: extended title, and small changes in the tex

The Relationship between Therapeutic Alliance and Service User Satisfaction in Mental Health Inpatient Wards and Crisis House Alternatives: A Cross-Sectional Study

Background Poor service user experiences are often reported on mental health inpatient wards. Crisis houses are an alternative, but evidence is limited. This paper investigates therapeutic alliances in acute wards and crisis houses, exploring how far stronger therapeutic alliance may underlie greater client satisfaction in crisis houses. Methods and Findings Mixed methods were used. In the quantitative component, 108 crisis house and 247 acute ward service users responded to measures of satisfaction, therapeutic relationships, informal peer support, recovery and negative events experienced during the admission. Linear regressions were conducted to estimate the association between service setting and measures, and to model the factors associated with satisfaction. Qualitative interviews exploring therapeutic alliances were conducted with service users and staff in each setting and analysed thematically. Results We found that therapeutic alliances, service user satisfaction and informal peer support were greater in crisis houses than on acute wards, whilst self-rated recovery and numbers of negative events were lower. Adjusted multivariable analyses suggest that therapeutic relationships, informal peer support and negative experiences related to staff may be important factors in accounting for greater satisfaction in crisis houses. Qualitative results suggest factors that influence therapeutic alliances include service user perceptions of basic human qualities such as kindness and empathy in staff and, at service level, the extent of loss of liberty and autonomy. Conclusions and Implications We found that service users experience better therapeutic relationships and higher satisfaction in crisis houses compared to acute wards, although we cannot exclude the possibility that differences in service user characteristics contribute to this. This finding provides some support for the expansion of crisis house provision. Further research is needed to investigate why acute ward service users experience a lack of compassion and humanity from ward staff and how this could be changed

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721