Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the ``classical'' relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed to an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).Comment: 27 pages latex, 1 figur

Arithmetic area for m planar Brownian paths

We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.Comment: 12 pages, 2 figure

Visual Journaling in Early Psychosis Treatment: An Art Therapy Intervention Design

This research will explore current theory and methods of practice to develop an intervention design for visual journaling that can be used during art therapy with people receiving early psychosis treatment. Essentially, the visual journal as symbol, process, and container of integrated knowledge situates art as a form of language. To justify a visual journal’s clinical scope of operations as an early psychosis intervention design, a number of methodological evidence-based concerns must be addressed first. Simply, these include determining with clarity the psychological mechanisms underlying psychosis and psychosis-like experiences; art therapy; and visual journaling. By reviewing relevant gaps in the psychological and psychiatric literature, this intervention’s metacognitive function and the choice of art therapy as a guiding framework together highlight an important bridge which may support the long-term needs of clients while advancing a field of research. That said, because the active uncovering and processing of crisis-related experiences for a clinically vulnerable population with reality-testing thought disorder poses an ethical concern, this research must also be thorough and parsimonious. Accordingly, the projected benefits and counter-indicated risks of visual journaling with clients who experience psychosis are critical considerations to be developed through a discussion of the triadic relationship’s fundamental qualities to art therapy. The presented hypothesis is limited as a first step and clinical recommendations need to be piloted before efficacy can be evaluated

The Local Time Distribution of a Particle Diffusing on a Graph

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included

Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The "Statistical Curse of the Second Half Rank" is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

Full field investigation of salt deformation at room temperature: cooperation of crystal plasticity and grain sliding

International audienceWe observed with optical and scanning electron microscopy halite samples during uniaxial compression. Surface displacement fields were retrieved from digital images taken at different loading stages thanks to digital image correlation (DIC) techniques, on the basis of which we could 1) compute global and local strain fields, 2) identify two co-operational deformation mechanisms. The latter were 1) crystal slip plasticity (CSP), as evidenced by the occurrence of slip lines and computed discrete intracrystalline slip bands at the grain surfaces, 2) interfacial micro-cracking and grain boundary sliding (GBS), as evidenced by the computed relative interfacial displacements. The heterogeneities of the strain fields at the aggregate and at the grain scale, and the local contributions of each mechanism were clearly related to the microstructure, i.e. the relative crystallographic orientations of neighboring grains and the interfacial orientations with respect to the principal stress

Brownian Motion in wedges, last passage time and the second arc-sine law

We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \{OI_i ; i=1,2,..., n\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\arcsin$ or $(\arcsin)^2$ functions. The original result of Levy is recovered as the special case $n=2$. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed