Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers

We consider three independent Brownian walkers moving on a line. The process terminates when the left-most walker (the `Leader') meets either of the other two walkers. For arbitrary values of the diffusion constants D_1 (the Leader), D_2 and D_3 of the three walkers, we compute the probability distribution P(m|y_2,y_3) of the maximum distance m between the Leader and the current right-most particle (the `Laggard') during the process, where y_2 and y_3 are the initial distances between the leader and the other two walkers. The result has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where \delta = (2\pi-\theta)/(\pi-\theta) and \theta = cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also determined exactly

Antisite Domains in Double Perovskite Ferromagnets: Impact on Magnetotransport and Half-metallicity

Several double perovskite materials of the form A_2BB'O_6 exhibit high ferromagnetic T_c, and significant low field magnetoresistance. They are also a candidate source of spin polarized electrons. The potential usefulness of these materials is, however, frustrated by mislocation of the B and B' ions, which do not organise themselves in the ideal alternating structure. The result is a strong dependence of physical properties on preparative conditions, reducing the magnetization and destroying the half-metallicity. We provide the first results on the impact of spatially correlated antisite disorder, as observed experimentally, on the ferromagnetic double perovskites. The antisite domains suppress magnetism and half-metallicity, as expected, but lead to a dramatic enhancement of the low field magnetoresistance.Comment: 6 pages, pdflatex, EPL styl

Transitions through Critical Temperatures in Nematic Liquid Crystals

We obtain ‘dynamic’ estimates for critical nematic liquid crystal (LC) temperatures with a slowly varying temperature-dependent control variable. We focus on two critical temperatures : the supercooling temperature below which the isotropic phase loses stability and the superheating temperature above which the ordered nematic states do not exist. In contrast to the static problem, the isotropic phase exhibits a memory effect below the supercooling temperature. This delayed loss of stability is independent of the rate of change of temperature and depends purely on the initial value of the temperature

Persistence and Quiescence of Seismicity on Fault Systems

We study the statistics of simulated earthquakes in a quasistatic model of two parallel heterogeneous faults within a slowly driven elastic tectonic plate. The probability that one fault remains dormant while the other is active for a time Dt following the previous activity shift is proportional to the inverse of Dt to the power 1+x, a result that is robust in the presence of annealed noise and strength weakening. A mean field theory accounts for the observed dependence of the persistence exponent x as a function of heterogeneity and distance between faults. These results continue to hold if the number of competing faults is increased. This is related to the persistence phenomenon discovered in a large variety of systems, which specifies how long a relaxing dynamical system remains in a neighborhood of its initial configuration. Our persistence exponent is found to vary as a function of heterogeneity and distance between faults, thus defining a novel universality class.Comment: 4 pages, 3 figures, Revte

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

Area Distribution of Elastic Brownian Motion

We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will stress on the power of self adjoint extension to investigate different possible boundary conditions for the stochastic processes.Comment: 18 pages, published versio

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

Understanding Search Trees via Statistical Physics

We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain exact asymptotic results. In particular, we show that the probability distributions of extreme observables associated with a random search tree such as the height and the balanced height of a tree have a traveling front structure. In addition, the variance of the number of nodes needed to store a data string of a given size N is shown to undergo a striking phase transition at a critical value of the branching ratio m_c=26. We identify the mechanism of this phase transition, show that it is generic and occurs in various other problems as well. New results are obtained when each element of the data string is a D-dimensional vector. We show that this problem also has a phase transition at a critical dimension, D_c= \pi/\sin^{-1}(1/\sqrt{8})=8.69363...Comment: 11 pages, 8 .eps figures included. Invited contribution to STATPHYS-22 held at Bangalore (India) in July 2004. To appear in the proceedings of STATPHYS-2