Persistence in q-state Potts model: A Mean-Field approach

We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density $P(t)$ of persistent spins is imposed. For this model, it is known that $P(t)$ follows a power-law decay with time, $P(t)\sim t^{-\theta(q)}$ where $\theta(q)$ is the $q$-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function $P_{2}(r,t)$ has the scaling form $P_{2}(r,t)=P(t)^{2}f(r/t^{{1/2}})$ for all values of the persistence exponent $\theta(q)$. The scaling function has the limiting behaviour $f(x)\sim x^{-2\theta}$ ($x\ll 1$) and $f(x)\to 1$ ($x\gg 1$). We then show within the Independent Interval Approximation (IIA) that the distribution $n(k,t)$ of separation $k$ between two consecutive persistent spins at time $t$ has the asymptotic scaling form $n(k,t)=t^{-2\phi}g(t,\frac{k}{t^{\phi}})$ where the dynamical exponent has the form $\phi$=max(${1/2},\theta$). The behaviour of the scaling function for large and small values of the arguments is found analytically. We find that for small separations $k\ll t^{\phi}, n(k,t)\sim P(t)k^{-\tau}$ where $\tau$=max($2(1-\theta),2\theta$), while for large separations $k\gg t^{\phi}$, $g(t,x)$ decays exponentially with $x$. The unusual dynamical scaling form and the behaviour of the scaling function is supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.

Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor

Synthesis, applications and mechanistic investigations of C2 symmetric guanidinium salts

A range of guanidinium catalysts was prepared in six or seven synthetic steps and applied to the phase transfer alkylation of a glycinate Schiff's base in 21–86% ee as well as the phase transfer epoxidation of some chalcones in 85–94% ee. Using a spectrophotometric method, pKa values in the range 13.2–13.9 in DMSO have been determined for some of the catalysts highlighting an increase in basicity relative to achiral tetramethylguanidine (pKa=13.0) and a mechanism involving the protonated guanidinium ion as a phase transfer catalyst is proposed. The use of two of the catalysts for the addition of nucleophiles in Michael addition reactions was investigated and both were found to be effective catalysts. A counterion effect was apparent in these reactions, but no enantioselectivity was observed

Propriedades biomecânicas da fáscia lata e do ligamento cruzado cranial de cães Biomechanical properties of canine fascia lata and cranial cruciate ligament

Preparações bilaterais do ligamento cruzado cranial e da fáscia lata de 15 cães foram testadas na máquina Instron, modelo 4482. Os animais, de ambos os sexos, idade entre um e quatro anos, pesavam em média 11,80 ± 1,99kg. Os retalhos de fáscia lata foram testados retilíneos e torcidos e o ligamento cruzado cranial foi testado mantendo um ângulo de 135° entre a tíbia e o fêmur e 0°, 15° de rotação externa e 15° de rotação interna da tíbia em relação ao fêmur. A velocidade dos testes de tração foi de 8,47mm por segundo. A força máxima dos retalhos de fáscia lata foi aproximadamente de 290 Newtons, e a tensão máxima, 28 Megapascal. A torção não influenciou na resistência dos retalhos de fáscia lata. A rotação externa e interna da tíbia de 15º também não influenciou na força máxima do ligamento cruzado cranial, que foi aproximadamente de 660 Newtons, nem na tensão máxima, que foi cerca de 75 Megapascal. Os retalhos de fáscia lata apresentaram 44% da força máxima e 37% da tensão máxima do ligamento, no entanto, os retalhos torcidos mostraram maior deformação do que os retalhos retilíneos, alcançando cerca de 70% da deformação do ligamento, sendo essa forma a mais indicada na substituição do ligamento cruzado cranial.<br>Bilateral preparations of fascia lata and cranial cruciate ligament from 15 dogs were tested in Instron machine, model 4482. Dogs were from both sexes, between one and four years of age and weighing in average about 11.80 ± 1.99kg. Fascia lata strips were tested straight and twisted and the cranial cruciate ligaments were tested with an angle of 135° between the femur and tibia and 0°, 15° of external tibial rotation and 15° of internal tibial rotation in relation to femur. The traction test velocity was 8.47mm per second. The maximum force of fascia lata strips was of approximately 290 Newtons and the maximum stress, 28 Megapascal. Similar results of strength and stress properties were found for the strips of fascia lata straight and twisted, although twisted strips presented a higher deformation than straight ones. External and internal tibial rotation did not influence the maximum force and maximum stress of the cranial cruciate ligament, that were of about 660 Newtons and 75 Megapascal, respectively. Fascia lata strips reached 44% of ligaments maximum force and 37% of maximum strain, and twisted strips reached 70% of ligaments maximum deformation, deserving straight strips to be recommended for cranial cruciate ligament substitution in dogs

Criteria of candidacy for unilateral cochlear implantation in postlingually deafened adults I: Theory and measures of effectiveness

Objectives: The objectives of this study were to distinguish the equivalent-effectiveness, health-economic, and actuarial approaches to specifying criteria of candidacy for medical interventions; to apply the equivalent-effectiveness approach to unilateral cochlear implantation for postlingually deafened adults; and to determine whether the criterion should take age at implantation and duration of profound deafness into account. Design: The study was designed as a prospective cohort study in 13 hospitals with four groups of severely-profoundly hearing-impaired subjects distinguished by their preoperative ability to identify words in sentences when aided acoustically. The groups represent a progressive relaxation of criteria of candidacy: Group I (N = 134) scored 0% correct without lipreading and did not improve their lipreading score significantly when aided; group II (N = 93) scored 0% without lipreading but did improve their lipreading score significantly when aided; group III (N = 53) scored 0% without lipreading when the to-be-implanted ear was aided but between 1% and ~50% when the other ear was aided. Group IV (N = 31) scored between 1% and ~50% without lipreading when the to-be-implanted ear was aided. Measures of speech intelligibility, health utility, and otologically relevant quality of life were obtained before surgery and 9 mo after surgery from each subject. Measures of effectiveness were calculated as the difference between 9-mo and preoperative scores. Results: Effectiveness differed only slightly between groups. Effectiveness was not strongly associated with age at the time of implantation. Greater effectiveness was associated with implantation in the ear with the shorter duration of profound deafness. Cochlear implantation was least effective when the preoperative audiological status of the better-hearing ear was good and the duration of profound deafness of the implanted ear was long. As a result, effectiveness was not significant for the subsets of groups III and IV, who were given implants in ears that had been profoundly deaf for more than 30 yr. Conclusions: The effectiveness of cochlear implantation differs little between groups of candidates who score zero with acoustic hearing aids before surgery and groups who score up to ~50% correct, thereby justifying a relaxation of the criterion of candidacy to embrace some members of the latter groups. The criterion should be based not only on preoperative speech intelligibility but also on duration of profound deafness in the to-be-implanted ear