The Lebwohl-Lasher (LL) model is the traditional model used to describe the nematic-isotropic transition of real liquid crystals. In this paper, we develop a numerical study of the temperature behaviour and of finite-size scaling of the two-dimensional (2D) LL-model. We discuss two possible scenarios. In the first one, the 2D LL-model presents a phase transition similar to the topological transition appearing in the 2D XY-model. In the second one, the 2D LL-model does not exhibit any critical transition, but its low temperature behaviour is rather characterized by a crossover from a disordered phase to an ordered phase at zero temperature. We realize and discuss various comparisons with the 2D XY-model and the 2D Heisenberg model. Having added finite-size scaling behaviour of the order parameter and conformal mapping of order parameter profile to previous studies, we analyze the critical scaling of the probability distribution function, hyperscaling relations and stiffness order parameter and conclude that the second scenario (no critical transition) is the most plausible.
Introduction: Adequate tooth-size ratios are required to ensure the satisfactory outcome of orthodontic treatment. Consequently, various methods of measuring tooth-size ratios have been developed being the Bolton ratio the most commonly accepted, known and used one. This ratio depending directly on mesiodistal tooth size has been associated with different ethnic backgrounds. Some authors suggest the need for specific standards for every population. Objectives: The objectives of our study were; to measure and to compare mesiodistal tooth sizes and the Anterior and Overall Bolton ratios in two different populations, one Peruvian and the other Spanish with the same digital method. Material and Methods: The sample included 149 individuals composed of two groups; 99 Spanish (mean age 14.19), 65 being females and 34 males and 50 Peruvian (mean age 14.46), 18 being males and 32 females. The mesiodistal sizes of each of the patients were measured using a digital method and the Anterior and Overall Bolton ratios were calculated. Results: Tooth size does indeed involve a strong ethnic component, and the Anterior Bolton ratio is specific for each ethnic group. Conclusions: The conclusions are; tooth sizes of the Peruvian population were greater than those of the Spanish population. The Anterior Bolton ratio of Peruvian individuals was greater than that of the Spanish, whereas no differences were found for Overall Bolton ratio. These differences suggest the need for specific standards for the Spanish and Peruvian population.
We review recent results on the effect of a specific type of quenched disorder on well known O(m)-vector models in three dimensions: the XY model (3DXY, m = 2) and the Ising model (3DIS, m = 1). Evidence of changes of criticality in both systems, when confined in aerogel pores, is briefly referenced. The 3DXY model represents the universality class to which the λ-transition of bulk superfluid 4 He belongs. Experiments report interesting changes of critical exponents for this transition, when superfluid 4 He is confined in aerogels. Numerical evidence has also been presented that the 3DXY model, confined in aerogel-like structures, exhibits critical exponents different from those of bulk, in agreement with experiments. Both results seem to contradict Harris criterion: being the specific heat exponent negative for the pure system (α 3DXY −0.011 < 0), changes should be explained in terms of the extended criterion due to Weinrib and Halperin, which requires disorder to be long-range correlated (LRC) at all scales. In numerical works, aerogels are simulated by the diffusion limited cluster-cluster aggregation (DLCA) algorithm, known to mimic the geometric features of aerogels. These objects, real or simulated, are fractal through some decades only, and present crossovers to homogeneous regimes at finite scales, so the violation to Harris criterion persists. The apparent violation has been explained in terms of hidden LRC subsets within aerogels [Phys. Rev. Lett., 2003, 90, 170602]. On the other hand, experiments on the liquid-vapor (LV) transition of 4 He and N 2 confined in aerogels, also showed changes in critical-point exponents. Being the LV critical-point in the O(1) universality class, criticality may be affected by both short-range correlated (SRC) and LRC subsets of disorder. Simulations of the 3DIS in DLCA aerogels can corroborate experimental results. Both experiments and simulations suggest a shift in critical exponents to values closer to the SRC instead of those of the LRC fixed point.
Photodamage starts early in childhood due to repeated and unprotected sun exposure. It is observed almost exclusively in individuals with white skin, especially skin phototypes I and II. Clinical studies show that 50 to 80% of an individual's life time ultraviolet (uv) radiation occurs before the age of 18 years. Photodamage, also known as dermatoheliosis, represents a polymorphic alteration of several structures of the skin, especially keratinocytes and melanocytes in the epidermis, the vascular system, and the dermal connective tissue. This damages caused by acute and chronic uv-exposure result in a substantially increased incidence of skin cancers. The severity of photodamages depends on constitual factors, e.g. skin phototype (skin color, capacity to tan), and on duration as well as intensity of sun exposure. Tanning for cosmetic purposes by sunbathing or by using artificial tanning devices is still widespread. Thus, it is important that clinicians are familiar with the clinical manifestations of photodamages and skin cancer. Further efforts to educate both public and medical professions are essential to direct more patients earlier to treatment. Furthermore new strategies need to be developed to influence behaviour as well as to increase awareness.
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