Computer-aided operation planning and 3-dimensional osteotomy guidance for alveolar distraction

Objectives: In alveolar distraction, in cases of severe atrophy in particular, it is often difficult to perform osteotomies in order to make a transport segment in optimal size and shape. Moreover care must be taken, not to damage the closely locating anato- mical structures such as the maxillary sinus, the inferior alveolar nerve, and the roots of the neighboring teeth. For setting ideal osteotomy lines exactly, we have developed a CT-based preoperative planning tool. Methods: 3-dimensional visual reconstruction of the jaw is created from the preoperative CT scans (1.0-mm slice thick- ness). Using the image-processing software Mimics (Materialise, Yokohama, Japan), various procedures of virtual cutting are simulated first to determine optimal osteotomy lines and to design an ideal transport segment. After the computer planning, data from the virtual solid model are transferred to a rapid prototype model, and a guiding splint is made to transfer the planned surgical simulation to the actual surgery. Results: The method was used in a case of severe atrophy of the anterior maxilla. The patient had a large maxillary sinus requir- ing a precise osteotomy in this critical area. Using the splint allowing a 3-dimensional guidance, alveolar osteotomies were easily done to achieve a transport segment in sufficient dimen- sion as planned, and any perforation of the maxillary sinus could be avoided. Finally the alveolar distraction of 10mm has suc- cessfully been performed. Conclusion: The preoperative planning method and the guiding splint described here are useful in problematic cases requiring an extremely precise osteotomy due to lack of bony space.

The behaviour of incompatible elements during hydrous melting of metasomatized peridotite at 4–6 GPa and 1000 °C–1200 °C

Trace element behavior during hydrous melting of a metasomatized garnet–peridotite was examined at pressures of 4–6 GPa and temperatures of 1000 °C–1200 °C, conditions appropriate for fluid penetrating the mantle wedge atop the subducting slab. Experiments were performed in a rocking multi-anvil apparatus using a diamond-trap setup. The compositions of the fluid and melt phases were measured using the cryogenic LA-ICP-MS technique. The water-saturated solidus of the K-lherzolite composition is located between 900 °C and 1000 °C at 4 GPa and between 1000 °C and 1100 °C at 5 and 6 GPa. The partition coefficients between fluid or melt and clinopyroxene reveal an asymmetric MREE trough with a minimum at Dy. The clinopyroxene in equilibrium with aqueous fluids is characterized by DUfluid–cpx > DThfluid–cpx while DUmelt–cpx tends to be similar to DThmelt–cpx. The partition coefficients between fluid or melt and garnet reveal very strong light to heavy REE fractionation, DLa/DLu from 95 (hydrous melt) to 1600 (aqueous fluid). The LILE are highly incompatible with partition coefficients > 50. The behavior of HFSE are decoupled, with DZr,Hf close to 1 while DNb,Ta > 10. Garnet is characterized by DUmelt/fluid–garnet < DThmelt/fluid–garnet. A comparison of our experimental partitioning results for trivalent cations as well as the results from the literature and the calculations carried out using the lattice strain model adapted to the presence of water in the bulk system indicates that H2O in the fluid or melt phase has a prominent effect on trace element partitioning. Garnet in mantle rocks in equilibrium with an aqueous fluid is characterized by significantly higher Do(3 +) for REE in the X site of the garnet compared with the partitioning values of the optimal cation in garnet in equilibrium with hydrous melts. Our data show for the first time that the change in the nature of the mobile phase (fluid vs. melt) does affect the affinities of trace elements into the garnet crystal at conditions below the second critical endpoint of the system. The same also applies for clinopyroxene, although this is less clear. Consequently, our new data allow for refinements in predictive modeling of element transfer from the slab to the mantle wedge and of possible compositions of metasomatized mantle that sources OIB magmatism.

Interfaces, strings, and a soft mode in the square lattice quantum dimer model

The quantum dimer model on the square lattice is a U(1) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static “electric” charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux ¼. A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.

An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

Topological lattice actions for the 2d XY model

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

Standard model cross-over on the lattice

With the physical Higgs mass the standard model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2)×U(1) gauge+Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only ∼5  GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result Tc=159.5±1.5  GeV. Outside of the narrow cross-over region the perturbative results agree well with nonperturbative ones.

Wetting and spreading of a surfactant film on solid particles: influence of sharp edges and surface irregularities

In addition to particle size and surface chemistry, the shape of particles plays an important role in their wetting and displacement by the surfactant film in the lung. The role of particle shape was the subject of our investigations using a model system consisting of a modified Langmuir-Wilhelmy surface balance. We measured the influence of sharp edges (lines) and other highly curved surfaces, including sharp corners or spikes, of different particles on the spreading of a dipalmitoylphosphatidyl (DPPC) film. The edges of cylindrical sapphire plates (circular curved edges, 1.65 mm radius) were wetted at a surface tension of 10.7 mJ/m2 (standard error (SE) = 0.45, n = 20) compared with that of 13.8 mJ/m2 (SE = 0.20, n = 20) for cubic sapphire plates (straight linear edges, edge length 3 mm) (p < 0.05). The top surfaces of the sapphire plates (cubic and cylindrical) were wetted at 8.4 mJ/m2 (SE = 0.54, n = 20) and 9.1 mJ/m2 (SE = 0.50, n = 20), respectively, but the difference was not significant (p > 0.05). The surfaces of the plates showed significantly higher resistance to spreading compared to that of the edges, as substantially lower surface tensions were required to initiate wetting (p < 0.05). Similar results were found for talc particles, were the edges of macro- and microcrystalline particles were wetted at 7.2 mJ/m2 (SE = 0.52, n = 20) and 8.2 mJ/m2 (SE = 0.30, n = 20) (p > 0.05), respectively, whereas the surfaces were wetted at 3.8 mJ/m2 (SE = 0.89, n = 20) and 5.8 mJ/m2 (SE = 0.52, n = 20) (p < 0.05), respectively. Further experiments with pollen of malvaceae and maize (spiky and fine knobbly surfaces) were wetted at 10.0 mJ/m2 (SE = 0.52, n = 10) and 22.75 mJ/m2 (SE = 0.81, n = 10), respectively (p < 0.05). These results show that resistance to spreading of a DPPC film on various surfaces is dependent on the extent these surfaces are curved. This is seen with cubic sapphire plates which have at their corners a radius of curvature of about 0.75 microm, spiky malvaceae pollen with an even smaller radius on top of their spikes, or talc with various highly curved surfaces. These highly curved surfaces resisted wetting by the DPPC film to a higher degree than more moderately curved surfaces such as those of cylindrical sapphire plates, maize pollens, or polystyrene spheres, which have a surface free energy similar to that of talc but a smooth surface. The macroscopic plane surfaces of the particles demonstrated the greatest resistance to spreading. This was explained by the extremely fine grooves in the nanometer range, as revealed by electron microscopy. In summary, to understand the effects of airborne particles retained on the surfaces of the respiratory tract, and ultimately their pathological potential, not only the particle size and surface chemistry but also the particle shape should be taken in consideration.