Bursting oscillations as well as the bifurcation mechanism in a non-smooth chaotic geomagnetic field model

Based on the chaotic geomagnetic field model, a non-smooth factor is introduced to explore complex dynamical behaviors of a system with multiple time scales. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamic behaviors. Due to the existence of non-smooth factors, different types of bifurcations are presented in spiking states, such as grazing-sliding bifurcation and across-sliding bifurcation. In addition, the non-smooth fold bifurcation may lead to the appearance of a special quiescent state in the interface as well as a non-smooth homoclinic bifurcation phenomenon. Due to these bifurcation behaviors, a special transition between spiking and quiescent state can also occur.

Evaluation of periodontal healing in class II furcation defects following guided tissue regeneration with two different types of poly lactic acid membranes

Background Guided tissue regeneration procedures provide predictable reconstruction of periodontal tissues in the treatment of furcation involvements in animals and huamns. This study was to compare long-term effectiveness of two different types of polylactic acid (PLA) membranes on periodontal regeneration in surgically created class II furcation defects in dogs.Methods Full thickness mucoperiosteal flap was raised on the buccal aspects of the experimental teeth and class II furcation defects having 5 mm vertical dimensions were created on mandibular premolar III and IV on each quadrant. The exposed root surfaces were thoroughly planed and PLA membranes were placed over the experimental defects on both sites. One site received liquid polymer membrane (LPM), and resorbable periodontal mesh (RPM) membranes were applied to the other site. The animals were sacrificed at 7 months after surgery and the specimens were processed for histological evaluation.Results The average length of new attachment formed on the treated roots in both groups ranged from 3. 02 mm to 4. 5 mm. Complete bone filling was observed at the furcation sites. No statistically significant differences were found between two membranes in any of the parameters (P>0. 05).Conclusion This study demonstrates favorable regenerative outcomes by the use of two different types of PLA membranes that could be used as alternatives for guided tissue regeneration (GTR).

Stability of aneurysm solutions in a fluid-filled elastic membrane tube

When a hyperelastic membrane tube is inflated by an internal pressure, a localized bulge will form when the pressure reaches a critical value. As inflation continues the bulge will grow until it reaches a maximum size after which it will then propagate in both directions to form a hat-like profile. The stability of such bulging solutions has recently been studied by neglecting the inertia of the inflating fluid and it was shown that such bulging solutions are unstable under pressure control. In this paper we extend this recent study by assuming that the inflation is by an inviscid fluid whose inertia we take into account in the stability analysis. This reflects more closely the situation of aneurysm forma- tion in human arteries which motivates the current series of studies. It is shown that fluid inertia would significantly reduce the growth rate of the unstable mode and thus it has a strong stabilizing effect.

FINITE-VOLUME TVD ALGORITHM FOR DAM-BREAK FLOWS IN OPEN CHANNELS

A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.