Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude

Photonic Clusters

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation.Comment: 4 pages, 3 figure

Отвод и постановка на кадастровый учет земельного участка Воронинского кладбища, с. Воронино Томской области

Отвод и постановка на кадастровый учет земельного участка Воронинского кладбища, с. Воронино Томской области.Elimination and cadastral registration of the land plot of the Voronin cemetery, p. Voronino, Tomsk Region

Conformal Mapping on Rough Boundaries I: Applications to harmonic problems

The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this boundary. We introduce a conformal mapping technique that is tailored to this problem in two dimensions. An efficient algorithm is introduced to compute the conformal map for arbitrarily chosen boundaries. Harmonic fields can then simply be read from the conformal map. We discuss applications to "equivalent" smooth interfaces. We study the correlations between the topography and the field at the surface. Finally we apply the conformal map to the computation of inhomogeneous harmonic fields such as the derivation of Green function for localized flux on the surface of a rough boundary

Microleakage of composite resin restorations in cervical cavities prepared by Er,Cr: YSGG laser radiation

Background: Evaluation of microleakage is important for assessing the success of new methods for surface preparation and new adhesive restorative materials. The aim of this laboratory study was to assess microleakage at the margins of composite restorations in Er,Cr:YSGG laser prepared cavities on the cervical aspects of teeth by means of dye penetration, and compare this with conventionally prepared and conditioned cavities. Methods: Class V cavities were produced on sound extracted human teeth, which had been assigned randomly to one of three groups (N = 10 each), as follows: Group 1 – prepared using a diamond cylindrical bur and then treated with 37% phosphoric acid; Group 2 – irradiated with an Er,Cr:YSGG laser (Biolase Waterlase) and then treated with 37% phosphoric acid; Group 3 – irradiated only with the laser. After application of bonding agent (Excite, Ivoclar Vivadent), all cavities were restored with composite resin (Heliomolar). After polishing the restorations, the teeth were thermocycled from 5–50°C for 500 cycles. Dye leakage was assessed after immersion in methylene blue, by examining longitudinal sections in a stereomicroscope at ×30 magnification. Results: The extent of dye penetration was lowest in the laser only group (Group 3). Penetration of dye to dentine and axial walls occurred in 80 per cent of conventionally prepared (bur + acid) specimens, but in the laser group, dye penetration to the axial wall occurred in only 30 per cent of cases. There was a strong statistical association between treatment group and the distribution of microleakage scores (Chi-square, P = 0.0023). Conclusions: For Class V cavities, with the adhesive materials employed, higher microleakage occurs with phosphoric acid etching of bur- or laser-cut surfaces, than with the surface created by use of the laser alone without additional conditioning

Antiphospholipid (Anticardiolipin) Syndrome Leading to Budd-Chiari Syndrome and Anomalous Hepatic Vein Collateral Formation Case Report

Abstract Most cases demonstrating extrahepatic venous collateral formation are the result of extensions of the portal venous system. This provides an outlet for venous drainage from the congested liver, usually in cases of portal hypertension. The case presented here, in a patient with systemic lupus erythematosus, antiphospholipid syndrome, and Budd-Chiari syndrome, is a demonstration of extrahepatic venous collateral formation originating from the hepatic veins in the liver. This rare case has features that are easily demonstrated using color and pulsed-wave Doppler sonography. Keywords lupus, antiphospholipid syndrome, anticardiolipin syndrome, Budd-Chiari syndrome, collateral vein Case Report A middle-aged woman with lupus, antiphospholipid (anticardiolipin) syndrome, and Budd-Chiari syndrome presented with progressive refractory ascites. She was referred to interventional radiology for consideration of a transjugular intrahepatic portosystemic shunt (TIPS) procedure. During the pre-TIPS angiographic assessment, a large anomalous vein was found arising from the middle hepatic vein of the liver, traversing laterally around the liver and inserting into the inferior vena cava (IVC) just above the renal veins. A web-like constricting band was also identified at the insertion point of this collateral vein into the IVC. The TIPS procedure was canceled upon this discovery, and instead the collateral was treated by balloon dilation to remove the constriction and increase flow from the liver into the IVC. After the angiography procedure was completed, a Doppler sonographic evaluation was requested to establish that flow was indeed going into the IVC from the collateral and that flow velocities in the collateral were not increased. The abdominal Doppler sonogram was performed using an Acuson Sequoia 512 (Siemens, New York, New York) with a 4-MHz curvilinear transducer. Color and spectral Doppler analyses demonstrated that the main, right, and left portal veins all exhibited hepatopedal flow. The left hepatic vein exhibited hepatofugal flow. However, a thrombus was identified at the junction of the middle and right hepatic veins with the IVC, which resulted in abnormal flow in these vessels. The left branch of the middle hepatic vein exhibited hepatofugal flow, but when the flow in this branch reached the junction with the IVC, it flowed in a retrograde manner up the right branch of the middle hepatic vein