On the Modified Crystalline Stefan Problem with Singular Data

We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length.     

Oxygen incorporation in polyethylene implanted with 150 keV Sb+ ions

Samples of polyethylene (PE) loaded with carbon black up to 8 wt.% and implanted with 150 keV Sb⁺ ions to the doses from 2×10¹³–2×10¹⁵ cm^–2 were studied using standard Rutherford Back Scattering (RBS) technique. On the PE samples implanted to the doses above 2×10¹⁴ cm^–2, a considerable surface carbonization is observed. The measured parameters of the Sb depth profile are compared with theoretical TRIM estimations. The projected range is by 25% lower than the theoretical one and the range straggling is about twice of that predicted. The differences are explained by stepwise polymer degradation during the ion bombardment. Strong oxidation of the ion implanted polymers is also observed. The oxygen depth profiles from the sample surface up to the depth comparable with Sb⁺ ion range evolve from nearly uniform one for low ion doses to highly non-uniform one for doses above 1×10¹⁵ cm^–2. The total oxygen content in the sample surface layer 300 nm thick reaches a maximum for the doses of (1–2)×10¹⁴ cm^–2.On leave from Belorussian State University, 220050 Minsk, Belarus.The authors thank the member of electrostatic accelerator group at INP for help during RBS measurements. The work was partly (V.H. and J.K.) supported by the Internal Grant Agency of the Academy of Sciences of Czech Republic under the grant No. 14805 and by the Internal Grant Agency of the Ministry of Education of Czech Republic under the grant No. 1002 (V.., V.R., V.H. and J.K.). In the final stage, the work was also supported by the Grant Agency of Czech Republic under the grant No. 202/93/0121.     

Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

Keratin Scaffolds Containing Casomorphin Stimulate Macrophage Infiltration and Accelerate Full-Thickness Cutaneous Wound Healing in Diabetic Mice

Impaired wound healing is a major medical challenge, especially in diabetics. Over the centuries, the main goal of tissue engineering and regenerative medicine has been to invent biomaterials that accelerate the wound healing process. In this context, keratin-derived biomaterial is a promising candidate due to its biocompatibility and biodegradability. In this study, we evaluated an insoluble fraction of keratin containing casomorphin as a wound dressing in a full-thickness surgical skin wound model in mice (n = 20) with iatrogenically induced diabetes. Casomorphin, an opioid peptide with analgesic properties, was incorporated into keratin and shown to be slowly released from the dressing. An in vitro study showed that keratin-casomorphin dressing is biocompatible, non-toxic, and supports cell growth. In vivo experiments demonstrated that keratin-casomorphin dressing significantly (p < 0.05) accelerates the whole process of skin wound healing to the its final stage. Wounds covered with keratin-casomorphin dressing underwent reepithelization faster, ending up with a thicker epidermis than control wounds, as confirmed by histopathological and immunohistochemical examinations. This investigated dressing stimulated macrophages infiltration, which favors tissue remodeling and regeneration, unlike in the control wounds in which neutrophils predominated. Additionally, in dressed wounds, the number of microhemorrhages was significantly decreased (p < 0.05) as compared with control wounds. The dressing was naturally incorporated into regenerating tissue during the wound healing process. Applied keratin dressing favored reconstruction of more regular skin structure and assured better cosmetic outcome in terms of scar formation and appearance. Our results have shown that insoluble keratin wound dressing containing casomorphin supports skin wound healing in diabetic mice.     

Effect of gas pressure on amplitude and duration of electron beam current in a gas-filled diode

The parameters of an electron beam generated in helium in the pressure range p = 10⁻⁴−12 atm are studied. Nanosecond high-voltage pulses are applied to a gap between a tubular cathode and planar anode, which is made of 45-μm-thick AlBe foil. Behind the anode, an electron beam is detected at a helium pressure of 12 atm. The pressure dependence of the beam current amplitude shows three peaks at p ≈ 0.01, ≈ 0.07, and ≈ 3 atm. The beam-induced glow of a luminescent film placed behind the foil and the discharge glow at different helium pressures in the gas-filled diode are photographed.     

Effect of the Radiation Power Density on the Sensitivity of a Diamond Detector

This paper presents the results of an experimental study of the sensitivity of a detector made of natural diamond of the IIa type as a function of the power density of the radiation of a pulsed xenon lamp. It has been shown that the sensitivity of the detector depends on the power density of the xenon lamp radiation and equals about (1–6)·10^–4 A/W. A monotonic decrease in sensitivity of the detector during a radiation pulse has been detected. The minimum resistance of the diamond crystal with an irradiated face of area 3 mm², placed 7 mm away from the axis of the xenon lamp, was 300 , which corresponds to a specific conductivity of 2.2 ^–1·m^–1.     

High-pressure runaway-electron-preionized diffuse discharges in a nonuniform electric field

High-pressure nanosecond diffuse (volume) discharges in a nonuniform electric field are studied experimentally using a recording system with a ?100-ps time resolution. As the voltage pulse shrinks to a width of ≈100 ps, the initiation of a diffuse discharge without a source of additional ionization is facilitated; specifically, a runaway-electron-preionized diffuse discharge is ignited in atmospheric-pressure air in the case of short interelectrode gaps. It is found that a major energy deposit into the plasma of this discharge is from an abnormal glow discharge following a maximum of the gap voltage.     

Generation of runaway electron subnanosecond pulses in nitrogen and helium at a voltage of 25 kV across the gap

The formation of a runaway electron beam in helium and nitrogen at a generator voltage of 25 kV is studied experimentally. At low generator voltages, an ultrashort avalanche electron beam (UAEB) is shown to form at the flat top of the voltage pulse and its delay time relative to the leading edge of the pulse may attain several tens of nanoseconds. The conditions of runaway electron beam generation depend on the pressure in the gas-filled diode. The FWHM of the beam current varies from 200 ps to several nanoseconds. Beam electron energy distributions at different pressures are obtained. It is found that, if the gap is preionized by an additional source, the UAEB generation conditions break.