Magnetic properties of ferrofluid emulsions: The effect of droplet elongation

The paper is concerned with a theoretical explanation of the experimentally observed effect of non-monotonic field dependence of the effective magnetic permeability of ferrofluid emulsion. In a weak magnetic field, the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Thus, the emulsion magnetic permeability increases in weak magnetic fields. Further strengthening of the external magnetic field cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Hence, the effective magnetic permeability of the ferrofluid emulsion starts decreasing. The developed theoretical model describes well the experimental observations

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

Aluminium Phthalocyanine Nanoparticles Application for Fluorescent Diagnostics and Photodynamic Therapy in Dentistry

Early diagnosis of tooth-enamel microcracks is of great importance in modern dentistry for caries prevention. It is known that the accumulation of the bacteria in the enamel microcracks can be reason of caries. A promising substance for early diagnostics of the accumulation of pathogenic microflora on the tooth enamel surface is aluminum phthalocyanine (AlPc). It could be observed that AlPc does not fluoresce in the nanoparticles form but in the monomeric molecular form it does. This allows identification of local pathological microflora accumulation within microcracks of the tooth enamel because AlPc nanoparticles (nAlPc) can be activated by pathological microflora. This paper describes the nAlPc application for fluorescent diagnostics (FD) of the enamel surface in vitro. To reduce the time from the beginning of interaction of nAlPc with the microflora to the appearance of nAlPc fluorescence, Protelan MST-35 surfactant was used as an additional activator. For FD in dentistry a model compound with nAlPc, Protelan MST-35 and with the complementary components was prepared. The following components were used as complementary: the methylparaben, carbopol, carboxymethyl cellulose, titanium dioxide, sodium phosphate, sodium saccharin and sorbitol, which are commonly used in toothpastes. Human teeth were used for the investigation of the interaction between nAlPc colloid and the model compound with nAlPc for the detection of microcracks and the areas of accumulation of pathogenic microflora on the enamel surface. Statistical processing of the experimental results showed the effectiveness of the surfactant usage for the additional activation of nAlPc and a reduction in the FD time. The application of nAlPc as a marker will make it possible to detect microcracks of the enamel tooth surface at the earliest stages and the areas of the pathogenic microflora accumulation, which can lead to the development of a caries. Keywords: fluorescent diagnostics, nanoparticles, aluminum phthalocyanine, Protelan MST-35, surfactants, enamel microcracks, tooth enamel

Oxidative dehydrogenation of 2,3,5-trimethyl-1,4-hydroquinone in the presence of titanium dioxide hydrogel

Liquid-phase oxidative dehydrogenation of 2,3,5-trimethyl-1,4-hydroquinone in the presence of titanium dioxide hydrogel was studied by a kinetic method. Associative interactions between the substrate, oxidant, and gel were detected by voltammetry and ESR and IR spectroscopy.Russian Foundation for Basic Researc

Investigation of Structure, Chemical and Phase Composition of Silicon Spring Steel Scale

The article presents the results of investigation of structure, chemical and phase composition of scale formed on siliceous spring steels during high-temperature heating prior to rolling. It is established that in 40S2 steel, the hematite layer bordering furnace atmosphere has a minimum thickness of about 40–60 μm, the magnetite layer has thickness of 250 ± 280 μm, the largest thickness of 800 ± 900 μm has wustite layer with secondary ferriferous oxide released during cooling, bordering the steel surface. The scale layer adjacent to the steel surface is characterized by a much greater macrostructural, chemical, and phase inhomogeneity. In addition towustite–ferriferous oxide mixture, iron silicates with an increased silicon content are present. Approaching the steel surface, the number of zones enriched with silicon increases. When 60S2ChA steel is heated to 1180–1200∘С, zones enriched with silicon are observed in the scale at a distance of 200 ± 250 μm from the metal surface, and when heated to temperatures of 1310 ± 1315∘C at a much larger distance, reaching700–800 μm. Keywords: scale, steel heating, siliceous springs steel, scale microstructur

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Live Birth of a Healthy Child in a Couple with Identical mtDNA Carrying a Pathogenic c.471_477delTTTAAAAinsG Variant in the MOCS2 Gene.

Molybdenum cofactor deficiency type B (MOCODB; #252160) is an autosomal recessive metabolic disorder that has only been described in 37 affected patients. In this report, we describe the presence of an in-frame homozygous variant (c.471_477delTTTAAAAinsG) in the MOCS2 gene in an affected child, diagnosed with Ohtahara syndrome according to the clinical manifestations. The analysis of the three-dimensional structure of the protein and the amino acid substitutions suggested the pathogenicity of this mutation. To prevent transmitting this mutation to the next generation, we used preimplantation genetic testing for the monogenic disorders (PGT-M) protocol to select MOCS2 gene mutant-free embryos for transfer in an in vitro fertilization (IVF) program. As a result, a healthy child was born. Interestingly, both parents of the proband shared an identical mitochondrial (mt) DNA control region, assuming their close relationship and thus suggesting that both copies of the nuclear rare variant c.471_477delTTTAAAAinsG may have been transmitted from the same female ancestor. Our estimation of the a priori probability of meeting individuals with the same mtDNA haplotype confirms the assumption of a possible distant maternal relationship among the proband's direct relatives

Precision measurements of large scale structure with future type Ia supernova surveys

Type Ia supernovae are currently the best known standard candles at cosmological distances. In addition to providing a powerful probe of dark energy they are an ideal source of information about the peculiar velocity field of the local universe. Even with the very small number of supernovae presently available it has been possible to measure the dipole and quadrupole of the local velocity field out to z~0.025. With future continuous all-sky surveys like the LSST project the luminosity distances of tens of thousands of nearby supernovae will be measured accurately. This will allow for a determination of the local velocity structure of the universe as a function of redshift with unprecedented accuracy, provided the redshifts of the host galaxies are known. Using catalogues of mock surveys we estimate that future low redshift supernova surveys will be able to probe sigma-8 to a precision of roughly 5% at 95% C.L. This is comparable to the precision in future galaxy and weak lensing surveys and with a relatively modest observational effort it will provide a crucial cross-check on future measurements of the matter power spectrum.Comment: 18 pages, 9 figures, submitted to JCA

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page