Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices

We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky (GP) equation with a periodic potential, we employ an envelope wave approximation to derive coupled-mode equations describing the slow BEC dynamics in the first spectral gap of the optical lattice. We construct exact analytical formulas describing gap soliton solutions and examine their spectral stability using the Chebyshev interpolation method. We show that these gap solitons are unstable far from the threshold of local bifurcation and that the instability results in the distortion of their shape. We also predict the threshold of the power of gap solitons near the local bifurcation limit.Comment: 8 pages, 4 figures (1 with six parts, 3 with two parts

The development of the urban settlement system in Belgorod oblast

We have investigated the urbanization processes in the region. The study revealed the characteristics of evolution of urban systems and of the urbanization development stages as well as ascertaining the current formation tendencies for large cities and their suburban zonesyesBelgorod State Universit

Weibel-dominated quasi-perpendicular shock: hybrid simulations and in situ observations

We directly compare hybrid kinetic simulations and in situ observations of a high Mach number high-$\beta$ shock in the Solar wind. We launch virtual probes to demonstrate that the model quantitatively reproduces the observations. The observed wave properties are caused by the ion Weibel instability in the shock foot. Parameters of reflected ions in the shock foot are extracted from simulations, and their coordinate dependencies are linearly approximated. These approximations could be used in analytical models. Due to strong magnetic variations at ramp the reflected ions density can be locally very high (nearly that of the incoming flow), which makes favourable conditions for the instability.Comment: 11 pages, 10 figure

Strong solutions of the thin film equation in spherical geometry

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile

Modern Understanding of the Gut Microbiotа in Patients with Diabetes Mellitus

Diabetes Mellitus (DM) is one of the most common non-communicable diseases in the world. Despite the long struggle with this nosology, the medical community still does not have a clear answer to all the pathogenetic links of this disease. Every year, the number of sugar-lowering medications increases, but most patients develop complications of diabetes. This is probably because not all aspects of the pathogenesis of DM have yet been studied, and therefore it is impossible to fully influence the course of this disease. One of the promising directions in the study of additional aspects of the pathogenesis of DM is the study of the gut microbiota of patients. Science knows the influence of microflora on the formation of eating behavior, various pathological processes, including inflammation, but this knowledge is limited. What influences the microflora itself and whether it is possible to change its composition with the help of changes in external factors? Additional research is required on the mutual influence of microflora and host organism, as well as the possibility of correcting these interactions. Several studies have confirmed the positive effect of lactobacilli on the physiological processes of the body. However, the human gut microbiota is very diverse, and the question of identifying bacteria that can participate and correct pathological processes requires additional research. Probably, if it is possible to influence the composition of the gut microbiota, the medical community can get a powerful tool for correcting many pathological conditions. It may be that this  component is the missing component necessary for a more accurate impact in the treatment of many diseases, including diabetes

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

Abstract. The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable

Current challenges to the sustainable development of rural communities in Russia's Central Chernozem Region

This paper analyses the role of urbanisation processes in population changes and transformation of rural community systems in the region; determines the level of horizontal mobility among the rural population, as well as its impact on settlement evolution; assesses the share of small and extremely small communities in settlement composition; and outlines these communities’ future development prospects

Periodic Travelling Waves in Dimer Granular Chains

We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist

English Reformer John Frith on Catholic Theology of Purgatory

The Catholic theology of purgatory and its refutation in the works of the ideologists of Protestantism in the first third of the XVI century is analyzed in the article. The works of the little-known in the domestic historiography of the English reformer John Frith (1503-1533) are investigated. Frith’s commitment to Protestant dogmas on justification by faith and the exceptional authority of Holy Scripture is shown. It is noted that Frith, following them, denied the existence of purgatory, since it cannot be confirmed by the Holy Scriptures, and he interpreted the “cleansing fire” mentioned in the New Testament texts symbolically as torment of conscience and repentance. It is claimed that the theologian considered faith to be the atoning sacrifice of Christ the only means of salvation. It is concluded that the denial of purgatory naturally led Frith to a refutation of the Catholic practice of papal acts of grace and their theological justification, for which he was arrested and sentenced to be burned. It is emphasized that J. Frith called purgatory "creation" of the Roman pontiff and saw purely material reasons for the emergence and existence of faith in purgatory. It is noted that criticism by the English reformer of the Catholic faith in purgatory was subsequently reflected in the Anglican creed