An adaptive octree finite element method for PDEs posed on surfaces

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk finite element space is defined on an octree grid which is locally refined or coarsened depending on error indicators and estimated values of the surface curvatures. The cartesian structure of the bulk mesh leads to easy and efficient adaptation process, while the trace finite element method makes fitting the mesh to the surface unnecessary. The number of degrees of freedom involved in computations is consistent with the two-dimension nature of surface PDEs. No parametrization of the surface is required; it can be given implicitly by a level set function. In practice, a variant of the marching cubes method is used to recover the surface with the second order accuracy. We prove the optimal order of accuracy for the trace finite element method in $H^1$ and $L^2$ surface norms for a problem with smooth solution and quasi-uniform mesh refinement. Experiments with less regular problems demonstrate optimal convergence with respect to the number of degrees of freedom, if grid adaptation is based on an appropriate error indicator. The paper shows results of numerical experiments for a variety of geometries and problems, including advection-diffusion equations on surfaces. Analysis and numerical results of the paper suggest that combination of cartesian adaptive meshes and the unfitted (trace) finite elements provide simple, efficient, and reliable tool for numerical treatment of PDEs posed on surfaces

Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method

An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed

Results of the August 1977 Soviet and American meterological rocketsonde intercomparison held at Wallops Island, Virginia

A coordinated program of rocketsonde investigations along about 60 deg E and 70 deg W between the United States and U.S.S.R. is discussed. The rocketsonde instruments used by the U.S. and U.S.S.R. were compared and the results are presented. The U.S. Super Loki Datasonde and the U.S.S.R. M100B rocketsonde are discussed. Results indicate that the U.S/U.S.S.R. rocketsonde measurement agreement improved since the 1973 intercomparisons. It was learned that the mean of the differences of the temperatures compare to within 6 C at about 60 km and to within 2 C near 50 km. Wind measurements were also found to agree

Развитие системы метрологического обеспечения в области вакуумных измерений: на примере ВНИИМ им. Д. И. Менделеева

The article deals with issues related to the improvement of the metrological support system in the field of vacuum measurements in the works of D. I. Mendeleyev Institute for Metrology (VNIIM). The relevance of vacuum technology and vacuum measurements for the industry of the Russian Federation is substantiated. The author shows the trends and strategies that dominate in this area in a historical retrospective. The main stages and results of theoretical and practical research work in the field of vacuum measurements carried out at the D. I. Mendeleyev Institute for Metrology (VNIIM) in recent years are described. It is emphasized that in the scientific community of the Russian Federation and D. I. Mendeleyev Institute for Metrology (VNIIM) there is a huge heuristic potential and a solid material base that allow us to expect the latest progressive approaches and solutions in the field of metrological support of vacuum measurementsВ статье рассмотрены вопросы, связанные с совершенствованием системы метрологического обеспечения в области вакуумных измерений в работах ФГУП «ВНИИМ им. Д. И. Менделеева». Обосновывается актуальность и востребованность вакуумной техники и вакуумных измерений для промышленности Российской Федерации. Автор показывает в исторической ретроспективе, какие тенденции и стратегии доминировали в данной области. Изложены основные этапы и результаты теоретических и практических научно-исследовательских работ в области вакуумных измерений, проведённых во ФГУП «ВНИИМ им. Д. И. Менделеева» за последнее время. Подчеркивается, что в научном сообществе Российской Федерации и ФГУП «ВНИИМ им. Д. И. Менделеева» существует колоссальный эвристический потенциал и солидная материальная база, которые позволяют ожидать новейших прогрессивных подходов и решений в области метрологического обеспечения вакуумных измерений

On the constants in a Kato inequality for the Euler and Navier-Stokes equations

We continue an analysis, started in [10], of some issues related to the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d. More specifically, we consider the quadratic term in these equations; this arises from the bilinear map (v, w) -> v . D w, where v, w : T^d -> R^d are two velocity fields. We derive upper and lower bounds for the constants in some inequalities related to the above bilinear map; these bounds hold, in particular, for the sharp constants G_{n d} = G_n in the Kato inequality | < v . D w | w >_n | <= G_n || v ||_n || w ||^2_n, where n in (d/2 + 1, + infinity) and v, w are in the Sobolev spaces H^n, H^(n+1) of zero mean, divergence free vector fields of orders n and n+1, respectively. As examples, the numerical values of our upper and lower bounds are reported for d=3 and some values of n. When combined with the results of [10] on another inequality, the results of the present paper can be employed to set up fully quantitative error estimates for the approximate solutions of the Euler/NS equations, or to derive quantitative bounds on the time of existence of the exact solutions with specified initial data; a sketch of this program is given.Comment: LaTeX, 39 pages. arXiv admin note: text overlap with arXiv:1007.4412 by the same authors, not concerning the main result

Anurans using in biomonitoring of uranium wastes’ influence on zoocoenosis

Дослідження впливу відходів підприємств із переробки уранової руди показали, що єдиний вид земноводних, який мешкає у стічних водах – озерна жаба (Rana ridibunda). Особини старших вікових груп цього виду амфібій частково пристосувалися до впливу полютантів стічних вод за рахунок зміни фізіолого-біохімічних параметрів органів, що беруть активну участь у метаболізмі. Дослідження впливу відходів підприємств із переробки уранової руди показали, що єдиний вид земноводних, який мешкає у стічних водах – озерна жаба (Rana ridibunda). Особини старших вікових груп цього виду амфібій частково пристосувалися до впливу полютантів стічних вод за рахунок зміни фізіолого-біохімічних параметрів органів, що беруть активну участь у метаболізмі. The research of influence of wastes of uranium ore processing enterprises showed that only one amphibian species inhabits the sewage – the lake frog. Individuals of senior age groups of this species partly adapted to pollutants influence due to the change of physiology-biochemical parameters of the organs, which actively participate in metabolism

Common mechanisms of placental dysfunction in preeclampsia, gestational diabetes, and COVID-19 in pregnant women

COVID-19 infection, preeclampsia and gestational diabetes mellitus in pregnancy cause similar changes in the placenta and influence development of the fetus between conception and birth in gestation. Proper uterine and placental vascularization is essential for normal fetal development. The transplacental exchange is regulated and maintained by the placental endothelium. During placental implantation, the trophoblast differentiates into two distinct layers, the inner cytotrophoblast and outer syncytiotrophoblast, which are key elements of the human placental barrier. Proinflammatory cytokines exacerbate ischemic events and create an upward spiral of an inflammatory reaction in the placenta. Placental pathology in gestational COVID-19 shows desquamation and damage of trophoblast and chronic histiocytic intervillositis. Similar lesions also occur in gestational diabetes mellitus and preeclampsia. The systemic inflammatory response of the mother, the increased inflammation in the placenta and cytokine production by placental trophoblasts should be monitored throughout pregnancy. Placental angiogenesis can be evaluated by serum vascular endothelial growth factor, Annexin A2, placental growth factor or sclerostin. Tissue damage can be assessed by measuring levels of serum lactate dehydrogenase and myeloperoxidase. Blood flow can be monitored with three-dimensional Doppler and pathological changes can be documented with paraffin-embedded tissue sections stained with hematoxylin and eosin, and electron microscope images as well as immunohistochemistry tests for vascular endothelial growth factor, placental growth factor, sclerostin and Annexin A2. The damage of maternal and fetal vascular perfusion (villitis and fibrin deposition) is a common mechanism of gestational diseases. The placenta lesions liberate anti-endothelial factors that lead to anti-angiogenic conditions and are the common mechanism of maternal placental vascular malperfusion in gestational diseases. Keywords: dysfunction, inflammation, pathology, placenta, pregnancy, vascularizatio

Evaluation of biochemical indicators in blood plasma of rats with tetracycline-induced hepatosis and their correction by milk phospholipids

Tetracycline is a drug with direct cytotoxic action on the liver, and therefore it is widely used in pharmaceutical studies of therapeutic effectiveness of hepatoprotective preparations. The aim of the present work was to determine the biochemical indicators in blood plasma of rats with tetracycline-induced hepatosis and correction properties of milk phospholipids under tetracycline-induced hepatosis in rats. To achieve this, Wistar rats were administered 250 mg/kg of 4% tetracycline hydrochloride suspension once a day intragastrically. As the corrective therapy, 1% solution of BAS “FLP-MD” was administered in liposomal form based on milk phospholipids. Under modeled steatohepatitis, significant destructive changes were observed in the cell membranes of hepatocytes in experimental rats. It was confirmed by higher activity of transaminase (in particular, activity of АSТ increased 4 times, that of ALT 1.7 times and the AST/ALT ratio was increased 2.4 times in blood plasma). The synthesis of clotting factors in livers of animals with hepatosis was inhibited. The content of fibrinogen in blood plasma decreased by 21%, factor II (prothrombin) by 27.8%, Xa-factor by 27.9%, and protein C by 40.6%. The animals also had hypochromic anemia, azotemia and bilirubinemia. The calcium-phosphor metabolism and hyperkalemia were observed. The liposomal BAS “FLP-MD” based on milk phospholipids diminished harmful effects of tetracycline, in particular supporting blood coagulation factors’ level restoration, and also by the activity of transaminases. According to the results, it may be used in prophylactics and pharmaceutical correction of steatohepatitis