Steady nearly incompressible vector fields in 2D: chain rule and renormalization

Given bounded vector field $b : \mathbb R^d \to \mathbb R^d$, scalar field $u : \mathbb R^d \to \mathbb R$ and a smooth function $\beta : \mathbb R \to \mathbb R$ we study the characterization of the distribution $\mathrm{div}(\beta(u)b)$ in terms of $\mathrm{div}\, b$ and $\mathrm{div}(u b)$. In the case of $BV$ vector fields $b$ (and under some further assumptions) such characterization was obtained by L. Ambrosio, C. De Lellis and J. Mal\'y, up to an error term which is a measure concentrated on so-called \emph{tangential set} of $b$. We answer some questions posed in their paper concerning the properties of this term. In particular we construct a nearly incompressible $BV$ vector field $b$ and a bounded function $u$ for which this term is nonzero. For steady nearly incompressible vector fields $b$ (and under some further assumptions) in case when $d=2$ we provide complete characterization of $\mathrm{div}(\beta(u) b)$ in terms of $\mathrm{div}\, b$ and $\mathrm{div}(u b)$. Our approach relies on the structure of level sets of Lipschitz functions on $\mathrm R^2$ obtained by G. Alberti, S. Bianchini and G. Crippa. Extending our technique we obtain new sufficient conditions when any bounded weak solution $u$ of $\partial_t u + b \cdot \nabla u=0$ is \emph{renormalized}, i.e. also solves $\partial_t \beta(u) + b \cdot \nabla \beta(u)=0$ for any smooth function $\beta : \mathbb R \to \mathbb R$. As a consequence we obtain new uniqueness result for this equation.Comment: 50 pages, 8 figure

On the structure of divergence-free measures on R^2

e consider the structure of divergence-free vector measures on the plane. We show that suchmeasures can be decomposed into measures induced by closed simple curves. More generally, we show that ifthe divergence of a planar vector-valued measure is a signed measure, then the vector-valued measure can bedecomposed into measures induced by simple curves (not necessarily closed). As an application we general-ize certain rigidity properties of divergence-free vector fields to vector-valued measures. Namely, we show thatif a locally finite vector-valued measure has zero divergence, vanishes in the lower half-space and the normalcomponent of the unit tangent vector of the measure is bounded from below (in the upper half-plane), thenthe measure is identically zero

Association of Polymorphisms of Serotonin Transporter (5HTTLPR) and 5-HT2C Receptor Genes with Criminal Behavior in Russian Criminal Offenders

Background: Human aggression is a heterogeneous behavior with biological, psychological, and social backgrounds. As the biological mechanisms that regulate aggression are components of both reward-seeking and adversity-fleeing behavior, these phenomena are difficult to disentangle into separate neurochemical processes. Nevertheless, evidence exists linking some forms of ag

Protected Long-Distance Guiding of Hypersound Underneath a Nanocorrugated Surface

In nanoscale communications, high-frequency surface acoustic waves are becoming effective data carriers and encoders. On-chip communications require acoustic wave propagation along nanocorrugated surfaces which strongly scatter traditional Rayleigh waves. Here, we propose the delivery of information using subsurface acoustic waves with hypersound frequencies of ∼20 GHz, which is a nanoscale analogue of subsurface sound waves in the ocean. A bunch of subsurface hypersound modes are generated by pulsed optical excitation in a multilayer semiconductor structure with a metallic nanograting on top. The guided hypersound modes propagate coherently beneath the nanograting, retaining the surface imprinted information, at a distance of more than 50 μm which essentially exceeds the propagation length of Rayleigh waves. The concept is suitable for interfacing single photon emitters, such as buried quantum dots, carrying coherent spin excitations in magnonic devices and encoding the signals for optical communications at the nanoscale

Research, Development and Application of Hybrid Model of Back-to-Back HVDC Link

Recent hybrid simulators (or co-simulators) of the electric power system are focused on scientific and research features to propose and develop novel and more accurate simulators. The present paper demonstrates one more hybrid modelling approach based on application and combination of three modeling approaches all together: physical, analog and digital. The primary focus of the proposed approach is to develop the simulation tool ensuring such vital characteristics as three-phase simulation and modeling of a single spectrum of processes in electric power system, without separation of the electromagnetic and electromechanical transient stages. Moreover, unlimited scalability of the electric power system model and real-time simulation to ensure the opportunity of data exchange with external devices have been considered. The description of the development of the hybrid model of back-to-back HVDC link based on the proposed approach is discussed and analyzed. To confirm properties of the mentioned hybrid simulation approach and hybrid model of back-to-back HVDC link, the simulation results of the interconnection of non-synchronously operating parts of the electric power system; power flow regulation; dynamic response to external fault and damping of power oscillation in electric power system are presented and examined. Moreover, to confirm the adequacy of the obtained results, the comparison with a detailed voltage source converter HVDC model (Simulink Matlab) and Eurostag software are introduced

Genetic fine mapping and genomic annotation defines causal mechanisms at type 2 diabetes susceptibility loci.

We performed fine mapping of 39 established type 2 diabetes (T2D) loci in 27,206 cases and 57,574 controls of European ancestry. We identified 49 distinct association signals at these loci, including five mapping in or near KCNQ1. 'Credible sets' of the variants most likely to drive each distinct signal mapped predominantly to noncoding sequence, implying that association with T2D is mediated through gene regulation. Credible set variants were enriched for overlap with FOXA2 chromatin immunoprecipitation binding sites in human islet and liver cells, including at MTNR1B, where fine mapping implicated rs10830963 as driving T2D association. We confirmed that the T2D risk allele for this SNP increases FOXA2-bound enhancer activity in islet- and liver-derived cells. We observed allele-specific differences in NEUROD1 binding in islet-derived cells, consistent with evidence that the T2D risk allele increases islet MTNR1B expression. Our study demonstrates how integration of genetic and genomic information can define molecular mechanisms through which variants underlying association signals exert their effects on disease

Synergistic Effect of Dielectric Barrier Discharge Plasma and TiO2-Pillared Montmorillonite on the Degradation of Rhodamine B in an Aqueous Solution

Photocatalytic, plasma and combined plasma–photocatalytic processes were applied for the destruction of a model pollutant, Rhodamine B dye, in an aqueous solution (concentration of 40 mg/L). For this purpose TiO2-pillared montmorillonite was used as a photocatalyst (characterized by X-ray analysis and low-temperature nitrogen adsorption/desorption). It was prepared by the method of intercalation of titanium hydroxocomplexes, including hydrothermal activation of the process and preliminary mechanical treatment of the layered substrate. The dielectric barrier discharge (DBD) plasma in the presence of photocatalysts increases the efficiency of dye degradation (100%, 8 s) compared to plasmolysis (94%) and UV photolysis (92%, 100 min of UV irradiation); in contrast to photolysis, destructive processes are more profound and lead to the formation of simple organic compounds such as carboxylic acids. The plasma–catalytic method enhances by 20% the energetic efficiency of the destruction of Rhodamine B compared to DBD plasma. The efficiency of dye destruction with the plasma–catalytic method increases with the improvement of the textural properties of the photocatalyst

Methylglyoxal-Modified Human Serum Albumin Binds to Leukocyte Myeloperoxidase and Inhibits its Enzymatic Activity

Hyperglycemia in diabetes mellitus induces modification of proteins by glucose and its derivative methylglyoxal (MG). Neutrophils perform their bactericidal activity mainly via reactive halogen (RHS) and oxygen (ROS) species generation catalyzed by myeloperoxidase (MPO) stored in neutrophil azurophilic granules (AGs) and membrane NADPH oxidase, respectively. Herein, we study the binding of human serum albumin (HSA) modified with MG (HSA-MG) to MPO and its effects on MPO activity and release by neutrophils. Peroxidase activity of MPO was registered by oxidation of 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt, and chlorinating activity by decolorization of Celestine blue B dye. Binding of HSA-MG to MPO was studied by affinity chromatography, disc-electrophoresis, ligand Western blotting and enzyme-linked solid phase immunoassay using monoclonal antibodies (mAbs) to MPO. ROS and RHS generation were detected by lucigenin (Luc) and luminol (Lum) chemiluminescence (CL), respectively. Neutrophil degranulation was assessed by flow cytometry using fluorescent labeled antibodies to the marker proteins CD63 from AGs and CD11b from peroxidase-negative granules (PNGs). NETosis was assayed by quantifying DNA network-like structures (NET-like structures) in blood smears stained by Romanowsky. HSA-MG bound to MPO, giving a stable complex (Kd = 1.5 nM) and competing with mAbs, and non-competitively inhibited peroxidase and chlorinating MPO activity and induced degranulation of PNGs but not of AGs. HSA-MG enhanced Luc-CL per se or following PMA, unlike Lum-CL, and did not affect spontaneous or PMA-stimulated NETosis. Thus, HSA modified under hyperglycemia-like conditions stimulated NADPH oxidase of neutrophils but dampened their functions dependent on activity of MPO, with no effect on its release via degranulation or NETosis. This phenomenon could underlie the downregulation of bactericidal activity of MPO and neutrophils, and hence of innate immunity, giving rise to wound healing impairment and susceptibility to infection in patients with hyperglycemia