Weak solutions for Euler systems with non-local interactions

We consider several modi cations of the Euler system of uid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2 ; 3. These models arise in the study of self-organisation in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of in nitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits in nitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction

Weak solutions for Euler systems with non-local interactions

We consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2, 3. These models arise in the study of self-organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global-in-Time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality).We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure-driven Euler system with non-local interaction terms as well as for the pressurelesssystem with Newtonian interaction

Absolute and Direct MicroRNA Quantification Using DNA–Gold Nanoparticle Probes

DNA-gold nanoparticle probes are implemented in a simple strategy for direct microRNA (miRNA) quantification. Fluorescently labeled DNA-probe strands are immobilized on PEGylated gold nanoparticles (AuNPs). In the presence of target miRNA, DNA-RNA heteroduplexes are formed and become substrate for the endonuclease DSN (duplex-specific nuclease). Enzymatic hydrolysis of the DNA strands yields a fluorescence signal due to diffusion of the fluorophores away from the gold surface. We show that the molecular design of our DNA-AuNP probes, with the DNA strands immobilized on top of the PEG-based passivation layer, results in nearly unaltered enzymatic activity toward immobilized heteroduplexes compared to substrates free in solution. The assay, developed in a real-time format, allows absolute quantification of as little as 0.2 fmol of miR-203. We also show the application of the assay for direct quantification of cancer-related miR-203 and miR-21 in samples of extracted total RNA from cell cultures. The possibility of direct and absolute quantification may significantly advance the use of microRNAs as biomarkers in the clinical praxis