Long time evolution of concentrated Euler flows with planar symmetry

We study the time evolution of an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks. We discuss how long this concentration persists, showing that in some cases this happens for quite long times. Moreover, we analyze a toy model that shows a similar behavior and gives some hints on the original proble

Time evolution of concentrated vortex rings

We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider $N$ disjoint vortex rings of size $\varepsilon$ and intensity of the order of $|\log\varepsilon|^{-1}$. We show that in the limit $\varepsilon\to 0$, when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time.Comment: 24 pages. This updated version provides a new Appendix B, containing the corrected proof of Lemma 3.1. For the sake of clarity, this proof has already been included in arXiv:2102.07807 (where the results of this article have been extended

The Vlasov-Poisson equation in R3\mathbb{R}^3 with infinite charge and velocities

We consider the Vlasov-Poisson equation in $\mathbb{R}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we prove existence and uniqueness of the solution, thus generalizing the analogous result given in [5] for data compactly supported in the velocities

Efficacy of a magnetic shield against a Vlasov-Poisson plasma

The aim of the paper is to test on a simple model how impenetrable may be a magnetic shield. We study the time evolution of a single species positive plasma, confined in the half-space $x_1>0$. The confinement is the result of a balance between a magnetic field and an external field, both singular at $x_1=0$; the magnetic field forbids the entrance of plasma particles in the region $x_1 \leq 0$, whereas the external field attracts the plasma particles towards $x_1=0$. The plasma has finite total charge and velocities distributed with a Maxwell-Boltzmann law.Comment: arXiv admin note: text overlap with arXiv:1602.04164, arXiv:1706.0873

Dynamics of Infinite Classical Anharmonic Crystals

We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential V and is subjected to a restoring force of potential U . We assume that U and V are even nonnegative polynomials of degree 2σ1 and 2σ2. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a perturbation. This is an extension to the case σ1 < 2σ2 − 1 of some already known results obtained for σ1 ≥ 2σ2 − 1

Long time localization of modified surface quasi-geostrophic equations

We discuss the time evolution of a two-dimensional active scalar flow, which extends some properties valid for a two-dimensional incompressible nonviscous fluid. In particular we study some characteristics of the dynamics when the field is initially concentrated in $N$ small disjoint regions, and we discuss the conservation in time of this localization property. We discuss also how long this localization persists, showing that in some cases this happens for quite long times

The social boders of the ethical theme

Тема этического получает новый поворот в свете вопросов статуса социальной структуры. Методологические основания открытого общества не выдерживают критики с позиций морального консерватизма.The ethical theme acquires a new turn in the light of questioning social structure status. Open society has no reliable methodological grounds to counterfeit moral conservative critique

Radical Prostatectomy and Intraoperative Radiation Therapy in High-Risk Prostate Cancer

Intraoperative electron beam radiotherapy (IOERT) for prostate cancer (PC) is a radiotherapeutic technique, giving high doses of radiation during radical prostatectomy (RP). This paper presents the published treatment approaches for intraoperative radiotherapy analyzing functional outcome, morbidity, and oncological outcome in patients with clinical intermediate-high-risk prostate cancer. A systematic review of the literature was performed, searching PubMed and Web of Science. A “free text” protocol using the term intraoperative radiotherapy and prostate cancer was applied. Ten records were retrieved and analyzed including more than 150 prostate cancer patients treated with IOERT. IOERT represents a feasible technique with acceptable surgical time and minimal toxicity. A greater number of cases and longer follow-up time are needed in order to assess the long-term side effects and oncological outcome