Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.Comment: 12 pages, 1 figur

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

Probing background ionization: Positive streamers with varying pulse repetition rate and with a radioactive admixture

Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower background ionization levels the streamers branch more and have a more feather-like appearance. This is observed both when varying the repetition rate and when adding Krypton 85, though side branches are longer with the radioactive admixture. But velocities and minimal diameters of streamers are virtually independent of the background ionization level. In air, the inception cloud breaks up into streamers at a smaller radius when the repetition rate and therefore the background ionization level is higher. When measuring the effects of the pulse repetition rate and of the radioactive admixture on the discharge morphology, we found that our estimates of background ionization levels are consistent with these observations; this gives confidence in the estimates. Streamer channels generally do not follow the paths of previous discharge channels for repetition rates of up to 10 Hz. We estimate the effect of recombination and diffusion of ions and free electrons from the previous discharge and conclude that the old trail has largely disappeared at the moment of the next voltage pulse; therefore the next streamers indeed cannot follow the old trail.Comment: 30 pages, 13 figure

Collective behavior of self-propelling particles with kinematic constraints: The relation between the discrete and the continuous description

In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we derive the continuous hydrodynamic model from the discrete description. The similarities and differences between the resulting model and the hydrodynamic model postulated in our previous papers are discussed. The results clarify the assumptions used to obtain a continuous description. © 2007 Elsevier B.V. All rights reserved

THE ROLE OF BRAF MUTATION STATUS IN SURGICAL TREATMENT OF WELL-DIFFERENTIATED THYROID CANCER

Background. Papillary thyroid carcinoma (PTC) accounts for 80 % of all well-differentiated thyroid cancers. Mutation of the BRAF gene (V600E) is one of the most common prognostic factors for PTC. Various studies showed different degree of correlation between BRAF (V600E) mutation and other prognostic factors.Materials and methods. 60 patients with PTC treated in P.A. Herzen Moscow Oncology Research Institute during 2014–2016 were included in this prospective study. Selection of patients was based on the results of fine-needle aspiration biopsy and polymerase chain reaction. Study participants were randomized into 2 groups: the first one included 45 patients harboring BRAF V600E mutation, the second one included 15 patients who lack this mutation. The following prognostic factors were evaluated in postoperative period: histological subtype of PTC, tumor invasion into the capsule of thyroid gland, multicentricity, presence of metastases in regional lymph nodes and distant metastases, TNM stage. Statistical data analysis was carried out using GraphPad Prism software.Results. Papillary thyroid cancer was diagnosed in 40 % of the patients, follicular thyroid cancer – in 60 % in both groups. Tumor invasion into the capsule of thyroid gland was identified in 88 and 40 % of the cases in the first and second group respectively; thyroid capsular invasion – in 26 and 10 %; multicentricity – in 20 and 10 %; microcarcinomas (0.3–1.0  cm) – in 57 and 60 %, metastasis to regional lymph nodes – in 40 and 30 %. 51 % of the patients in the first group were found to have pT1 thyroid cancer with tumor capsular invasion without spreading beyond. After surgical treatment 23 % of the patients from the first group had changes in tumor stage from cT1–2  to pT3 according to routine histological examination results. Distant metastases were observed in 5 % of the cases in the first group and in 10 % in the second group. We found a statistically significant association between BRAF (V600E) mutation and tumor invasion into the capsule of thyroid gland (p < 0.05). At the same time neither multicentricity nor metastases in regional lymph nodes were associated with BRAF-mutation (p > 0.05). Conclusions. BRAF mutation in patients with PTC is associated with tumor invasion into the capsule of thyroid gland; this should imply the use of more aggressive treatment strategy (surgery). Further studies are needed to clarify the existing data