Smooth rationally connected threefolds contain all smooth curves

We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We give some details about the toric case.Comment: Version 1 was called "Any smooth toric threefold contains all curves". This version is completely rewritten and proves a much stronger result, following suggestions of Janos Kolla

Computational Investigation of the Near-Field Plasma Plume in Ion-Ion Propulsion

A two-fluid computational model of plasma flows was developed to investigate the plume of an ion-ion propulsion system. The densities of positive and negative ions, along with the associated values of net charge, electric field, and electric potential were calculated throughout the domain. The computational domain was chosen to be large enough (25 thruster diameters downstream of the accelerating grids) to examine the neutralization of the plume. The resulting plasma electric potential and charge neutrality at the downstream end of the domain are shown. The results from this simulation are compared to existing literature on ion-ion plasma thrusters

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that SL$(n,\mathbb{Z})$ and its congruence subgroups have the $R_\infty$-property. Further we show that any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion free non-elementary hyperbolic group, or SL$(n,\mathbb{Z})$, Sp$(2n,\mathbb{Z})$ or a principal congruence subgroup of SL$(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian manifold of constant negative curvature

Single microcolony diffusion analysis in Pseudomonas aeruginosa biofilms

© 2019, The Author(s). The influence of the biofilm matrix on molecular diffusion is commonly hypothesized to be responsible for emergent characteristics of biofilms such as nutrient trapping, signal accumulation and antibiotic tolerance. Hence quantifying the molecular diffusion coefficient is important to determine whether there is an influence of biofilm microenvironment on the mobility of molecules. Here, we use single plane illumination microscopy fluorescence correlation spectroscopy (SPIM-FCS) to obtain 3D diffusion coefficient maps with micrometre spatial and millisecond temporal resolution of entire Pseudomonas aeruginosa microcolonies. We probed how molecular properties such as size and charge as well as biofilm properties such as microcolony size and depth influence diffusion of fluorescently labelled dextrans inside biofilms. The 2 MDa dextran showed uneven penetration and a reduction in diffusion coefficient suggesting that the biofilm acts as a molecular sieve. Its diffusion coefficient was negatively correlated with the size of the microcolony. Positively charged dextran molecules and positively charged antibiotic tobramycin preferentially partitioned into the biofilm and remained mobile inside the microcolony, albeit with a reduced diffusion coefficient. Lastly, we measured changes of diffusion upon induction of dispersal and detected an increase in diffusion coefficient inside the biofilm before any loss of biomass. Thus, the change in diffusion is a proxy to detect early stages of dispersal. Our work shows that 3D diffusion maps are very sensitive to physiological changes in biofilms, viz. dispersal. However, this study also shows that diffusion, as mediated by the biofilm matrix, does not account for the high level of antibiotic tolerance associated with biofilms

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used

Does threat trigger prosociality? The relation between basic individual values, threat appraisals, and prosocial helping intentions during the COVID-19 pandemic

Prosociality is often considered as quintessential in coping with the threats of health emergencies. As previous research has suggested, prosocial behaviors are shaped by both dispositional factors and situational cues about the helping situation. In the present research, we investigated whether “bonding” types of prosociality, helping directed towards close others within one’s social network, and “bridging” types of prosociality, helping directed towards vulnerable people across group boundaries, are predicted by basic individual values and threat appraisals concerning COVID-19. During the pandemic, we conducted a cross-sectional study in the US and India (Ntotal = 954), using the Schwartz value inventory and a multifaceted measure of threat assessment to predict prosocial helping intentions. After controlling for other value and threat facets, self-transcendence values and threat for vulnerable groups uniquely predicted both bonding and bridging types of prosociality. Furthermore, threat for vulnerable groups partially mediated the effect of self-transcendence on prosocial helping intentions: People who endorsed self-transcendent values were particularly concerned by the effect of the pandemic on vulnerable groups, and thus willing to engage in prosocial behaviours to help those in need. Our findings support the idea that prosociality is stimulated by empathic concerns towards others in need and underline the importance for future research to consider the broad spectrum of threats appraised by people during health emergencies