Kelvin-Helmholtz instability in solar chromospheric jets: theory and observation

Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-peed jets in the wings of the Hα line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the Hα line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale Hα jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.

Electron acoustic soliton energy of the Kadomtsev-Petviashvili equation in the Earth’s magnetotail region at critical ion density

The nonlinear properties of small amplitude electron-acoustic solitary waves (EAWs) in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. At the critical ion density, the KP equation is not appropriate for describing the system. Hence, a new set of stretched coordinates
is considered to derive the modified KP equation. Moreover, the solitary solution, soliton energy and the associated electric field at the critical ion density were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments, such as Earth’s magnetotail region.

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

A Simultaneous Equation Approach to Estimating HIV Prevalence with Non-Ignorable Missing Responses

Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach which accounts for non-ignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogeneous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parametrization of the smoothing criterion which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe and Zambia.

Automated Equation Formulation for Causal Loop Diagrams

The annotation of Business Dynamics models with parameters and equations, to simulate the system under study and further evaluate its simulation output, typically involves a lot of manual work. In this paper we present an approach for automated equation formulation of a given Causal Loop Diagram (CLD) and a set of associated time series with the help of neural network evolution (NEvo). NEvo enables the automated retrieval of surrogate equations for each quantity in the given CLD, hence it produces a fully annotated CLD that can be used for later simulations to predict future KPI development. In the end of the paper, we provide a detailed evaluation of NEvo on a business use-case to demonstrate its single step prediction capabilities.