Signatures of Secondary Collisionless Magnetic Reconnection Driven by Kink Instability of a Flux Rope

The kinetic features of secondary magnetic reconnection in a single flux rope undergoing internal kink instability are studied by means of three-dimensional Particle-in-Cell simulations. Several signatures of secondary magnetic reconnection are identified in the plane perpendicular to the flux rope: a quadrupolar electron and ion density structure and a bipolar Hall magnetic field develop in proximity of the reconnection region. The most intense electric fields form perpendicularly to the local magnetic field, and a reconnection electric field is identified in the plane perpendicular to the flux rope. An electron current develops along the reconnection line in the opposite direction of the electron current supporting the flux rope magnetic field structure. Along the reconnection line, several bipolar structures of the electric field parallel to the magnetic field occur making the magnetic reconnection region turbulent. The reported signatures of secondary magnetic reconnection can help to localize magnetic reconnection events in space, astrophysical and fusion plasmas

Pengaruh Pendapatan Asli Daerah, Dana Alokasi Uumu, Dan Dana Alokasi Khusus Terhadap Belanja Modal (Studi Kasus Pada Pemerintah Daerah Kabupaten Dan Kota Di Provinsi Sulawesi Utara)

. The main purpose of regional autonomy implementation is to improve public services and to develop the regional economy in Indonesia. Due to limited resources, local government should be able to allocate the earning income for productive output. However, in fact, the local government tends to allocate the income for Operating Expenditures. This research aims to analyze the effects of Regional Real Income, General Allocation Fund, and Special Allocation Fund to the Capital Expenditure. This is a quantitative research. The data used in this study research were APBD budget District and City in North Sulawesi Province from 2011 to 2015. The analysis method applied in this study research was multiple regression analysis and supported by SPSS Version 23. The result shows that Regional Real Income and the Special Allocation Fund influence positively and significantly Capital Expenditures. On the other hand, the General Allocation Fund does not affect Capital Expenditure

Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics of the system without being required to solve the Smoluchowski-Poisson system explicitly. We also develop the analogy between self-gravitating systems and two-dimensional point vortices and derive a Virial-like relation for the vortex system

Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems

We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.Comment: Submitted to Journal of Statistical Mechanics: Theory and Experimen

Self-gravitating Brownian systems and bacterial populations with two or more types of particles

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature

We provide an exact analytical solution of the collapse dynamics of self-gravitating Brownian particles and bacterial populations at zero temperature. These systems are described by the Smoluchowski-Poisson system or Keller-Segel model in which the diffusion term is neglected. As a result, the dynamics is purely deterministic. A cold system undergoes a gravitational collapse leading to a finite time singularity: the central density increases and becomes infinite in a finite time t_coll. The evolution continues in the post collapse regime. A Dirac peak emerges, grows and finally captures all the mass in a finite time t_end, while the central density excluding the Dirac peak progressively decreases. Close to the collapse time, the pre and post collapse evolution is self-similar. Interestingly, if one starts from a parabolic density profile, one obtains an exact analytical solution that describes the whole collapse dynamics, from the initial time to the end, and accounts for non self-similar corrections that were neglected in previous works. Our results have possible application in different areas including astrophysics, chemotaxis, colloids and nanoscience

Thermodynamics of self-gravitating systems

Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a ``gravothermal catastrophe'': it can achieve ever increasing values of entropy by developing a dense and hot ``core'' surrounded by a low density ``halo''. In this paper, we study the phase transition between ``equilibrium'' states and ``collapsed'' states with the aid of a simple relaxation equation [Chavanis, Sommeria and Robert, Astrophys. J. 471, 385 (1996)] constructed so as to increase entropy with an optimal rate while conserving mass and energy. With this numerical algorithm, we can cover the whole bifurcation diagram in parameter space and check, by an independent method, the stability limits of Katz [Mon. Not. R. astr. Soc. 183, 765 (1978)] and Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)]. When no equilibrium state exists, our relaxation equation develops a self-similar collapse leading to a finite time singularity.Comment: 54 pages. 25 figures. Submitted to Phys. Rev.

de Sitter symmetry of Neveu-Schwarz spinors

We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group $SL(2,R)$. We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.Comment: 24 page

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure

Post-collapse dynamics of self-gravitating Brownian particles in D dimensions

We address the post-collapse dynamics of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, the post-collapse evolution is marked by the formation of a Dirac peak with increasing mass. The density profile outside the peak evolves self-similarly with decreasing central density and increasing core radius. In the microcanonical ensemble, the post-collapse regime is marked by the formation of a ``binary''-like structure surrounded by an almost uniform halo with high temperature. These results are consistent with thermodynamical predictions