Neutron Stars in the Symmetron Model

Screening mechanisms are often deployed by dark energy models to conceal the effects of their new degrees of freedom from the scrutiny of terrestrial and solar system experiments. However, the extreme properties of nuclear matter may lead to a partial failure of screening mechanisms inside the most massive neutron stars observed in nature, opening up the possibility of probing these theories with neutron star observations. In this work, we explore equilibrium and stability properties of neutron stars in two variants of the symmetron model. We show that around sufficiently compact neutron stars, the symmetron is amplified with respect to its background (cosmological) value by several orders of magnitude, and that the properties of such unscreened stars are sensitive to corrections to the leading linear coupling between the symmetron and matter.

Transition to Fully or Partially Arrested State in Coupled Logistic Maps on a Ladder

Layered structures are an object of interest for theoretical and experimental reasons. In this work, we study coupled map lattice on a ladder. The ladder consists of two one-dimensional chains coupled at every point. We study linearly and nonlinearly coupled logistic maps in this system and study transition to nonzero persistence, in particular. We coarse-grain the variable value by assigning spin [Formula: see text] ([Formula: see text]) to sites that have value greater (less) than the fixed point and compute the number of sites that have not changed their spin values at all even times till the given time [Formula: see text]. The fraction of such sites at a given time [Formula: see text] is known as persistence. In our system, we observe a power-law of persistence at the critical value of coupling. This transition is also accompanied by long-range antiferromagnetic ordering for nonlinear coupling and long-range ferromagnetic ordering for linear coupling. The number of domain walls decay as [Formula: see text] at the critical point in both cases. The persistence exponent is 0.375 for a nonlinear case with two layers which is an exponent for the voter model on the ladder as well as for the Ising model at zero temperature or voter model in 1D. For linear coupling, we obtain a smaller persistence exponent.

Cluster Synchronization in a Network of Nonlinear Systems with Directed Topology and Competitive Relationships

This paper studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within the same cluster have the same intrinsic dynamics, whereas node dynamics between different clusters differ. In the same cluster, there only exist cooperative relationships, and there may have competitive relationships among nodes belonging to different clusters. Under the assumptions that each node satisfies one-sided Lipschitz condition, and the digraphs of each cluster are strongly connected, some sufficient conditions for cluster synchronization in the cases of linear coupling and nonlinear coupling are obtained respectively. The obtained conditions are presented as some algebraic conditions which are easy to solve. Finally, our results are validated by two numerical simulations.

Elements of future snowpack modeling – part 1: A physical instability arising from the non-linear coupling of transport and phase changes

The incorporation of vapor transport has become a key demand for snowpack modeling where accompanied phase changes give rise to a new, non-linear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for one-dimensional snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, non-linear PDE's. To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using FEniCS. We solely focus on the non-linear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that different, existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. For heterogeneous situations in which the snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to a non-linear advection of the ice phase that amplifies existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the non-linear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid-vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions.

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

Interaction Between Two Jackiw-Rebbi States in Interfaced Binary Waveguide Arrays with Cubic-quintic Nonlinearity

We study the coupling and switching effects of two discrete relativistic quantum Jackiw-Rebbi states in interfaced binary waveguide arrays with cubic-quintic nonlinearity. Like in the case with Kerr nonlinearity, two Jackiw-Rebbi states can couple efficiently to each other in the low-power regime, show the switching effect in the intermediate-power regime, and possess the trapping effect in the high-power regime. However, in the case with cubic-quintic nonlinearity, if the input Jackiw-Rebbi state power is increased further, one can observe the quasi-linear coupling effect between two Jackiw-Rebbi states which has not been found between two Jackiw-Rebbi states in interfaced binary waveguide arrays with Kerr nonlinearity.