New dynamical features of pure k-essential cosmologies

We come back on the dynamical properties of [Formula: see text]-essential cosmological models and show how the interesting phenomenological features of those models are related to the existence of boundaries in the phase surface. We focus our attention to the branching curves where the energy density has an extremum and the effective speed of sound diverges. We discuss the behaviour of solutions of a general class of cosmological models exhibiting such curves and give two possible interpretations; the most interesting possibility regards the arrow of time that is reversed in trespassing the branching curve. This study teaches to us something new about general FLRW cosmologies where the fluids driving the cosmic evolution have equations of state that are multivalued functions of the energy density and other thermodynamical quantities.

A varying dark energy effective speed of sound parameter in the phantom Universe

We analyse the phenomenological effects of a varying Dark Energy (DE) effective speed of sound parameter, $$c^{2}_{\text {sd}}$$ c sd 2 , on the cosmological perturbations of three phantom DE models. Each of these models induce a particular abrupt future event known as Big Rip (BR), Little Rip (LR), and Little Sibling of the Big Rip (LSBR). In this class of abrupt events, all the bound structures in the Universe would be ripped apart at a finite cosmic time. We compute the evolution of the perturbations, $$f\sigma _{8}$$ f σ 8 growth rate and forecast the current matter power spectrum. We vary the $$c^{2}_{\text {sd}}$$ c sd 2 parameter in the interval [0, 1] and compute the relative deviation with respect $$c^{2}_{\text {sd}}=1$$ c sd 2 = 1 . In addition, we analyse the effect of gravitational potential sign flip that occurs at very large scale factors as compared with the current one.

Analysis of methods determining the value of the vessel’s critical speed when entering the lock chamber minimum width

The paper presents an analysis of analytical dependencies to determine the value of the critical speed of the vessel when entering the lock chamber. It is presented the analysis of analytical dependences for determining the value of the critical ship’s speed when entering the lock chamber, obtained by various authors earlier in the course of model and full-scale tests. The main factors affecting the safety of the approach process are noted. It was established that the critical velocity values calculated by various methods give a spread of values. However, some of them do not allow determining the value of the critical speed when the vessel enters the lock at high values of the constraint coefficient. It is indicated that the safe and effective speed of entry into the lock depends on the speed of the stream flowing around the hull of the vessel, which, in turn, is determined by the height of the shear wave in front of the ship’s bow (i.e., the slope of the free surface of the water). These factors lead to the conclusion that further research is necessary

Soliton Decomposition of the Box-Ball System

The box-ball system (BBS) was introduced by Takahashi and Satsuma as a discrete counterpart of the Korteweg-de Vries equation. Both systems exhibit solitons whose shape and speed are conserved after collision with other solitons. We introduce a slot decomposition of ball configurations, each component being an infinite vector describing the number of size k solitons in each k-slot. The dynamics of the components is linear: the kth component moves rigidly at speed k. Let $\zeta $ be a translation-invariant family of independent random vectors under a summability condition and $\eta $ be the ball configuration with components $\zeta $ . We show that the law of $\eta $ is translation invariant and invariant for the BBS. This recipe allows us to construct a large family of invariant measures, including product measures and stationary Markov chains with ball density less than $\frac {1}{2}$ . We also show that starting BBS with an ergodic measure, the position of a tagged k-soliton at time t, divided by t converges as $t\to \infty $ to an effective speed $v_k$ . The vector of speeds satisfies a system of linear equations related with the generalised Gibbs ensemble of conservative laws.

Contribution to Improving the Quality of Traffic in Mobile Networks

Today, mobile networks are faced with congestion which results in regular slowness given the variation in the actual speed of the network, that is to say the time required to transmit all of the data from a point to another. In third and fourth generation mobile networks, actual throughput is not directly measurable, it actually consists of three separate indicators, latency, jitter and loss rate. Many studies have shown that these parameters have a particular influence on congestion problems. In practice, the effective speed on the network is inversely proportional to the latency. However, the bit rate is four times the latency. Next, jitter is the variation of latency over time, impacting the flow by influencing latency. In this article, we have examined the analysis of traffic congestion in third and fourth generation networks in order to make a comparative study of the congestion rate for good decision-making.