Step, dip, and bell-shape traveling waves in a (2 + 1)-chemotaxis model with traction and long-range diffusion

In this paper, a new (2 + 1)-dimensional chemotaxis model is introduced, the focus being the understanding of influences of cooperative mechanisms from traction forces, long-range diffusion to chemotaxis on the dynamical characteristics of waves and their transport. Applying the F-expansion method, three families of new traveling wave solutions of bacterial density and chemoattractant concentration are constructed, including step, dip, and bell-shape wave profiles. The dependence of the conditions of existence of our solutions with respect to the model parameters is fully clarified. We found that traction and long-range diffusion slow down the waves and entail the transport of a small number of particles. Surprisingly, the long-range diffusion increases the thickness of the wave but does not alter its magnitude. Amongst families of solutions constructed, dip waves travel faster may be used to explain fast coordination amongst particles. As they support the transport of large amounts of cells, step waves could explain the transport of particles in high dense media. Intensive numerical simulations corroborate with a pretty much accuracy our theoretical analysis, confirming the robustness of our predictions. Traction, long-range diffusion and chemotaxis deeply affect the wave dynamics, they must be taken into account for a better understanding of chemotaxis systems.

The Recovery and Concentration of Spodumene Using Dense Media Separation

In coming years, global lithium production is expected to increase as the result of widespread electric vehicle adoption. To meet the expected increase in demand, lithium must be sourced from both brine and hard-rock deposits. Heavy liquid separation (HLS) and dense media separation (DMS) tests were conducted on the pegmatites from Hidden Lake, NWT, Canada to demonstrate the potential role of this technology in the concentration of spodumene (LiAlSi2O6) from hard-rock sources. A continuously operated DMS circuit test, conducted on +840 µm material, produced a concentrate grading 6.11% Li2O with ~50% lithium recovery. The circuit rejected 50% of the original mass to tailings, with only 8% lithium losses. Sensitivity analysis showed that minor changes (+/−0.05) in the DMS-specific gravity cut point resulted in significant changes to the mass rejected and to the concentrate grade produced; this may limit the feasibility and operability of the downstream grinding and flotation circuits. The results demonstrate the potential for DMS in the concentration of spodumene from the Hidden Lake pegmatites, and by extension, the potential for DMS in the concentration of spodumene from other hard-rock occurrences.

Refined description of momentum transfer in real liquid mixtures

Viscosity coefficients are required to calculate various heat and mass transfer processes. There is not strict theory that allows calculating viscosity coefficients in real systems. The kinetic theory of dense media for the model of solid sphere, which takes into account only the presence of its own volume of particles, allows us to calculate the transfer coefficients in ideal mixtures. A real mixture of different events the forces of attraction play a significant role in their characteristic behavior at different concentrations of the mixture. The problem of taking into account the real interaction between molecules can be solved using methods of thermodynamics irreversible processes. The formalism of such a solution of kinetic equations is based on a model representation of the behavior of molecules in real systems when indirectly obtaining information about a specific interaction of particles through the value of the chemical potential or activity. This work is a continuation of the development of other published works. To account for the interaction between molecules in real systems, a thermodynamic model of an ideal associated Prigogine solution is used. This model assumed that non-ideal systems can represented as ideal under certain conditions and assumes that attractive forces can act between particles. It is possible to form complexes and their interaction. In accordance with the definition of the chemical potential introduced by Lewis, real systems with particle density n_(i )are replaced by an equivalent ideal mixture with activity a. In this paper, we refine the generalized kinetic equations of dense media used as an ideal comparison system for real solutions. A new expression for the flow term in the kinetic equation is obtained.

The structure of hydrodynamic γ-ray burst jets

ABSTRACT After being launched, gamma-ray burst (GRB) jets propagate through dense media prior to their breakout. The jet-medium interaction results in the formation of a complex structured outflow, often referred to as a ‘structured jet’. The underlying physics of the jet-medium interaction that sets the post-breakout jet morphology has never been explored systematically. Here, we use a suite of 3D simulations to follow the evolution of hydrodynamic long and short gamma-ray bursts (lGRBs and sGRBs) jets after breakout to study the post-breakout structure induced by the interaction. Our simulations feature Rayleigh–Taylor fingers that grow from the cocoon into the jet, mix cocoon with jet material and destabilize the jet. The mixing gives rise to a previously unidentified region sheathing the jet from the cocoon, which we denote the jet–cocoon interface (JCI). lGRBs undergo strong mixing, resulting in most of the jet energy to drift into the JCI, while in sGRBs weaker mixing is possible, leading to a comparable amount of energy in the two components. Remarkably, the jet structure (jet-core plus JCI) can be characterized by simple universal angular power-law distributions, with power-law indices that depend solely on the mixing level. This result supports the commonly used power-law angular distribution, and disfavours Gaussian jets. At larger angles, where the cocoon dominates, the structure is more complex. The mixing shapes the prompt emission light curve and implies that typical lGRB afterglows are different from those of sGRBs. Our predictions can be used to infer jet characteristics from prompt and afterglow observations.

The structure of weakly magnetized γ-ray burst jets

ABSTRACT The interaction of gamma-ray burst (GRB) jets with the dense media into which they are launched promote the growth of local hydrodynamic instabilities along the jet boundary. In a companion paper, we study the evolution of hydrodynamic (unmagnetized) jets, finding that mixing of jet–cocoon material gives rise to an interface layer, termed jet–cocoon interface (JCI), which contains a significant fraction of the system energy. We find that the angular structure of the jet + JCI, when they reach the homologous phase, can be approximated by a flat core (the jet) + a power-law function (the JCI) with indices that depend on the degree of mixing. In this paper, we examine the effect of subdominant toroidal magnetic fields on the jet evolution and morphology. We find that weak fields can stabilize the jet against local instabilities. The suppression of the mixing diminishes the JCI and thus reshapes the jet’s post-breakout structure. Nevertheless, the overall shape of the outflow can still be approximated by a flat core + a power-law function, although the JCI power-law decay is steeper. The effect of weak fields is more prominent in long GRB jets, where the mixing in hydrodynamic jets is stronger. In short GRB jets, there is small mixing in both weakly magnetized and unmagnetized jets. This result influences the expected jet emission which is governed by the jet’s morphology. Therefore, prompt and afterglow observations in long GRBs may be used as probes for the magnetic nature at the base of the jets.