Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

The study of mathematical modeling of the stability analysis of Lassa fever was examined. A mathematical model for the spread and control of Lassa fever was formulated and analyzed. The model incorporates a control parameter, the use of condom to control human to human transmission through sexual contact with opposite sex. The disease free and endemic equilibrium states were analyzed.

Spatio-Temporal Patterns of Predator–Prey Model with Allee Effect and Constant Stocking Rate for Predator

A diffusive predator–prey model with Allee effect and constant stocking rate for predator is investigated and it is shown that Allee effect is the decisive factor driving the formation of Turing pattern. Furthermore, it is observed that Turing pattern appears only when the diffusion rate of the prey is faster than that of the predator, which is just opposite to the condition of Turing pattern in the classical predator–prey system. Some sufficient conditions are obtained to ensure the asymptotical stability of a spatially homogeneous steady-state solution. The existence and nonexistence of positive nonconstant steady-state solutions are investigated to understand the mechanisms of generating spatiotemporal patterns. Furthermore, Hopf and steady-state bifurcations are analyzed in detail by using Lyapunov–Schmidt reduction.

Hypothetical Control of Fatal Quarrel Variability

Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit by a double Pareto probability density function (PDF). We use the fractional probability calculus to frame our arguments and to parameterize a hypothetical control process to temper a Lévy process through a collective-induced potential. Thus, the PDF is shown to be a consequence of the complexity of the underlying social network. The analytic steady-state solution to the fractional Fokker-Planck equation (FFPE) is fit to a forty-year fatal quarrel (FQ) dataset.

The Sensitization of Scintillation in Polymeric Composites Based on Fluorescent Nanocomplexes

The sensitization of scintillation was investigated in crosslinked polymeric composite materials loaded with luminescent gold clusters aggregates acting as sensitizers, and with organic dye rhodamine 6G as the emitting species. The evolution in time of the excited states population in the systems is described by a set of coupled rate equations, in which steady state solution allowed obtainment of an expression of the sensitization efficacy as a function of the characteristic parameters of the employed luminescent systems. The results obtained indicate that the realization of sensitizer/emitter scintillating complexes is the strategy that must be pursued to maximize the sensitization effect in composite materials.

Modelling Surtseyan Ejecta

<p>Surtseyan ejecta are formed in shallow sub-aqueous volcanic eruptions. They occur when water, containing a slurry of previously erupted material, is washed into the volcanic vent. This slurry is incorporated into the magma and ejected from the volcano inside a ball of magma. These magma bombs containing entrained material are called, Surtseyan ejecta or Surtseyan bombs. At the time of entrainment there is a large temperature difference between the magma (at approximately 1000°C) and the slurry (at approximately 20°C). As the inclusion temperature increases, the water contained in the slurry evaporates, causing an increase in the pressure at the boundary of the entrainment. This pressure increase is offset by the vapour diffusing through the pores of the magma. If the pressure exceeds the tensile strength of the surrounding magma the Surtseyan ejecta will rupture. The volcanological question of interest is whether the magma ruptures. There is evidence of intact ejecta so it can be concluded that rupture does not always occur. We have developed a set of equations that transiently model the changes in temperature and pressure in Surtseyan ejecta. Numerical solutions show that the pressure rapidly increases to a stable value. Because the pressure reaches equilibrium a steady-state solution can be used to determine the maximum pressure and a criterion for rupture.</p>

Modelling Surtseyan Ejecta

<p>Surtseyan ejecta are formed in shallow sub-aqueous volcanic eruptions. They occur when water, containing a slurry of previously erupted material, is washed into the volcanic vent. This slurry is incorporated into the magma and ejected from the volcano inside a ball of magma. These magma bombs containing entrained material are called, Surtseyan ejecta or Surtseyan bombs. At the time of entrainment there is a large temperature difference between the magma (at approximately 1000°C) and the slurry (at approximately 20°C). As the inclusion temperature increases, the water contained in the slurry evaporates, causing an increase in the pressure at the boundary of the entrainment. This pressure increase is offset by the vapour diffusing through the pores of the magma. If the pressure exceeds the tensile strength of the surrounding magma the Surtseyan ejecta will rupture. The volcanological question of interest is whether the magma ruptures. There is evidence of intact ejecta so it can be concluded that rupture does not always occur. We have developed a set of equations that transiently model the changes in temperature and pressure in Surtseyan ejecta. Numerical solutions show that the pressure rapidly increases to a stable value. Because the pressure reaches equilibrium a steady-state solution can be used to determine the maximum pressure and a criterion for rupture.</p>

Fully differentiable optimization protocols for non-equilibrium steady states

In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is needed for the computation of desired physical observables. For inverse design or optimal control of such systems, the common approaches are based on brute-force search strategies. Here, we present a novel methodology, based on automatic differentiation, capable of differentiating the steady state solution with respect to any parameter of the Liouvillian. Our approach has a low memory cost, and is agnostic to the exact algorithm for computing the steady state. We illustrate the advantage of this method by inverse designing the parameters of a quantum heat transfer device that maximizes the heat current and the rectification coefficient. Additionally, we optimize the parameters of various Lindblad operators used in the simulation of energy transfer under natural incoherent light. We also present a sensitivity analysis of the steady state for energy transfer under natural incoherent light as a function of the incoherent- light pumping rate.

Dissociation and recombination in the electrolyte flow model

We propose a one-dimensional model for the dilute aqueous solution of NaCl which is treated as an incompressible fluid placed in the external electric field. This model is based on the Poisson-Nernst-Planck system of equations, which also contains the constant flow velocity as a parameter and considers the dissociation and the recombination of ions. We study the steady-state solution analytically and prove that it is a stable equilibrium. Analyzing the numerical solutions, we demonstrate the importance of dissociation and recombination for the physical meaningfulness of the model.