Analytical Solution and Quasi-Periodic Behavior of a Charged Dilaton Black Hole

With the vast breakthrough brought by the Event Horizon Telescope, the theoretical analysis of various black holes has become more critical than ever. In this paper, the second-order asymptotic analytical solution of the charged dilaton black hole flow in the spinodal region is constructed from the perspective of dynamics by using the two-timing scale method. Through a numerical comparison with the original charged dilaton black hole system, it is found that the constructed analytical solution is highly consistent with the numerical solution. In addition, several quasi-periodic motions of the charged dilaton black hole flow are numerically obtained under different groups of irrational frequency ratios, and the phase portraits of the black hole flow with sufficiently small thermal parameter perturbation display good stability. Finally, the final evolution state of black hole flow over time is studied according to the obtained analytical solution. The results show that the smaller the integral constant of the system, the greater the periodicity of the black hole flow.

A stepwise mechanism for aqueous two-phase system formation in concentrated antibody solutions

Aqueous two-phase system (ATPS) formation is the macroscopic completion of liquid–liquid phase separation (LLPS), a process by which aqueous solutions demix into 2 distinct phases. We report the temperature-dependent kinetics of ATPS formation for solutions containing a monoclonal antibody and polyethylene glycol. Measurements are made by capturing dark-field images of protein-rich droplet suspensions as a function of time along a linear temperature gradient. The rate constants for ATPS formation fall into 3 kinetically distinct categories that are directly visualized along the temperature gradient. In the metastable region, just below the phase separation temperature, Tph, ATPS formation is slow and has a large negative apparent activation energy. By contrast, ATPS formation proceeds more rapidly in the spinodal region, below the metastable temperature, Tmeta, and a small positive apparent activation energy is observed. These region-specific apparent activation energies suggest that ATPS formation involves 2 steps with opposite temperature dependencies. Droplet growth is the first step, which accelerates with decreasing temperature as the solution becomes increasingly supersaturated. The second step, however, involves droplet coalescence and is proportional to temperature. It becomes the rate-limiting step in the spinodal region. At even colder temperatures, below a gelation temperature, Tgel, the proteins assemble into a kinetically trapped gel state that arrests ATPS formation. The kinetics of ATPS formation near Tgel is associated with a remarkably fragile solid-like gel structure, which can form below either the metastable or the spinodal region of the phase diagram.

Hydrotropy and scattering: pre-ouzo as an extended near-spinodal region

The relationship between hydrotropic solubilization and mesoscale structuring has been clarified from the first principles of chemical and statistical thermodynamics.

Effect of Dislocations on Spinodal Decomposition, Precipitation, and Age-hardening of Cu–Ti Alloy

In age-hardenable Cu–Ti alloys, cold work before aging enhances their mechanical properties and shortens the aging time for obtaining the maximum hardness. In order to discuss hardening behaviors, microstructural evolutions such as dislocation rearrangements, progress of spinodal decomposition, and subsequent precipitation from the spinodal region during aging need to be analyzed precisely. Therefore, we employed a probing method combining the small- and the wide-angle X-ray scattering methods to characterize the precipitate size and the progress of spinodal decomposition, respectively. Sideband peaks appearing adjacent to Bragg reflection peaks in the X-ray diffraction patterns of a copper matrix were analyzed to estimate the development of compositional modulations of titanium accompanied by spinodal decomposition. The results of these analytical procedures revealed that the growth rates of the spinodal region and nanometer-scales precipitates in Cu–Ti alloys are less susceptible to dislocations introduced during cold working before aging, and that dislocations introduced during prior cold working annihilate in the initial aging stage. Consequently, overaging, which is mainly induced by dislocation annihilation, in a cold-worked Cu–Ti alloy occurs after a shorter aging time than in an unworked alloy.

Pattern formation of the stationary Cahn-Hilliard model

We investigate critical points of the free energy Eε(u) of the Cahn–Hilliard model over the unit square under the constraint of a mean value ü. We show that for any fixed value ü in the so-called spinodal region and to any mode of an infinite class, there are critical points of Eε(u) having the characteristic symmetries of that mode provided ε > 0 is small enough. As ε tends to zero, these critical points have singular limits forming characteristic patterns for each mode. Furthermore, any singular limit is a stable critical point of E0(u)). Our method consists of a global bifurcation analysis of critical points of the energy Eε(u) where the bifurcation parameter is the mean value ü.