Equilibrium and stability of relativistic stars in extended theories of gravity

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman–Oppenheimer–Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar–tensor gravity.     

Strategies for differentiation of isobaric flavonoids using liquid chromatography coupled to electrospray ionization mass spectrometry

Flavonoids are a class of secondary plant metabolites existing in great variety in nature. Due to this variety, identification can be difficult, especially as overlapping compounds in both chromatographic separations and mass spectrometric detection are common. Methods for distinguishing isobaric flavonoids using MS² and MS³ have been developed. Chromatographic separation of various plant extracts was done with RP‐HPLC and detected with positive ESI‐MS operated in information‐dependent acquisition (IDA) mode. Two methods for the determination of flavonoid identity and substitution pattern, both featuring IDA criteria, were used together with the HPLC equipment. A third method where the collision energy was ramped utilized direct infusion. With the developed strategies, it is possible to differentiate between many isobaric flavonoids. Various classes of flavonoids were found in all of the plant extracts, in the red onion extract 45 components were detected and for 29 of them the aglycone was characterized, while the substituents were tentatively identified for 31 of them. For the strawberry extract, those numbers were 66, 30 and 60, and for the cherry extract 99, 56 and 71. The great variety of flavonoids, several of them isobaric, found in each of the extracts highlights the need for reliable methods for flavonoid characterization. Methods capable of differentiating between most of the isobars analyzed have been developed. Copyright © 2014 John Wiley & Sons, Ltd.     

Cumulative Clearness Index Frequency Distributions on the Territory of the Russian Federation

Cumulative distributions of clearness index values are constructed for the territory of Russia based on ground observation results and NASA POWER data. The obtained distributions lie close to each other, which means that the NASA POWER data can be used in solar power installations simulation at temperate and high latitudes. Approximation of the obtained distributions is carried out. The values of equation coefficients for the cumulative clearness index distributions constructed for a wide range of climatic conditions are determined. Equations proposed for a tropical climate are used in the calculations, so they can be regarded as universal ones.     

Generalized clearness index frequency curves for the Russian Federation

Actinometric data of World Radiation Data Center and NASA POWER were used to get daily clearness index frequencies for Russia. The results obtained provide the opportunity to estimate more accurately the output of various types of solar power plants. Frequencies determined using the data sources indicated correlate well and differ from universal dependences that were recommended earlier for the entire globe.     

On a nonlinear hyperbolic problem arising in two-phase flows in naturally fractured reservoirs

A system of two first-order quasilinear equations consisting of one nonhomogenous hyperbolic conservation law and an ordinary differential equation is investigated in two spatial dimensions. The initial boundary-value problem is solved for the system and existence, uniqueness, and stability theorems are proved. We also obtain a result on the behavior of the solution when time goes to infinity which agrees with practical experience. These results offer mathematical validation to computer models in current usage for the numerical simulation of multiphase flow in naturally fractured reservoirs.     

Asymptotic Stability of Riemann Solutions for a Class of Multidimensional Systems of Conservation Laws with Viscosity

We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. In particular, we obtain the uniqueness of the self-similar L^∞ entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in L_loc¹ of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, tξ)→R(ξ) as t→∞, in L_loc¹(ℝⁿ), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem.     

Solution to the initial boundary-value problem for the regularized Buckley-Leverett system

We solve the initial boundary-value problem for the regularized Buckley-Leverett system, which describes the flow of two immiscible incompressible fluids through a porous medium. This is the case of the flow of water and oil in an oil reservoir. The system is formed by a hyperbolic equation and an elliptic equation coupled by a vector field which represents the total velocity of the mixture. The regularization is done by means of a filter acting on the velocity field. We consider the critical situation in which we inject pure water into the reservoir. At this critical value for the water saturation, the spatial components of the characteristics of the hyperbolic equation vanish and this motivates the use of a new technique to prove the achievement of the boundary condition for the hyperbolic equation. We treat the case of a horizontal plane reservoir. We also prove that the time averages of the saturation component of the solution converge to one, as the time interval increases indefinitely, for almost all points of the reservoir, with a rate of convergence which depends only on the flux function.     

Uniqueness and Stability of Riemann Solutions¶with Large Oscillation in Gas Dynamics

We prove the uniqueness of Riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 × 3 system of Euler equations in gas dynamics. The proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane. The uniqueness of Riemann solutions yields their inviscid large-time stability under arbitrarily large perturbation of the Riemann initial data, as long as the corresponding solutions are in L ^∞ and have local bounded total variation satisfying a natural condition on its growth with time. No specific reference to any particular method for constructing the entropy solutions is needed. The uniqueness result for Riemann solutions can easily be extended to entropy solutions U(x,t), piecewise Lipschitz in x, for any t > 0, with arbitrarily large oscillation. Received: 23 April 2001 / Accepted: 20 September 2001