Gravitational decoupling of generalized Horndeski hybrid stars

Gravitational decoupled compact polytropic hybrid stars are here addressed in generalized Horndeski scalar-tensor gravity. Additional physical properties of hybrid stars are scrutinized and discussed in the gravitational decoupling setup. The asymptotic value of the mass function, the compactness, and the effective radius of gravitational decoupled hybrid stars are studied for both cases of a bosonic and a fermionic prevalent core. These quantities are presented and discussed as functions of Horndeski parameters, the decoupling parameter, the adiabatic index, and the polytropic constant. Important corrections to general relativity and generalized Horndeski scalar-tensor gravity, induced by the gravitational decoupling, comply with available observational data. Particular cases involving white dwarfs, boson stellar configurations, neutron stars, and Einstein–Klein–Gordon solutions, formulated in the gravitational decoupling context, are also scrutinized.

Vertex Turán problems for the oriented hypercube

In this short note we consider the oriented vertex Turán problem in the hypercube: for a fixed oriented graph F → \vec F , determine the maximum cardinality e x v ( F → , Q → n ) e{x_v}\left( {\vec F,{{\vec Q}_n}} \right) of a subset U of the vertices of the oriented hypercube Q → n {\vec Q_n} such that the induced subgraph Q → n [ U ] {\vec Q_n}\left[ U \right] does not contain any copy of F → \vec F . We obtain the exact value of e x v ( P k , → Q n → ) e{x_v}\left( {\overrightarrow {{P_k},} \,\overrightarrow {{Q_n}} } \right) for the directed path P k → \overrightarrow {{P_k}} , the exact value of e x v ( V 2 → , Q n → ) e{x_v}\left( {\overrightarrow {{V_2}} ,\,\overrightarrow {{Q_n}} } \right) for the directed cherry V 2 → \overrightarrow {{V_2}} and the asymptotic value of e x v ( T → , Q n → ) e{x_v}\left( {\overrightarrow T ,\overrightarrow {{Q_n}} } \right) for any directed tree T → \vec T .

A Randomly Weighted Minimum Arborescence with a Random Cost Constraint

We study the minimum spanning arborescence problem on the complete digraph [Formula: see text], where an edge e has a weight We and a cost Ce, each of which is an independent uniform random variable Us, where [Formula: see text] and U is uniform [Formula: see text]. There is also a constraint that the spanning arborescence T must satisfy [Formula: see text]. We establish, for a range of values for [Formula: see text], the asymptotic value of the optimum weight via the consideration of a dual problem.

Million node fracture: size matters?

Transmissivity of self-affine fractures was computed numerically as a function of the grid size. One-million-node fractures (1024 × 1024 nodes) with fractal dimensions of 2.2–2.6 were cut into successively smaller fractures (“generations”), and transmissivities computed. The number of fractures in each generation was increased by a factor of 4. Considerable scatter in transmissivity was observed for smaller grid sizes. Average transmissivity of the fractures in the generation decreased with the grid size, without approaching any asymptotic value, which indicates no representative elementary volume (REV). This happened despite the average mean aperture being the same in each generation. The results indicate that it is not possible to estimate the transmissivity of a large fracture by cutting it into smaller fractures, running flow simulations on those and averaging the results. The decrease in transmissivity with the grid size was found to be due to an increase in the flow tortuosity.

Gravitational decoupling and superfluid stars

The gravitational decoupling is applied to studying minimal geometric deformed (MGD) compact superfluid stars, in covariant logarithmic scalar gravity on fluid branes. The brane finite tension is shown to provide more realistic values for the asymptotic value of the mass function of MGD superfluid stars, besides constraining the range of the self-interacting scalar field, minimally coupled to gravity. Several other physical features of MGD superfluid stars, regulated by the finite brane tension and a decoupling parameter, are derived and discussed, with important corrections to the general-relativistic limit that corroborate to current observational data.

ON SOME LOGARITHMIC INEQUALITIES

We establish some inequalities involving $\log(1+x)$ using elementary techniques. Using these inequalities, we show an alternate approach to evaluate the integral $\int\limits_1^\infty \frac{\log t}{t^2}\,dt$. This integral is later used to evaluate the asymptotic value of a logarithmic sum.

A Randomly Weighted Minimum Spanning Tree with a Random Cost Constraint

We study the minimum spanning tree problem on the complete graph $K_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent copy of the random variable $U^\gamma$ where $\gamma\leq 1$ and $U$ is the uniform $[0,1]$ random variable. There is also a constraint that the spanning tree $T$ must satisfy $C(T)\leq c_0$. We establish, for a range of values for $c_0,\gamma$, the asymptotic value of the optimum weight via the consideration of a dual problem.

Experimental Study of Bubble Formation from a Micro-Tube in Non-Newtonian Fluid

Over the last few years, microbubbles have found application in biomedicine. In this study, the characteristics of bubbles formed when air is introduced from a micro-tube (internal diameter 110 μm) in non-Newtonian shear thinning fluids are studied. The dependence of the release time and the size of the bubbles on the gas phase rate and liquid phase properties is investigated. The geometrical characteristics of the bubbles are also compared with those formed in Newtonian fluids with similar physical properties. It was found that the final diameter of the bubbles increases by increasing the gas flow rate and the liquid phase viscosity. It was observed that the bubbles formed in a non-Newtonian fluid have practically the same characteristics as those formed in a Newtonian fluid, whose viscosity equals the asymptotic viscosity of the non-Newtonian fluid, leading to the assumption that the shear rate around an under-formation bubble is high, and the viscosity tends to its asymptotic value. To verify this notion, bubble formation was simulated using Computational Fluid Dynamics (CFD). The simulation results revealed that around an under-formation bubble, the shear rate attains a value high enough to lead the viscosity of the non-Newtonian fluid to its asymptotic value.