Heat engine in the three-dimensional spacetime

We define a kind of heat engine via three-dimensional charged BTZ black holes. This case is quite subtle and needs to be more careful. The heat flow along the isochores does not equal to zero since the specific heat $C_V\neq0$ and this point completely differs from the cases discussed before whose isochores and adiabats are identical. So one cannot simply apply the paradigm in the former literatures. However, if one introduces a new thermodynamic parameter associated with the renormalization length scale, the above problem can be solved. We obtain the analytical efficiency expression of the three-dimensional charged BTZ black hole heat engine for two different schemes. Moreover, we double check with the exact formula. Our result presents the first specific example for the sound correctness of the exact efficiency formula. We argue that the three-dimensional charged BTZ black hole can be viewed as a toy model for further investigation of holographic heat engine. Furthermore, we compare our result with that of the Carnot cycle and extend the former result to three-dimensional spacetime. In this sense, the result in this paper would be complementary to those obtained in four-dimensional spacetime or ever higher. Last but not the least, the heat engine efficiency discussed in this paper may serve as a criterion to discriminate the two thermodynamic approaches introduced in Ref.[29] and our result seems to support the approach which introduces a new thermodynamic parameter $R=r_0$.Comment: Revised version. Discussions adde

A micromechanical model on specific damping capacity caused by micro cracks

Dispersed micro cracks are widely found in engineer materials, e.g. concrete, ceramic and composite. Specific damping capacity (SDC) caused by friction on micro crack surfaces (FSDC) was investigated in this study. Firstly, frictional energy dissipation (FED) of individual micro crack was modeled analytically and it was further validated by unit cell FE approach. Then, the model was employed in macro-scale cantilever beams involving regular and random multi micro cracks respectively. FEDs and FSDCs of the beams with different micro crack angles and densities are predicted. The study indicated that FED (and FSDC) depends on crack angle and stress state in structure. FSDC is independent to magnitudes of load and modulus of material in elastic scope. To materials with low viscosity, damping might increase significantly with the presence of multi micro cracks of high density

Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle