Adoption of simultaneous different strategies against different opponents enhances cooperation

The emergence of cooperation has been widely studied in the context of game theory on structured populations. Usually the individuals adopt one strategy against all their neighbors. The structure can provide reproductive success for the cooperative strategy, at least for low values of defection tendency. Other mechanisms, such punishment, can also be responsible for cooperation emergence. But what happens if the players adopt simultaneously different strategies against each one of their opponents, not just a single one? Here we study this question in the prisoner dilemma scenario structured on a square lattice and on a ring. We show that if an update rule is defined in which the players replace the strategy that furnishes the smallest payoff, a punishment response mechanism against defectors without imputing cost to the punishers appears, cooperation dominates and, even if the tendency of defection is huge, cooperation still remains alive

Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling

We extend previous simplicial minisuperspace models to account for arbitrary scalar coupling \eta R\phi^2.Comment: 24 pages and 9 figures. Accepted for publication by Classical and Quantum Gravit

High strength steel in fire

High-performance materials are necessary to meet the future demands of the construction industry, which is strongly influenced by a growing population and depletion of natural resources. Sustainable development is central to research and development into innovative structural materials, and requires solutions to be economically viable whilst equally providing a positive contribution towards environmental and social factors. High strength steels (HSS) have the potential to contribute towards such demands by reducing the weight of structures when employed in appropriate applications. Lighter structures require smaller foundations, shorter transportation and construction times and also lower CO2 emissions. A particular challenge related to the use of HSS in structures include increased likelihood of stability issues resulting from the reduction in section thickness, and limiting deflection and vibration criteria are also more likely to be critical. Nevertheless, when used appropriately, they can provide a sustainable solution. Their use in structural applications is further hindered by a lack of performance data and design guidance under fire conditions. This paper compares the mechanical properties, particularly strength and stiffness of HSS (yield strengths between 460-700 MPa) and mild steel (yields between 235-460 MPa) at elevated temperatures, through a critical review of published literature. Various alloying and processing routes used to achieve high yield strength are assessed. At the same time, the review considers available information on the strengthening mechanisms that can be utilised to retain the strength and/or stiffness of the material in the event of a fire. Using the information gathered, an extensive testing programme is developed which will enable design guidance for the fire design of HSS structures to be proposed.Engineering and Physical Sciences Research Council, TW

Small ball probability for the condition number of random matrices

Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb P}\big\{s_{\max}(A)/s_{\min}(A)\leq n/t\big\}\leq 2\exp(-c t^2),\quad t\geq 1,$$ where $c>0$ may only depend on the subgaussian moment. Although the estimate can be obtained as a combination of known results and techniques, it was not noticed in the literature before. As a key step of the proof, we apply estimates for the singular values of $A$, ${\mathbb P}\big\{s_{n-k+1}(A)\leq ck/\sqrt{n}\big\}\leq 2 \exp(-c k^2), \quad 1\leq k\leq n,$ obtained (under some additional assumptions) by Nguyen.Comment: Some changes according to the Referee's comment

Growth rate and superconducting properties of Gd-Ba-Cu-O bulk superconductors melt processed in air

A generic Mg-doped Nd-Ba-Cu-O seed crystal has been developed recently for the fabrication of any type of rare earth (RE) based (RE)-Ba-Cu-O single grain bulk superconductor in air. The new generic seed simplifies significantly the top seeded melt growth (TSMG) process for light rare earth based (Nd, Sm, Gd, or mixed rare earth elements) bulk superconductors, in particular. GdBCO single grains have been fabricated successfully in air using the new seed in a cold-seeding process. In this study, precursor powders were enriched with different amounts of BaO2 to investigate the extent of substitution of Gd for Ba in the Gd1+xBa2-xCu3O7-delta solid solution phase. The growth process of large single grains in air was investigated at various growth temperatures under isothermal processing conditions. Crystal growth rate as a function of under-cooling and BaO2 content has been determined from these experiments. The spatial variation of Tc and transition temperature width for applied field aligned along the a/b and c-axis of grains fabricated with different BaO2 content has also been investigated in order to understand the extent of the formation of Gd/Ba solid solution with varying growth temperature and precursor composition. These results have been used to establish the optimum conditions for fabricating solid solution-free, large single grains of GdBCO in air

Strongly coupled artificial bulk HTS grain boundaries with high critical current densities

A multi-seeding process has been developed to fabricate single Y-Ba-Cu-O (YBCO) grains containing strong artificial grain boundaries. Multi-seeding of heterogeneous YBCO grains with controlled orientation was achieved using large Sm-Ba-Cu-O (SmBCO) single crystal seeds of rod-like geometry with slots of various widths (up to 13 mm) cut into their bottom surface (i.e. parallel to the c-axis of the seed) to produce a bridge-like structure. Several YBCO grains with artificial grain boundaries were fabricated from these seed crystals and used to investigate the effect of varying the distance between the individual grain nucleation sites and the grain orientation (in-plane and out of plane) on the nature of grain boundaries. The measured local magnetic critical current density (Jc) and the magnitude of the trapped field across these artificial grain boundaries indicate that seed alignment is a key parameter in achieving strongly-coupled grain boundaries in multi-seeded grains