A potential approach to solutions for set games

Concerning the solution theory for set games, the paper introduces a new solution by allocating, to any player, the items (taken from an universe) that are attainable for the player, but can not be blocked (by any coalition not containing the player). The resulting value turns out to be an utmost important concept for set games to characterize the family of set game solutions that possess a so-called potential representation (similar to the potential approaches applied in both physics and cooperative game theory). An axiomatization of the new value, called Driessen--Sun value, is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property

A uniform approach to semi-marginalistic values for set games

Concerning the solution theory for set games, the paper focuses on a family of solutions, each of which allocates to any player some type of marginalistic contribution with respect to any coalition containing the player. Here the marginalistic contribution may be interpreted as an individual one, or a coalitionally one. For any value of the relevant family, an axiomatization is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property. We present two proof techniques, each of which is based on the decomposition of any arbitrary set game into a union of either simple set games or elementary set games, the solutions of which are much easier to determine. A simple respectively elementary set game is associated with an arbitrary, but fixed item of the universe respectively coalition

Onset of unsteady horizontal convection in rectangle tank at Pr=1Pr=1

The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical Rayleigh number $Ra_c$ is obtained as $Ra_c=5.5377\times 10^8$ for the middle plume forcing at $Pr=1$, which is much larger than the formerly obtained value. Besides, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses about the destabilization of the flow is numerically proved, i.e. the middle plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in pres

Contact law and impact responses of laminated composites

Static identation tests were performed to determine the law of contact between a steel ball and glass/epoxy and graphite/epoxy laminated composites. For both composites the power law with an index of 1.5 was found to be adequate for the loading curve. Substantial permanent deformations were noted after the unloading. A high order beam finite element was used to compute the dynamic contact force and response of the laminated composite subjected to the impact of an elastic sphere. This program can be used with either the classical Hertzian contact law or the measured contact law. A simple method is introduced for estimating the contact force and contact duration in elastic impacts

Multivalley engineering in semiconductor microcavities

We consider exciton-photon coupling in semiconductor microcavities in which separate periodic potentials have been embedded for excitons and photons. We show theoretically that this system supports degenerate ground-states appearing at non-zero in-plane momenta, corresponding to multiple valleys in reciprocal space, which are further separated in polarization corresponding to a polarization-valley coupling in the system. Aside forming a basis for valleytronics, the multivalley dispersion is predicted to allow for spontaneous momentum symmetry breaking and two-mode squeezing under non-resonant and resonant excitation, respectively.Comment: Manuscript: 7 pages, 7 figures, published in Scientific Reports 7, 45243 (2017

The angular momentum of a magnetically trapped atomic condensate

For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vorticity of magnetically trapped atomic quantum gases.Comment: 4 pages, 1 figure