Optimal coalition formation and surplus distribution: Two sides of one coin

A fuzzy coalitional game represents a situation in which players can vary the intensity at which they participate in the coalitions accessible to them, as opposed to the treatment as a binary choice in the non-fuzzy (crisp) game. Building on the property - not made use of so far in the literature of fuzzy games - that a fuzzy game can be represented as a convex program, this paper shows that the optimum of such a program determines the optimal coalitions as well as the optimal rewards for the players, two sides of one coin. Furthermore, this program is seen to provide a unifying framework for representing the core, the least core, and the (fuzzy) nucleolus, among others. Next, we derive conditions for uniqueness of core rewards and to deal with non-uniqueness we introduce a family of parametric perturbations of the convex program that encompasses a large number of well-known concepts for selection from the core, including the Dutta-Ray solution (Dutta and Ray, 1989), the equal sacrifice solution (Yu, 1973), the equal division solution (Selten, 1972) and the tau-value (Tijs, 1981). We also generalize the concept of the Grand Coalition of contracting players by allowing for multiple technologies, and we specify the conditions for this allocation to be unique and Egalitarian. Finally, we show that our formulation offers a natural extension to existing models of production economies with threats and division rules for common surplus.     

Relation between soil matrix potential changes and water conversion ratios during methane hydrate formation processes in loess

With a new apparatus designed and assembled by ourselves, the matrix potential of non-saturated loess was firstly measured and studied during methane hydrate formation processes. The experimental results showed that during two formation processes, the matrix potential changes of the loess all presented a good linear relationship with water conversion ratios. In addition, although it was well known that the secondary gas hydrate formation was easier than the initial, our experimental results showed that the initial hydrate formation efficiency in non-saturated loess was higher than that of the secondary.     

The laser polarization as control parameter in the formation of laser-induced periodic surface structures: Comparison of numerical and experimental results

Considering self-organized surface pattering upon multi-pulse femtosecond laser irradiation, in particularly the strong dependence of ripples orientation on the laser polarization, we present numerical simulations from an adopted surface erosion model and compare the result to our experimental data on laser-induced nanostructures formation. We present the surface morphologies obtained by this model for different polarizations of the incident laser electric field and show good agreement with ripple formation produced by laser ablation experiments. The correlation of ripples orientation with laser polarization can be described within a model where the polarization causes a breaking of symmetry at the surface. Further we discuss a time evolution of pattern formation. Our results support the non-linear self-organization mechanism of pattern formation on the surface of solids.     

Self-organized patterns and traffic flow in Colonies of organisms: from bacteria and social insects to vertebrates

Flocks of birds and schools of fish are familiar examples of spatial patterns formed by living organisms. In contrast to the patterns on the skins of, say, zebras and giraffes, the patterns of our interest are transient although different patterns change over different timescales. The aesthetic beauty of these patterns has attracted the attention of poets and philosophers for centuries. Scientists from various disciplines, however, are in search of common underlying principles that give rise to the transient patterns in colonies of organisms. Such patterns are observed not only in colonies of organisms as simple as single-cell bacteria, but also in social insects like ants and termites. They are also observed in colonies of vertebrates as complex as birds and fish, and in human societies. In recent years, physicists have utilized the framework of statistical physics to understand these patterns. In this article, we present an overview emphasizing the common trends that rely on theoretical modeling of these systems using the so-called agent-based Lagrangian approach.     

Cerium isotope effects in Ce(III) malate and lactate complex formation studied by long-distance displacement chromatography

Isotope effects of cerium were observed in malate and lactate complex formations during the long-distance displacement chromatographic processes at 313 K. Heavier isotopes were found fractionated in the frontal edges of the Ce adsorption bands in both the systems, registering a preference of the heavier isotopes for the Ce(III) complexes in the solution phase over the simply hydrated Ce(III) ions in the resin phase. The fractionation coefficients ? for the ¹³⁶Ce/¹⁴⁰Ce, ¹³⁸Ce/¹⁴⁰Ce and ¹⁴²Ce/¹⁴⁰Ce isotopic pairs were 7.1 × 10^?6, 5.2 × 10^?6 and ?2.1 × 10^?6 for the malate system, and 4.8 × 10^?6, 4.5 × 10^?6 and?2.6×10^?6 for the lactate system, respectively. They all show the mass-dependent law if the deviation of ? for the ¹³⁸Ce/¹⁴⁰Ce pair was considered merely due to the isobaric interference in Ce isotopic ratio measurements, suggesting the molecular vibration, rather than the nuclear field shift, mainly contributes to the Ce isotope effects in the complex formation systems. The absolute values of ? between the two systems are comparable, suggesting no instinct difference in structural properties between Ce malate and lactate complexes involved.     

Numerical study of the effects of gravity on soot formation in laminar coflow methane/air diffusion flames under different air stream velocities

Numerical simulations of laminar coflow methane/air diffusion flames at atmospheric pressure and different gravity levels were conducted to gain a better understanding of the effects of gravity on soot formation by using relatively detailed gas-phase chemistry and complex thermal and transport properties coupled with a semi-empirical two-equation soot model. Thermal radiation was calculated using the discrete-ordinates method coupled with a non-grey model for the radiative properties of CO, CO₂, H₂O, and soot. Calculations were conducted for three coflow air velocities of 77.6, 30, and 5 cm/s to investigate how the coflowing air velocity affects the flame structure and soot formation at different levels of gravity. The coflow air velocity has a rather significant effect on the streamwise velocity and the fluid parcel residence time, especially at reduced gravity levels. The flame height and the visible flame height in general increase with decreasing the gravity level. The peak flame temperature decreases with decreasing either the coflow air stream velocity or the gravity level. The peak soot volume fraction of the flame at microgravity can either be greater or less than that of its normal gravity counterpart, depending on the coflow air velocity. At sufficiently high coflow air velocity, the peak soot volume fraction increases with decreasing the gravity level. When the coflow air velocity is low enough, soot formation is greatly suppressed at microgravity and extinguishment occurs in the upper portion of the flame with soot emission from the tip of the flame owing to incomplete oxidation. The numerical results provide further insights into the intimate coupling between flame size, residence time, thermal radiation, and soot formation at reduced gravity level. The importance of thermal radiation heat transfer and coflow air velocity to the flame structure and soot formation at microgravity is demonstrated for the first time.     

Mechanical erosion by flowing lava

Hot lava is a viscous fluid that, driven by gravity, moves along the Earth's surface. Intuitively, one attributes constructional properties to lava–it accumulates in volcanic landforms, compound lava fields and, in the end, entire mountains. On the other hand, there are also examples of the erosive power of lava: on Earth and especially on other planets in the Solar System, there exist channels incised by flowing lava. The origins of these erosive features have long been debated among volcanologists and planetologists. The dominant paradigm is thermal erosion, although it leaves many questions open. After the 2001 eruption on Mount Etna we found a lava channel whose features cannot be explained in the frame of thermal erosion. On the basis of our observations, we have developed a model for mechanical erosion that explains the main field observations, and opens alternative ways to describe erosion by flowing lava.     

Animal network phenomena: Insights from triadic games

Triadic interactions have a very important role to play in games of animal conflict on complex networks, because triads are both the simplest groups in which asymmetric network phenomena can be studied and the groups beyond dyads in which analysis of population games is most likely to be tractable, especially when allowing for intrinsic variation. Here we demonstrate how analytical models of triadic games can yield novel insights into a variety of behavioral phenomena within networks, including coalition formation, eavesdropping, and victory displays. © 2008 Wiley Periodicals, Inc. Complexity, 2009     

Pairwise-stability and Nash equilibria in network formation

Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks. We thank William Thomson, an associate editor and two anonymous referees for their suggestions that led to substantial improvements. We also thank Sjaak Hurkens, Bettina Klaus, Jordi Massó and Giovanni Neglia for helpful conversations. The first author gratefully acknowledges the financial support from the Spanish Ministry of Education and FEDER through grant SEJ2005-01481/ECON, the Fundación BBVA and the Barcelona Economics Program of XREA. The second author is grateful to the Netherlands Organization for Scientific Research (NWO) for its support under grant VIDI-452-06-013.     

The product of generalized subnormal subgroups in finite groups

We study the structure of some classes of finite groups with a given system of commuting generalized subnormal subgroups. In particular, our results yield a characterization of superradical and Shemetkov formations.