Set Of Stable Configurations Research Articles

Dynamical evolutions of -boson stars in spherical symmetry

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars (BSs) by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number . We call such solutions ‘-boson stars’. Here, we perform a series of fully non-linear dynamical simulations of perturbed -BSs in order to study their stability, and the final fate of unstable configurations. We show that for each value of , the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with BSs, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

Multiple and inverse topplings in the Abelian Sandpile Model

The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resembling avalanches in piles of sand. The fundamental moves defining the dynamics are encoded by the toppling rules. The transition monoid corresponding to this dynamics in the set of stable configurations is abelian, a property which seems at the basis of our understanding of the model. By including also antitoppling rules, we introduce and investigate a larger monoid, which is not abelian anymore. We prove a number of algebraic properties of this monoid, and describe their practical implications on the emerging structures of the model.

The probability of majority rule instability in the 2D euclidean model with an even number of voters

The classic instability theorems of Euclidean voting theory definitively treat all cases except that of an even number of voters in two dimensions. For that case, all that has been known is that the set of stable configurations is neither measure 0 nor measure 1. We prove that instability occurs with probability converging rapidly to 1 as the population increases.

INTERACTION ENERGY IN MAYA-OIL ASPHALTENES: A MOLECULAR MECHANICS STUDY

The interaction energy in vacuum between large-scale (630 atom) Maya-oil asphaltenes and that for an asphaltene-resin dimer has been calculated using molecular mechanics for various relative orientations and distances, keeping a frozen-structure scheme. In the case of asphaltene-asphaltene interactions, it is found that the anti-aliphatic conformation (i.e., with the monomer alkyl branches far away from each other) with parallel well-defined aromatic regions constitutes the most stable structure for an asphaltene dimer. For the asphaltene-resin case, a set of stable configurations is found mainly associated with the exposed asphaltene aromatic regions. In this paper, a survey of the interaction energy for a particular asphaltene-resin configuration is reported and compared with the asphaltene-asphaltene case. The interaction energies as a function of relative distance are parameterized through an analytical expression distinguishing among Coulomb, dispersion, and London contributions. Finally, an effective-medium approach to estimate the effect of the embedding medium on the interaction energy is proposed through a dielectric scaling of the Coulomb and London contributions.

THE DYNAMICS ON THE CELL SPACES WITH $ p $ STATES UNDER THE LOCAL TRANSFORMATIONS SATISFYING THE PRINCIPLE OF LOCAL MAJORITY

In order to understand biological phenomena, a new mathematical field was proposed by T. Kitagawa in 1970 and it was named bio mathematics. T. Kitagawa and M. Yamaguchi discussed cell spaces which are one of approaches to establish biomathematics. More than two states are introduced in the cell space. By algebraic methods, in a cell space with four or two states it is proved that a set of all configurations is a vector space and a set of all possible stable configurations is a vector subspace. Thus, in the cell space with four or two states any stable configuration is represented by a superposition of elementary stable configurations. Furthermore, it is proved that in the cell space with two states, there exists one to one correspondence between the set of stable configurations and the set of garden of Eden configurations. The invariant boundary is introduced in the celI space with two states, which generate some variant cell subspaces whose configuration oscillates among definite configurations. The possible positions of this cell subspace are investigated.