Galaxy rotation curves in the light of the Spinor Theory of Gravity

We analyze the recently obtained static and spherically symmetric solutions of the Spinor Theory of Gravity (STG) which, in the weak field limit, presents an effective Newtonian potential that contains an extra logarithmic behavior. We apply this solution to the description of the galaxy rotation curves finding an interesting analogy with the dark matter halo profile proposed by Navarro, Frenk and White.

Gintropy: Gini Index Based Generalization of Entropy

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs–Boltzmann–Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.

Square Roots of Real 3 × 3 Matrices vs. Quartic Polynomials with Real Zeros

Abstract There is an interesting analogy between the description of the real square roots of 3×3 matrices and the zeros of the (depressed) real quartic polynomials. This analogy, which in fact better explains the nature of the zeros of those polynomials, is unveiled through a natural use of the Cayley-Hamilton theorem.

Particle entropy and depairing in hot nuclei

The nuclear level densities and single particle entropies are predicted for nuclei in the mass region [Formula: see text] within a framework of statistical theory of hot nuclei method. In this method, particle-number and energy conservation as well as nuclear pairing correlations are included in the partition function of grand canonical ensemble. The suppression of pairing correlations is distinctly noticed in temperature dependence of entropies between the critical temperatures [Formula: see text] MeV and [Formula: see text] MeV for [Formula: see text], [Formula: see text] and [Formula: see text] isotopes of the elements. These structural thermodynamic entropies are interpreted as a remarkable signature of the superfluid to normal phase transition connected to the vanishing of pairing gap. The calculated level densities are compared with recent experimental values. In addition, the single particle entropy of intermediate-mass nuclei is depicted as half of the entropy of mid-shell nuclei in the rare-earth region. As a consequence, the [Formula: see text] shell closure of [Formula: see text]V carries low entropy at low excitation energy presents an interesting analogy to the [Formula: see text] shell closure of [Formula: see text]Ni. Merely, in the case of odd–even [Formula: see text] has higher entropy than the even–even [Formula: see text] nucleus.

Nambu-Goldstone-Leggett modes in multi-condensate superconductors

Multi-gap superconductors exhibit interesting properties. In an N-gap superconductor, we have in general U(1)N phase invariance. This multiple-phase invariance is partially or totally spontaneously broken in a superconductor. The Nambu-Goldstone modes, as well as Higgs modes, are important and will play an important role in multi-condensate superconductors. The additional phase invariance leads to a new quantum phase, with help of frustrated Josephson effects, such as the time-reversal symmetry breaking, the emergence of massless modes and fractionally quantized-flux vortices. There is a possibility that half-flux vortices exist in two-component superconductors in a magnetic field. The half-quantum flux vortex can be interpreted as a monopole, and two half-flux vortices form a bound state connected by a domain wall. There is an interesting analogy between quarks and fractionally quantized-flux vortices in superconductors.

MORAL CLUMSINESS

What would happen if one morning you wake up clumsy, as if your sense of touch were unreliable, arbitrarily on and off? And what would this clumsiness look like if we could transfer it to the moral sense? The article expounds an interesting analogy between the sense of touch, loosely construed, and the moral sense: just as a sort of consistency is necessary for the sense of touch to do its job, so it is for the moral sense to play its part. Touch enables us to navigate the everyday world of coffee pots and staircases; our moral sensibility comes into play when we act or when we judge our actions and those of others, and plays a directive role in what we feel, how we feel it, and how we react to it. Taking the analogy further, I will suggest that inconsistency causes, in both cases, a certain clumsiness, and that clumsiness is linked to arbitrariness – like the person that helps others in dire need, but only does so on some rainy days.

Non Unitary Random Walks

International audience Motivated by the recent refutation of information loss paradox in black hole by Hawking, we investigate the new concept of {\it non unitary random walks}. In a non unitary random walk, we consider that the state 0, called the {\it black hole}, has a probability weight that decays exponentially in $e^{-\lambda t}$ for some $\lambda>0$. This decaying probabilities affect the probability weight of the other states, so that the the apparent transition probabilities are affected by a repulsion factor that depends on the factors $\lambda$ and black hole lifetime $t$. If $\lambda$ is large enough, then the resulting transition probabilities correspond to a neutral random walk. We generalize to {\it non unitary gravitational walks} where the transition probabilities are function of the distance to the black hole. We show the surprising result that the black hole remains attractive below a certain distance and becomes repulsive with an exactly reversed random walk beyond this distance. This effect has interesting analogy with so-called dark energy effect in astrophysics.

Inner and Outer Horizons of Time Experience

Human experience of temporal durations exhibits a multi-regional structure, with more or less distinct boundaries, or horizons, on the scale of physical duration. The inner horizons are imposed by perceptual thresholds for simultaneity (≈ 3 ms) and temporal order (≈ 30 ms), and are determined by the dynamical properties of the neural substrate integrating sensory information. Related to the inner horizon of experienced time are perceptual or cognitive “moments.” Comparative data on autokinetic times suggest that these moments may be relatively invariant (≈ 102 ms) across a wide range of species. Extension of the “sensible present” (≈ 3 s) defines an intermediate horizon, beyond which the generic experience of duration develops. The domain of immediate duration experience is delimited by the ultimate outer horizon at about ≈102 s, as evidenced by analysis of duration reproduction experiments (reproducibility horizon), probably determined by relaxation times of “neural accumulators.” Beyond these phenomenal horizons, time is merely cognitively (re)constructed, not actually experienced or “perceived,” a fact that is frequently ignored by contemporary time perception research. The nyocentric organization of time experience shows an interesting analogy with the egocentric organization of space, suggesting that structures of subjective space and time are derived from active motion as a common experiential basis.