4,604 research outputs found
Syntactic and Rees Indices of Subsemigroups
No full textAbstractWe define two different notions of index for subsemigroups of semigroups: the (right) syntactic index and the Rees index. We investigate the relationships between them and with the group index. In particular, we show that the syntactic index is a generalisation of both the group index and the Rees index. We use this fact to prove further similarities between the group index and the Rees index. It turns out, however, that very few of the nice properties of the group index are inherited by the syntactic index
The 2D/3D dynamics of wall-bounded low-Rm magnetohydrodynamic (MHD) turbulence
No full textWith this experimental study, we give evidence that the dynamics of low-Rm MHD turbulence depends on the diffusion length l_z, which corresponds to the distance over which the Lorentz force is able to diffuse momentum before it is balanced by inertia
Automatic semigroups with subsemigroups of finite Rees index
No full textThe notion of automaticity has been widely studied in groups and some progress has been made in understanding this notion in the wider context of semigroups. The purpose of this paper is to study the connections between the automaticity of semigroups S and T where T is a subsemigroup of finite Rees index in S.</p
Encoding of temporal probabilities in the human brain
No full textAnticipating the timing of future events is a necessary precursor to preparing actions and allocating resources to sensory processing. This requires elapsed time to be represented in the brain and used to predict the temporal probability of upcoming events. While neuropsychological, imaging, magnetic stimulation studies, and single-unit recordings implicate the role of higher parietal and motor-related areas in temporal estimation, the role of earlier, purely sensory structures remains more controversial. Here we demonstrate that the temporal probability of expected visual events is encoded not by a single area but by a wide network that importantly includes neuronal populations at the very earliest cortical stages of visual processing. Moreover, we show that activity in those areas changes dynamically in a manner that closely accords with temporal expectations
Triangular Constellations in Flows
No full textParticles advected on the surface of a fluid can exhibit fractal clustering. The local structure of a fractal set is described by its dimension , which is the exponent of a power-law relating the mass in a ball to its radius : . It is desirable to characterise the {\em shapes} of constellations of points sampling a fractal measure, as well as their masses. The simplest example is the distribution of shapes of triangles formed by triplets of points, which we investigate for fractals generated by chaotic dynamical systems. The most significant parameter describing the triangle shape is the ratio of its area to the radius of gyration squared. We show that the probability density of has a phase transition: is independent of and approximately uniform below a critical flow compressibility , which we estimate. For the distribution appears to be described by two power laws: when , and when
Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
No full textWe investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2D, with no dependence along the vertical? We restrict attention to low-magnetic-Reynolds number (Rm) flow. Because liquid metals have low magnetic Prandtl number, such low- flows can have a kinetic Reynolds number as large as one million and therefore be strongly turbulent. We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number Rm << 1: we prove that the flow becomes exactly 2D asymptotically in time, regardless of the initial condition and provided the interaction parameter N is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2D flow. We then consider the full-magnetohydrodynamic equations and we prove that, for low enough Rm and large enough N, the flow becomes exactly two-dimensional in the long-time limit provided the initial vertically-dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3D attractors may also exist and be attained for strong enough initial 3D perturbations. These results shed some light on the existence of a dissipative anomaly for magnetohydrodynamic flows subject to a strong external magnetic field
The Decay of Wall Bounded MHD Turbulence at Low RM
No full textWe have developed a new spectral method to simulate flows with very fine boundary layers present. We apply it to calculate the evolution of freely decaying MHD turbulence between isolating walls. By comparison them with results obtained in fully periodic domain we quantify the influence of the channel walls on the character of freely decaying MHD turbulence
Invoking the virial theorem to understand the impact of (dry) mergers on the - relation
Full text linkWhile dry mergers can produce considerable scatter in the (black hole mass,
)-(spheroid stellar mass, ) and -(spheroid half-light radius, ) diagrams, the virial theorem
is used here to explain why the scatter about the -(velocity
dispersion, ) relation remains low in the face of such mergers. Its
small scatter has been claimed as evidence of feedback from active galactic
nuclei (AGNs). However, it is shown that galaxy mergers also play a significant
role. The major merger of two S0 galaxies with
M advances a system along a slope of 5 in the - diagram. However, a major EE galaxy merger moves a system
(slightly) along a trajectory with a slope of 9, while mergers of
lower-mass S0 galaxies with M move
(slightly) along a trajectory with a slope of 3. This produces a steeper
distribution for the E (and Es,e) galaxies in the -
diagram, reported here to have a slope of 7.270.91, compared to the S0
galaxies which have a slope of 5.680.60. This result forms an important
complement to the AGN feedback models like that from Silk and Rees, providing a
more complete picture of galaxy/(black hole) coevolution. It also has important
implications for nanohertz gravitational wave research. Abridged.Comment: To appear in MNRAS (12 pages, including 7 figures and a 2 page
Appendix
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