Star Formation Rate from Dust Infrared Emission

We examine what types of galaxies the conversion formula from dust infrared (IR) luminosity into the star formation rate (SFR) derived by Kennicutt (1998) is applicable to. The ratio of the observed IR luminosity, $L_{\rm IR}$, to the intrinsic bolometric luminosity of the newly (\la 10 Myr) formed stars, $L_{\rm SF}$, of a galaxy can be determined by a mean dust opacity in the interstellar medium and the activity of the current star formation. We find that these parameters area being $0.5 \le L_{\rm IR}/L_{\rm SF} \le 2.0$ is very large, and many nearby normal and active star-forming galaxies really fall in this area. It results from offsetting two effects of a small dust opacity and a large cirrus contribution of normal galaxies relative to starburst galaxies on the conversion of the stellar emission into the dust IR emission. In conclusion, the SFR determined from the IR luminosity under the assumption of $L_{\rm IR}=L_{\rm SF}$ like Kennicutt (1998) is reliable within a factor of 2 for all galaxies except for dust rich but quiescent galaxies and extremely dust poor galaxies.Comment: Accepted by ApJL: 6 pages (emulateapj5), 2 figures (one is an extra figure not appeared in ApJL

Biospheric context of Siberian development

Recent publications on human appropriation of Net Primary Production (NPP) raise the question of how much of the biosphere’s productivity we can appropriate in a sustainable way. This article brings the issue into the context of Siberian development. In contrast to many other regions of the world, the population density in Siberia is still very low as compared to the NPP supplied by regional ecosystems. Hence, it is not too late to raise the question on how much of the NPP supplied by Siberian ecosystems we can appropriate in a sustainable way

Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

Non-self-adjoint resolutions of the identity and associated operators

Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity \{X(\lambda)\}_{\lambda\in {\mb R}}, whose adjoints constitute also a resolution of the identity, are studied . In particular, it is shown that a closed operator $B$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $B=TAT^{-1}$ where $A$ is self-adjoint and $T$ is a bounded operator with bounded inverse

Homogeneous and heterogeneous nucleation of skyrmions in thin layers of cubic helimagnets

Formation of isolated chiral skyrmions by homogeneous and heterogeneous nucleation has been studied in thin layers of cubic helimagnets via elongation of torons and chiral bobbers, correspondingly. Both torons and bobbers are localized in three dimensions, contain singularities, and according to the theoretical analysis within the standard phenomenological models can exist as metastable states in saturated and modulated phases of noncentrosymmetric ferromagnets. Their elongation into the defect-free skyrmion filament is facilitated by small anisotropic contributions making skyrmion cores negative with respect to the surrounding parental state. We show that isolated magnetic torons pose the same problem of compatibility with a surrounding phase as the torons in confinement-frustrated chiral nematics [I. Smalyukh et al., Nature Mater 9, 139-145 (2010)]. We underline the distinct features of magnetic and liquid-crystals torons and calculate phase diagrams indicating their stability regions