Design of conditions for emergence of self-replicators

A self-replicator is usually understood to be an object of definite form that promotes the conversion of materials in its environment into a nearly identical copy of itself. The challenge of engineering novel, micro- or nano-scale self-replicators has attracted keen interest in recent years, both because exponential amplification is an attractive method for generating high yields of specific products, and also because self-reproducing entities have the potential to be optimized or adapted through rounds of iterative selection. Substantial steps forward have been achieved both in the engineering of particular self-replicating molecules, and also in characterizing the physical basis for possible mechanisms of self-replication. At present, however, there is need for a theoretical treatment of what physical conditions are most conducive to the emergence of novel self-replicating structures from a reservoir of building blocks on a desired time-scale. Here we report progress in addressing this need. By analyzing the dynamics of a generic class of heterogeneous particle mixtures whose reaction rates emerge from basic physical interactions, we demonstrate that the spontaneous discovery of self-replication is controlled by relatively generic features of the chemical space, namely: the dispersion in the distribution of reaction timescales and bound-state energies. Based on this analysis, we provide quantitative criteria that may aid experimentalists in designing a system capable of producing self-replicators, and in estimating the likely timescale for exponential growth to start.Comment: Supplementary Information is under the Ancillary Files ---

Gravitationally Bound Bose Condensates with Rotation

We develop a self-consistent, Gravitoelectromagnetic (GEM) formulation of a slowly rotating, self-gravitating and dilute Bose-Einstein condensate (BEC), intended for astrophysical applications in the context of dark matter halos. GEM self-consistently incorporates the effects of frame dragging to lowest order in $v/c$ via the Gravitomagnetic field. BEC dark matter has attracted attention as an alternative to Cold dark matter (CDM) and Warm dark matter (WDM) for some time now. The BEC is described by the Gross-Pitaevskii-Poisson (GPP) equation with an arbitrary potential allowing for either attractive or repulsive interactions. Owing to the difficulty in obtaining exact solutions to the GEM equations of motion without drastic approximations, we employ the variational method to examine the conditions under which rotating condensates, stable against gravitational collapse, may form in models with attractive and repulsive quartic interactions. We also describe the approximate dynamics of an imploding and rotating condensate by employing a collective coordinate description in terms of the condensate radius.Comment: 23 pages, 7 figures. Version to appear in Phys. Rev.

Application of a Reynolds stress turbulence model to the compressible shear layer

Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers. However, attempts to extend these models to the high-speed, compressible shear layer have been less effective. In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation. The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments. Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure. This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence. The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data. Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased. Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number

On the Thermodynamic Geometry of Hot QCD

We study the nature of the covariant thermodynamic geometry arising from the free energy of hot QCD. We systematically analyze the underlying equilibrium thermodynamic configurations of the free energy of 2- and 3-flavor hot QCD with or without including thermal fluctuations in the neighborhood of the QCD transition temperature. We show that there exists a well-defined thermodynamic geometric notion for QCD thermodynamics. The geometry thus obtained has no singularity as an intrinsic Riemannian manifold. We further show that there is a close connection of this geometric approach with the existing studies of correlations and quark number susceptibilities in hot QCD.Comment: 15 pages, 12 figures, Keywords: Thermodynamic Geometry, Hot QCD, Quasi-particles, PACS: 12.38.-t; 05.70.Fh; 02.40.Ky; 12.40.E

Electrical transport properties of nanostructured ferromagnetic perovskite oxides La_0.67Ca_0.33MnO_3 and La_0.5Sr_0.5CoO_3 at low temperatures (5 K > T >0.3 K) and high magnetic field

We report a comprehensive study of the electrical and magneto-transport properties of nanocrystals of La_0.67Ca_0.33MnO_3 (LCMO) (with size down to 15 nm) and La_0.5Sr_0.5CoO_3 (LSCO) (with size down to 35 nm) in the temperature range 0.3 K to 5 K and magnetic fields upto 14 T. The transport, magnetotransport and non-linear conduction (I-V curves) were analysed using the concept of Spin Polarized Tunnelling in the presence of Coulomb blockade. The activation energy of transport, \Delta, was used to estimate the tunnelling distances and the inverse decay length of the tunnelling wave function (\chi) and the height of the tunnelling barrier (\Phi_B). The magnetotransport data were used to find out the magnetic field dependences of these tunnelling parameters. The data taken over a large magnetic field range allowed us to separate out the MR contributions at low temperatures arising from tunnelling into two distinct contributions. In LCMO, at low magnetic field, the transport and the MR are dominated by the spin polarization, while at higher magnetic field the MR arises from the lowering of the tunnel barrier by the magnetic field leading to an MR that does not saturate even at 14 T. In contrast, in LSCO, which does not have substantial spin polarization, the first contribution at low field is absent, while the second contribution related to the barrier height persists. The idea of inter-grain tunnelling has been validated by direct measurements of the non-linear I-V data in this temperature range and the I-V data was found to be strongly dependent on magnetic field. We made the important observation that a gap like feature (with magnitude ~ E_C, the Coulomb charging energy) shows up in the conductance g(V) at low bias for the systems with smallest nanocrystal size at lowest temperatures (T < 0.7 K). The gap closes as the magnetic field and the temperature are increased.Comment: 13 figure

Effect of Low Refocusing Angle in T1-Weighted Spin Echo and Fast Spin Echo MRI on Low-Contrast Detectability: A Comparative Phantom Study at 1.5 and 3 Tesla

MRI tissue contrast is not well preserved at high field. In this work, we used a phantom with known, intrinsic contrast (3.6%) for model tissue pairs to test the effects of low angle refocusing pulses and magnetization transfer from adjacent slices on intrinsic contrast at 1.5 and 3 Tesla. Only T1-weighted spin echo sequences were tested since for such sequences the contrast loss, tissue heating, and image quality degradation at high fields seem to present significant diagnostic and quality issues. We hypothesized that the sources of contrast loss could be attributed to low refocusing angles that do not fulfill the Hahn spin echo conditions or to magnetization transfer effects from adjacent slices in multislice imaging. At 1.5 T the measured contrast was 3.6% for 180° refocusing pulses and 2% for 120° pulses, while at 3 T, it was 4% for 180° and only 1% for 120° refocusing pulses. There was no significant difference between single slice and multislice imaging suggesting little or no role played by magnetization transfer in the phantom chosen. Hence, one may conclude that low angle refocusing pulses not fulfilling the Hahn spin echo conditions are primarily responsible for significant deterioration of T1-weighted spin echo image contrast in high-field MRI