A Three-Function Variational Principle for Stationary Nonbarotropic Magnetohydrodynamics

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of nonbarotropic stationary magnetohydrodynamics can be derived for magnetic fields that lie on surfaces. A variational principle is given in terms of three independent variables for stationary nonbarotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables that appear in the standard equations of nonbarotropic magnetohydrodynamics, which are the magnetic field, the velocity field, the specific entropy, and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

A Three Function Variational Principle for Stationary Non-Barotropic Magnetohydrodynamics

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for magnetic fields which lie on surfaces. A variational principle is given in terms of three independent variables for stationary non-barotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field, the velocity field, the specific entropy and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

Higher entropy observed in SARS-CoV-2 genomes from the first COVID-19 wave in Pakistan

Background We investigated the genome diversity of SARS-CoV-2 associated with the early COVID-19 period to investigate evolution of the virus in Pakistan. Materials and methods We studied ninety SARS-CoV-2 strains isolated between March and October 2020. Whole genome sequences from our laboratory and available genomes were used to investigate phylogeny, genetic variantion and mutation rates of SARS-CoV-2 strains in Pakistan. Site specific entropy analysis compared mutation rates between strains isolated before and after June 2020. Results In March, strains belonging to L, S, V and GH clades were observed but by October, only L and GH strains were present. The highest diversity of clades was present in Sindh and Islamabad Capital Territory and the least in Punjab province. Initial introductions of SARS-CoV-2 GH (B.1.255, B.1) and S (A) clades were associated with overseas travelers. Additionally, GH (B.1.255, B.1, B.1.160, B.1.36), L (B, B.6, B.4), V (B.4) and S (A) clades were transmitted locally. SARS-CoV-2 genomes clustered with global strains except for ten which matched Pakistani isolates. RNA substitution rates were estimated at 5.86 x10−4. The most frequent mutations were 5’ UTR 241C > T, Spike glycoprotein D614G, RNA dependent RNA polymerase (RdRp) P4715L and Orf3a Q57H. Strains up until June 2020 exhibited an overall higher mean and site-specific entropy as compared with sequences after June. Relative entropy was higher across GH as compared with GR and L clades. More sites were under selection pressure in GH strains but this was not significant for any particular site. Conclusions The higher entropy and diversity observed in early pandemic as compared with later strains suggests increasing stability of the genomes in subsequent COVID-19 waves. This would likely lead to the selection of site-specific changes that are advantageous to the virus, as has been currently observed through the pandemic.

Primordial nucleosynthesis constraints on high-z energy releases

ABSTRACT The cosmic microwave background (CMB) spectrum provides tight constraints on the thermal history of the universe up to z ∼ 2 × 106. At higher redshifts, thermalization processes become very efficient so that even large energy releases do not leave visible imprints in the CMB spectrum. In this paper, we show that the consistency between the accurate determinations of the specific entropy at primordial nucleosynthesis and at the electron–photon decoupling implies that no more than 7.8 per cent of the present-day CMB energy density could have been released in the post-nucleosynthesis era. As pointed out by previous studies, primordial nucleosynthesis complements model independent constraints provided by the CMB spectrum, extending them by two orders of magnitude in redshift.

Mirror principle and the red-giant bump: the battle of entropy in low-mass stars

ABSTRACT The evolution of low-mass stars into red giants is still poorly understood. During this evolution the core of the star contracts and, simultaneously, the envelope expands – a process known as the ‘mirror’. Additionally, there is a short phase where the trend for increasing luminosity is reversed. This is known as the red giant branch bump. We explore the underlying physical reasons for these two phenomena by considering the specific entropy distribution in the star and its temporal changes. We find that between the luminosity maximum and luminosity minimum of the bump there is no mirror present and the star is fully contracting. The contraction is halted and the star regains its mirror when the hydrogen-burning shell reaches the mean molecular weight discontinuity. This marks the luminosity minimum of the bump.

Testing the entropy calibration of the radii of cool stars: models of α Centauri A and B

We present models of α Centauri A and B implementing an entropy calibration of the mixing-length parameter αMLT, recently developed and successfully applied to the Sun (Spada et al. 2018, ApJ, 869, 135). In this technique the value of αMLT in the 1D stellar evolution code is calibrated to match the adiabatic specific entropy derived from 3D radiation-hydrodynamics simulations of stellar convective envelopes, whose effective temperature, surface gravity, and metallicity are selected consistently along the evolutionary track. The customary treatment of convection in stellar evolution models relies on a constant, solar-calibrated αMLT. There is, however, mounting evidence that this procedure does not reproduce the observed radii of cool stars satisfactorily. For instance, modelling α Cen A and B requires an ad-hoc tuning of αMLT to distinct, non-solar values. The entropy-calibrated models of α Cen A and B reproduce their observed radii within $1\%$ (or better) without externally adjusted parameters. The fit is of comparable quality to that of models with freely adjusted αMLT for α Cen B (within 1 σ), while it is less satisfactory for α Cen A (within ≈2.5 σ). This level of accuracy is consistent with the intrinsic uncertainties of the method. Our results demonstrate the capability of the entropy calibration method to produce stellar models with radii accurate within $1\%$. This is especially relevant in characterising exoplanet-host stars and their planetary systems accurately.

Study on a Quaternary Working Pair of CaCl2-LiNO3-KNO3/H2O for an Absorption Refrigeration Cycle

When compared with LiBr/H2O, an absorption refrigeration cycle using CaCl2/H2O as the working pair needs a lower driving heat source temperature, that is, CaCl2/H2O has a better refrigeration characteristic. However, the crystallization temperature of CaCl2/H2O solution is too high and its absorption ability is not high enough to achieve an evaporation temperature of 5 °C or lower. CaCl2-LiNO3-KNO3(15.5:5:1)/H2O was proposed and its crystallization temperature, saturated vapor pressure, density, viscosity, specific heat capacity, specific entropy, and specific enthalpy were measured to retain the refrigeration characteristic of CaCl2/H2O and solve its problems. Under the same conditions, the generation temperature for an absorption refrigeration cycle with CaCl2-LiNO3-KNO3(15.5:5:1)/H2O was 7.0 °C lower than that with LiBr/H2O. Moreover, the cycle’s COP and exergy efficiency with CaCl2-LiNO3-KNO3(15.5:5:1)/H2O were approximately 0.04 and 0.06 higher than those with LiBr/H2O, respectively. The corrosion rates of carbon steel and copper for the proposed working pair were 14.31 μm∙y−1 and 2.04 μm∙y−1 at 80 °C and pH 9.7, respectively, which were low enough for engineering applications.