Neutrinos and the Supernova Origin of the Elements

Intense fluxes of neutrinos are emitted by the hot neutron star produced in a supernova. The electron neutrino and antineutrino capture reactions on neutrons and protons, respectively, provide heating to drive a wind from the hot neutron star. The same reactions also determine the neutron-richness of the wind material. Nucleosynthesis via rapid neutron capture, the r-process, may occur in the wind material as it expands away from the neutron star. The neutron-richness of the wind material, and hence, the r-process nucleosynthesis therein, are sensitive to mixing between the muon (or tauon) neutrino/antineutrino and the electron (or sterile) neutrino/antineutrino. Indirect arguments and direct tests for the supernova origin of the r-process elements are discussed with a goal to establish supernova r-process nucleosynthesis as an important probe for neutrino mixing.Comment: 6 pages including 2 figures, to appear in the Proceedings of Neutrino 200

Mathematical Formalism for Isothermal Linear Irreversibility

We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of the coefficients of the equations is given. The existence of a linear stationary irreversible process is established. Concerning reversibility, we show that there is a contradistinction between any 1-dimensional stationary Gaussian process and stationary Gaussian process of dimension $n>1$. A concrete criterion for differentiating stationarity and sweeping behavior is also obtained. The mathematical result is a natural generalization of Einstein's fluctuation-dissipation relation, and provides a rigorous basis for the isothermal irreversibility in a linear regime which is the basis for applying Onsager's theory to macromolecules in aqueous solution.Comment: 15 page

Statistical Thermodynamics of General Minimal Diffusion Processes: Constuction, Invariant Density, Reversibility and Entropy Production

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the elliptic operator, time-reversibility, and zero entropy production rate of the stationary diffusion process. A thermodynamic theory for diffusion processes emerges.Comment: 23 page

The most plausible explanation of the cyclical period changes in close binaries: the case of the RS CVn-type binary WW Dra

We searched the orbital period changes in 182 EA-type (including the 101 Algol systems used by \cite{hal89}), 43 EB-type and 53 EW-type binaries with known both the mass ratio and the spectral type of their secondary components. We reproduced and improved the same diagram as Hall's (1989) according to the new collected data. Our plots do not support the conclusion derived by \cite{hal89} that all cases of cyclical period changes are restricted to binaries having the secondary component with spectral types later than F5. The presence of period changes also among stars with secondary component of early type indicates that the magnetic activity is one cause, but not the only one, for the period variation. It is discovered that cyclic period changes, likely due to the presence of a third body are more frequent in EW-type binaries among close binaries. Therefore, the most plausible explanation of the cyclical period changes is the LTTE via the presence of a third body. By using the century-long historical record of the times of light minimum, we analyzed the cyclical period change in the Algol binary WW Dra. It is found that the orbital period of the binary shows a $\sim112.2 \textbf{\textrm{yr}}$ cyclic variation with an amplitude of $\sim0.1977\textbf{\textrm{days}}$. The cyclic oscillation can be attributed to the LTTE via a third body with a mass no less than $6.43 M_{\odot}$. However, no spectral lines of the third body were discovered indicating that it may be a candidate black hole. The third body is orbiting the binary at a distance shorter than 14.4 AU and it may play an important role in the evolution of this system.Comment: 9 pages, 5 figures, published by MNRA

Neutrino Gravitational Redshift and the Electron Fraction Above Nascent Neutron Stars

Neutrinos emitted from near the surface of the hot proto-neutron star produced by a supernova explosion may be subject to significant gravitational redshift at late times. Electron antineutrinos decouple deeper in the gravitational potential well of the neutron star than do the electron neutrinos, so that the electron antineutrinos experience a larger redshift effect than do the electron neutrinos. We show how this differential redshift can increase the electron fraction Ye in the neutrino-heated ejecta from the neutron star. Any r-process nucleosynthesis originating in the neutrino-heated ejecta would require a low Ye, implying that the differential redshift effect cannot be too large. In turn, this effect may allow nucleosynthesis to probe the nuclear equation of state parameters which set the neutron star radius and surface density scale height at times of order tpb = 10 to 25 s after core bounce.Comment: 4 pages, uses espcrc2.sty, contribution to Festschrift for G. E. Brown on the occasion of his 70th birthda

Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State

A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement are stochastic; the former is represented by a master equation for a set of discrete states, and the latter is described by a continuous Smoluchowski equation. Combining these two equations into one, a comprehensive theory for the Brownian dynamics and statistical thermodynamics of single macromolecules arises. This approach is shown to have wide applications. It is applied to protein-ligand dissociation under external force, unfolding of polyglobular proteins under extension, movement along linear tracks of motor proteins against load, and enzyme catalysis by single fluctuating proteins. As a generalization of the classic polymer theory, the dynamic equation is capable of characterizing a single macromolecule in aqueous solution, in probabilistic terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient relaxation kinetics, and most importantly and novel (3) nonequilibrium steady-state with heat dissipation. A reversibility condition which guarantees an equilibrium solution and its thermodynamic stability is established, an H-theorem like inequality for irreversibility is obtained, and a rule for thermodynamic consistency in chemically pumped nonequilibrium steady-state is given.Comment: 23 pages, 4 figure