Global well-posedness of the ocean primitive equations with nonlinear thermodynamics

We consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the "primitive equations", coupled to advection-diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space H-1. The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245-267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739-2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science

Strong solvability of a variational data assimilation problem for the primitive equations of large-scale atmosphere and ocean dynamics

For the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose novel elements is to use norms in the variational cost functional that reflects the H1-regularity of strong solutions of the primitive equations. For such a cost functional, we prove the existence of minima and a first-order adjoint condition for strong solutions that provides the basis for computing these minima. We prove the local convergence of a gradient-based descent algorithm to optimal initial conditions using the second-order adjoint primitive equations. The algorithmic modifications due to the H1-norms are straightforwardly to implement into a variational algorithm that employs the standard L2-metrics. © 2021, The Author(s)

Design of helicopter rotor blades for optimum dynamic characteristics

The mass and stiffness distributions for helicopter rotor blades are tailored in such a way to give a predetermined placement of blade natural frequencies. The optimal design is pursued with respect of minimum weight, sufficient inertia, and reasonable dynamic characteristics. Finite element techniques are used as a tool. Rotor types include hingeless, articulated, and teetering

Reversable heat flow through the carbon nanotube junctions

Microscopic mechanisms of externally controlled reversable heat flow through the carbon nanotube junctions (NJ) are studied theoretically. Our model suggests that the heat is transfered along the tube section ${\cal T}$ by electrons ($e$) and holes ($h$) moving ballistically in either in parallel or in opposite directions and accelerated by the bias source-drain voltage $V_{\rm SD}$ (Peltier effect). We compute the Seebeck coefficient $\alpha$, electric $\sigma$ and thermal $\kappa$ conductivities and find that their magnitudes strongly depend on $V_{\rm SD}$ and $V_{\rm G}$. The sign reversal of $\alpha$ versus the sign of $V_{\rm G}$ formerly observed experimentally is interpreted in this work in terms of so-called chiral tunneling phenomena (Klein paradox)

On worst-case investment with applications in finance and insurance mathematics

We review recent results on the new concept of worst-case portfolio optimization, i.e. we consider the determination of portfolio processes which yield the highest worst-case expected utility bound if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are consequences of a Bellman principle for worst-case bounds. They are by construction non-constant ones and thus differ from the usual constant optimal portfolios in the classical examples of the Merton problem. A particular application of such strategies is to model crash possibilities where both the number and the height of the crash is uncertain but bounded. We further solve optimal investment problems in the presence of an additional risk process which is the typical situation of an insurer

Axion Dark Matter and Cosmological Parameters

We observe that photon cooling after big bang nucleosynthesis (BBN) but before recombination can remove the conflict between the observed and theoretically predicted value of the primordial abundance of $^7$Li. Such cooling is ordinarily difficult to achieve. However, the recent realization that dark matter axions form a Bose-Einstein condensate (BEC) provides a possible mechanism, because the much colder axions may reach thermal contact with the photons. This proposal predicts a high effective number of neutrinos as measured by the cosmic microwave anisotropy spectrum.Comment: 4 pages, one figure. Version to appear in Phys. Rev. Lett., incorporating useful comments by the referees and emphasizing that photon cooling by axion BEC is a possibility, not a certaint

Pristine CNO abundances from Magellanic Cloud B stars II. Fast rotators in the LMC cluster NGC 2004

We present spectroscopic abundance analyses of three main-sequence B stars in the young Large Magellanic Cloud cluster NGC 2004. All three targets have projected rotational velocities around 130 km/s. Techniques are presented that allow the derivation of stellar parameters and chemical abundances in spite of these high v sin i values. Together with previous analyses of stars in this cluster, we find no evidence among the main-sequence stars for effects due to rotational mixing up to v sin i around 130 km/s. Unless the equatorial rotational velocities are significantly larger than the v sin i values, this finding is probably in line with theoretical expectations. NGC 2004/B30, a star of uncertain evolutionary status located in the Blue Hertzsprung Gap, clearly shows signs of mixing in its atmosphere. To verify the effects due to rotational mixing will therefore require homogeneous analysis of statistically significant samples of low-metallicity main-sequence B stars over a wide range of rotational velocities.Comment: 12 pages, 5 figures, 2 tables; accepted for publication in ApJ (vol. 633, p. 899

Gaia FGK Benchmark Stars: Effective temperatures and surface gravities

Large Galactic stellar surveys and new generations of stellar atmosphere models and spectral line formation computations need to be subjected to careful calibration and validation and to benchmark tests. We focus on cool stars and aim at establishing a sample of 34 Gaia FGK Benchmark Stars with a range of different metallicities. The goal was to determine the effective temperature and the surface gravity independently from spectroscopy and atmospheric models as far as possible. Fundamental determinations of Teff and logg were obtained in a systematic way from a compilation of angular diameter measurements and bolometric fluxes, and from a homogeneous mass determination based on stellar evolution models. The derived parameters were compared to recent spectroscopic and photometric determinations and to gravity estimates based on seismic data. Most of the adopted diameter measurements have formal uncertainties around 1%, which translate into uncertainties in effective temperature of 0.5%. The measurements of bolometric flux seem to be accurate to 5% or better, which contributes about 1% or less to the uncertainties in effective temperature. The comparisons of parameter determinations with the literature show in general good agreements with a few exceptions, most notably for the coolest stars and for metal-poor stars. The sample consists of 29 FGK-type stars and 5 M giants. Among the FGK stars, 21 have reliable parameters suitable for testing, validation, or calibration purposes. For four stars, future adjustments of the fundamental Teff are required, and for five stars the logg determination needs to be improved. Future extensions of the sample of Gaia FGK Benchmark Stars are required to fill gaps in parameter space, and we include a list of suggested candidates.Comment: Accepted by A&A; 34 pages (printer format), 14 tables, 13 figures; language correcte

Design of helicopter rotor blades for optimum dynamic characteristics

The possibilities and limitations of tailoring blade mass and stiffness distributions to give an optimum blade design in terms of weight, inertia, and dynamic characteristics are discussed. The extent that changes in mass of stiffness distribution can be used to place rotor frequencies at desired locations is determined. Theoretical limits to the amount of frequency shift are established. Realistic constraints on blade properties based on weight, mass, moment of inertia, size, strength, and stability are formulated. The extent that the hub loads can be minimized by proper choice of E1 distribution, and the minimum hub loads which can be approximated by a design for a given set of natural frequencies are determined. Aerodynamic couplings that might affect the optimum blade design, and the relative effectiveness of mass and stiffness distribution on the optimization procedure are investigated