On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Dicopper(II) complexes of a new di-para-xylyldioxatetraazamacrocycle and cascade species with dicarboxylate anions: thermodynamics and structural properties

The new dioxatetraazamacrocycle (L-1) was synthesized by a 2 + 2 condensation and characterized. Stability constants of its copper(II) complexes were determined by spectrophotometry in DMSO at 298.2 K in 0. 10 mol dm(-3) KClO4. Mainly dinuclear complexes are formed and the presence of mononuclear species is dependent on the counterion (Cl- or ClO4-). The association constants of the dinuclear copper(II) complexes with dicarboxylate anions [oxalate (oxa(2-)), malonate (mal(2-)), succinate (suc(2-)), and glutarate (glu(2-))] were also determined by spectrophotometry at 298.2 K in DMSO, and it was found that values decrease with an increase of the alkyl chain between the carboxylate groups. X-Band EPR spectra of the dicopper(II) complexes and of their cascade species in frozen DMSO exhibit dipole-dipole coupling, and their simulation, together with their UV-vis spectra, showed that the copper centres of the complexes in solution had square pyramidal geometries though with different distortions. From the experimental data, it was also possible to predict the Cu...Cu distances, the minimum being found at 6.4 angstrom for the (Cu2LCl4)-Cl-1 complex and then successively this distance slightly increases when the chloride anions are replaced by dicarboxylate anions, from 6.6 angstrom for oxa(2-) to 7.8 for glu(2-). The crystal structures of the dinuclear copper cascade species with oxa(2-) and suc(2-) were determined and showed one anion bridging both copper centres and Cu...Cu distances of 5.485(7) angstrom and 6.442(8) angstrom, respectively.

Thermodynamics of climate change: generalized sensitivities

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO2 concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO2 concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO2 concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Cation distribution and mixing thermodynamics in Fe/Ni thiospinels

The structural analogy between Ni-doped greigite minerals (Fe3S4) and the (Fe,Ni)S clusters present in biological enzymes has led to suggestions that these minerals could have acted as catalysts for the origin of life. However, little is known about the distribution and stability of Ni dopants in the greigite structure. We present here a theoretical investigation of mixed thiospinels (Fe1

First-principles study of the inversion thermodynamics and electronic structure of FeM2X4 (thio)spinels (M = Cr, Mn, Co, Ni; X = O, S)

FeM2X4 spinels, where M is a transition metal and X is oxygen or sulfur, are candidate materials for spin filters, one of the key devices in spintronics. We present here a computational study of the inversion thermodynamics and the electronic structure of these (thio)spinels for M = Cr, Mn, Co, Ni, using calculations based on the density functional theory with on-site Hubbard corrections (DFT+U). The analysis of the configurational free energies shows that different behaviour is expected for the equilibrium cation distributions in these structures: FeCr2X4 and FeMn2S4 are fully normal, FeNi2X4 and FeCo2S4 are intermediate, and FeCo2O4 and FeMn2O4 are fully inverted. We have analyzed the role played by the size of the ions and by the crystal field stabilization effects in determining the equilibrium inversion degree. We also discuss how the electronic and magnetic structure of these spinels is modified by the degree of inversion, assuming that this could be varied from the equilibrium value. We have obtained electronic densities of states for the completely normal and completely inverse cation distribution of each compound. FeCr2X4, FeMn2X4, FeCo2O4 and FeNi2O4 are half-metals in the ferrimagnetic state when Fe is in tetrahedral positions. When M is filling the tetrahedral positions, the Cr-containing compounds and FeMn2O4 are half-metallic systems, while the Co and Ni spinels are insulators. The Co and Ni sulfide counterparts are metallic for any inversion degree together with the inverse FeMn2S4. Our calculations suggest that the spin filtering properties of the FeM2X4 (thio)spinels could be modified via the control of the cation distribution through variations in the synthesis conditions.

On phantom thermodynamics

The thermodynamic properties of dark energy fluids described by an equation of state parameter omega = p/rho are rediscussed in the context of FRW type geometries. Contrarily to previous claims, it is argued here that the phantom regime omega < -1 is not physically possible since that both the temperature and the entropy of every physical fluids must be always positive definite. This means that one cannot appeal to negative temperature in order to save the phantom dark energy hypothesis as has been recently done in the literature. Such a result remains true as long as the chemical potential is zero. However, if the phantom fluid is endowed with a non-null chemical potential, the phantom field hypothesis becomes thermodynamically consistent, that is, there are macroscopic equilibrium states with T > 0 and S > 0 in the course of the Universe expansion. (C) 2008 Elsevier B.V. All rights reserved.

A Precise Formulation of the Third Law of Thermodynamics

The third law of thermodynamics is formulated precisely: all points of the state space of zero temperature I""(0) are physically adiabatically inaccessible from the state space of a simple system. In addition to implying the unattainability of absolute zero in finite time (or ""by a finite number of operations""), it admits as corollary, under a continuity assumption, that all points of I""(0) are adiabatically equivalent. We argue that the third law is universally valid for all macroscopic systems which obey the laws of quantum mechanics and/or quantum field theory. We also briefly discuss why a precise formulation of the third law for black holes remains an open problem.

Phantom accretion by black holes and the generalized second law of thermodynamics

The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the generalized second law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by the generalized second law. (C) 2010 Elsevier B.V. All rights reserved.

Thermodynamics and Lithium Intercalation in CeO(2)-TiO(2) Thin Film

The kinetics and the thermodynamics of electrochemical intercalation of lithium into CeO(2)-TiO(2) films prepared by the sol-gel process were studied by galvanostatic intermittent titration technique (GITT) as function of the depth of lithium intercalation. The open-circuit-potential versus x in Li(x)(CeO(2)-TiO(2)) curve consists of two straight lines with different slopes, one in the range of 0.03 <= x <= 0.09 and the other of 0.09 < x <= 0.15. The standard Gibbs energy for lithium intercalation Delta G(1)(0) was 6kJ/mol for x = 0.09 in Li(x)(CeO(2)-TiO(2)) at room temperature. The chemical diffusion coefficient value, D(Li+), of lithium intercalation into thin film oxide was 2.14.10(-11) cm(2)/s at x = 0.15, and the value of the component diffusion coefficient D(Li+),(k) was about one order of magnitude lower than the coefficient of chemical diffusion.

Stoichiometry and thermodynamics of the interaction between the C-terminus of human 90 kDa heat shock protein Hsp90 and the mitochondrial translocase of outer membrane Tom70

A large majority of the 1000-1500 proteins in the mitochondria are encoded by the nuclear genome, and therefore, they are translated in the cytosol in the form and contain signals to enable the import of proteins into the organelle. The TOM complex is the major translocase of the outer membrane responsible for preprotein translocation. It consists of a general import pore complex and two membrane import receptors, Tom20 and Tom70. Tom70 contains a characteristic TPR domain, which is a docking site for the Hsp70 and Hsp90 chaperones. These chaperones are involved in protecting cytosolic preproteins from aggregation and then in delivering them to the TOM complex. Although highly significant, many aspects of the interaction between Tom70 and Hsp90 are still uncertain. Thus, we used biophysical tools to study the interaction between the C-terminal domain of Hsp90 (C-Hsp90), which contains the EEVD motif that binds to TPR domains, and the cytosolic fragment of Tom70. The results indicate a stoichiometry of binding of one monomer of Tom70 per dimer of C-Hsp90 with a K(D) of 360 30 nM, and the stoichiometry and thermodynamic parameters obtained suggested that Tom70 presents a different mechanism of interaction with Hsp90 when compared with other TPR proteins investigated. (C) 2011 Elsevier Inc. All rights reserved.

Thermodynamics of a Peyrard-Bishop One-Dimensional Lattice with On-site Hump Potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermodynamics of quasi-particles

We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems with a temperature dependent Hamiltonian. We show that there are, in principle, an infinite number of solutions.