Numerical implementation and oceanographic application of the thermodynamic potentials of liquid water, water vapour, ice, seawater and humid air – Part 2: The library routines

The SCOR/IAPSO<sup>1</sup> Working Group 127 on Thermodynamics and Equation of State of Seawater has prepared recommendations for new methods and algorithms for numerical estimation of the the thermophysical properties of seawater. As an outcome of this work, a new International Thermodynamic Equation of Seawater (TEOS–10) was endorsed by IOC/UNESCO<sup>2</sup> in June 2009 as the official replacement and extension of the 1980 International Equation of State, EOS-80. As part of this new standard a source code package has been prepared that is now made freely available to users via the World Wide Web. This package includes two libraries referred to as the SIA (Sea-Ice-Air) library and the GSW (Gibbs SeaWater) library. Information on the GSW library may be found on the TEOS-10 web site (<a href="http://www.TEOS-10.org" target="_blank">http://www.TEOS-10.org</a>). This publication provides an introduction to the SIA library which contains routines to calculate various thermodynamic properties as discussed in the companion paper. The SIA library is very comprehensive, including routines to deal with fluid water, ice, seawater and humid air as well as equilibrium states involving various combinations of these, with equivalent code developed in different languages. The code is hierachically structured in modules that support (i) almost unlimited extension with respect to additional properties or relations, (ii) an extraction of self-contained sub-libraries, (iii) separate updating of the empirical thermodynamic potentials, and (iv) code verification on different platforms and between different languages. Error trapping is implemented to identify when one or more of the primary routines are accessed significantly beyond their established range of validity. The initial version of the SIA library is available in Visual Basic and FORTRAN as a supplement to this publication and updates will be maintained on the TEOS-10 web site. <br><br> <sup>1</sup>SCOR/IAPSO: Scientific Committee on Oceanic Research/International Association for the Physical Sciences of the Oceans<br> <sup>2</sup>IOC/UNESCO: Intergovernmental Oceanographic Commission/United Nations Educational, Scientific and Cultural Organizatio

Thermodynamic properties of sea air

Very accurate thermodynamic potential functions are available for fluid water, ice, seawater and humid air covering wide ranges of temperature and pressure conditions. They permit the consistent computation of all equilibrium properties as, for example, required for coupled atmosphere-ocean models or the analysis of observational or experimental data. With the exception of humid air, these potential functions are already formulated as international standards released by the International Association for the Properties of Water and Steam (IAPWS), and have been adopted in 2009 for oceanography by IOC/UNESCO. <br><br> In this paper, we derive a collection of formulas for important quantities expressed in terms of the thermodynamic potentials, valid for typical phase transitions and composite systems of humid air and water/ice/seawater. Particular attention is given to equilibria between seawater and humid air, referred to as "sea air" here. In a related initiative, these formulas will soon be implemented in a source-code library for easy practical use. The library is primarily aimed at oceanographic applications but will be relevant to air-sea interaction and meteorology as well. <br><br> The formulas provided are valid for any consistent set of suitable thermodynamic potential functions. Here we adopt potential functions from previous publications in which they are constructed from theoretical laws and empirical data; they are briefly summarized in the appendix. The formulas make use of the full accuracy of these thermodynamic potentials, without additional approximations or empirical coefficients. They are expressed in the temperature scale ITS-90 and the 2008 Reference-Composition Salinity Scale

Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness

We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success ("fitness"), they are an essential prerequisite for innovation. Together with a selection of above-average technologies due to imitation behavior, they are the "driving force" for the continuous increase in fitness. We will give analytical solutions for the probability distribution of technologies for special cases and in the limit of large times. The selection dynamics is modelled by a "proportional imitation" of better technologies. However, the assessment of a technology's fitness may be imperfect and, therefore, vary stochastically. We will derive conditions, under which wrong assessment of fitness can accelerate the innovation dynamics, as it has been found in some surprising numerical investigations.Comment: For related work see http://www.helbing.or

The related-key analysis of feistel constructions

Lecture Notes in Computer Science, Volume 8540, 2015.It is well known that the classical three- and four-round Feistel constructions are provably secure under chosen-plaintext and chosen-ciphertext attacks, respectively. However, irrespective of the number of rounds, no Feistel construction can resist related-key attacks where the keys can be offset by a constant. In this paper we show that, under suitable reuse of round keys, security under related-key attacks can be provably attained. Our modification is substantially simpler and more efficient than alternatives obtained using generic transforms, namely the PRG transform of Bellare and Cash (CRYPTO 2010) and its random-oracle analogue outlined by Lucks (FSE 2004). Additionally we formalize Luck’s transform and show that it does not always work if related keys are derived in an oracle-dependent way, and then prove it sound under appropriate restrictions

Optimal Self-Organization

We present computational and analytical results indicating that systems of driven entities with repulsive interactions tend to reach an optimal state associated with minimal interaction and minimal dissipation. Using concepts from non-equilibrium thermodynamics and game theoretical ideas, we generalize this finding to an even wider class of self-organizing systems which have the ability to reach a state of maximal overall ``success''. This principle is expected to be relevant for driven systems in physics like sheared granular media, but it is also applicable to biological, social, and economic systems, for which only a limited number of quantitative principles are available yet.Comment: This is the detailled revised version of a preprint on ``Self-Organised Optimality'' (cond-mat/9903319). For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://angel.elte.hu/~vicsek

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Modeling Supply Networks and Business Cycles as Unstable Transport Phenomena

Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the well-known instability of supply chains (the so-called ``bullwhip effect''). That is, small variations in the consumption rate can cause large variations in the production rate of companies generating the requested product. Interestingly, the resulting oscillations have characteristic frequencies which are considerably lower than the variations in the consumption rate. This suggests that instabilities of supply chains may be the reason for the existence of business cycles. At the same time, we establish some link to queuing theory and between micro- and macroeconomics.Comment: For related work see http://www.helbing.or

10-Round Feistel is Indifferentiable from an Ideal Cipher

We revisit the question of constructing an ideal cipher from a random oracle. Coron et al.~(Journal of Cryptology, 2014) proved that a 14-round Feistel network using random, independent, keyed round functions is indifferentiable from an ideal cipher, thus demonstrating the feasibility of such a construction. Left unresolved is the best possible efficiency of the transformation. We improve upon the result of Coron et al.\ and show that 10 rounds suffice

Could Seals Prevent Cod Recovery in the Baltic Sea?

Fish populations are increasingly affected by multiple human and natural impacts including exploitation, eutrophication, habitat alteration and climate change. As a result many collapsed populations may have to recover in ecosystems whose structure and functioning differ from those in which they were formerly productive and supported sustainable fisheries. Here we investigate how a cod (Gadus morhua) population in the Baltic Sea whose biomass was reduced due to a combination of high exploitation and deteriorating environmental conditions might recover and develop in the 21st century in an ecosystem that likely will change due to both the already started recovery of a cod predator, the grey seal Halichoerus grypus, and projected climate impacts. Simulation modelling, assuming increased seal predation, fishing levels consistent with management plan targets and stable salinity, shows that the cod population could reach high levels well above the long-term average. Scenarios with similar seal and fishing levels but with 15% lower salinity suggest that the Baltic will still be able to support a cod population which can sustain a fishery, but biomass and yields will be lower. At present knowledge of cod and seal interactions, seal predation was found to have much lower impact on cod recovery, compared to the effects of exploitation and salinity. These results suggest that dual management objectives (recovery of both seal and cod populations) are realistic but success in achieving these goals will also depend on how climate change affects cod recruitment