We review the available experimental information on the thermodynamic properties of supercooled water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are also discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.

http://www.mesothermal.umd.edu/pubs/JCP_136_2012.pdf

Thermodynamics of supercooled water.

We review the available experimental information on the thermodynamic properties of supercooled ordinary and heavy water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.

Thermodynamics of supercooled water

We study the 3d Ising universality class using the functional renormalization group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and antisymmetric corrections to scaling, the anomalous dimension, the scaling solution, and the eigenperturbations at criticality. We also study the cross correlations of scaling exponents, their dependence on dimensionality, and the numerical convergence of the derivative expansion. Collecting all available data from functional renormalization group studies to date, we estimate that systematic errors are in good agreement with findings from Monte Carlo simulations, ϵ-expansion techniques, and resummed perturbation theory.

/pdf/ising-exponents-from-the-functional-renormalisation-group-4x3nujo6tk.pdf

Ising exponents from the functional renormalisation group

Thermodynamic properties of the ST2 model for supercooled liquid water exhibit anomalies similar to those observed in real water. A possible explanation of these anomalies is the existence of a metastable, liquid-liquid transition terminated by a critical point. This phenomenon, whose possible existence in real water is the subject of much current experimental work, has been unambiguously demonstrated for this particular model by most recent simulations. In this work, we reproduce the anomalies of two versions of the ST2 model with an equation of state describing water as a non-ideal "mixture" of two different types of local molecular order. We show that the liquid-liquid transition in the ST2 water is energy-driven. This is in contrast to another popular model, mW, in which non-ideality in mixing of two alternative local molecular orders is entropy-driven, and is not sufficiently strong to induce a liquid-liquid transition.

Two-state thermodynamics of the ST2 model for supercooled water

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1756-8765.2011.01162.x

Multifractal Dynamics in the Emergence of Cognitive Structure

After a review of the history and an assessment of the current status of the subject, we present light-scattering data to determine the critical correlation-function exponents for an aqueous electrolyte solution yielding the experimental values γ=1.238±0.012, ν=0.629±0.003, η=0.032±0.013. We conclude the paper with some comments concerning the temperature dependence of non-asymptotic effective critical-exponent values of fluids.

Experimental Critical-Exponent Values for Fluids

Methods and apparatus for remote, passive detection of underwater objects using combined spectral and polarimetric imaging. In one example, a tunable multi-band spectro-polarimeter includes an imaging detector array that receives electromagnetic radiation from a viewed scene, a plurality of tunable spectral filters configured to filter the electromagnetic radiation into at least first and second spectral bands, and a plurality of polarization filters configured to filter each of the first and second spectral bands into at least two different polarization states, a first region of the detector array receiving the first spectral band and producing first polarimetric image data, and a second region of the detector array simultaneously receiving the second spectral band and producing second polarimetric image data, and a controller that receives and processes the first and second polarimetric image data to detect a target object in the viewed scene.

Joseph G. Shanks

Papers

Experimental Critical-Exponent Values for Fluids

Tunable multi-band spectro-polarimeter