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Time irreversibility as an indicator of approaching tipping points in Earth subsystems

With shifting environmental trends, many Earth system elements may be poised to undergo critical transitions or ‘tipping’. Reliable anticipation of these tipping elements is vital to inform policy decisions. Many of the current methods for tipping point detection are based on loss of resilience or ‘critical slowdown’ of the system as it approaches a tipping point. However, these methods are prone to false alarms; the detected slowdown may be an artifact of nonstationary noise unrelated to tipping behavior. Here, we explore the efficacy of early warning signs based on a nonequilibrium thermodynamics framework. The model-free detection method relies on the increased intrinsic time-irreversibility due to detailed balance breaking, preceding the onset of tipping or instabilities. We demonstrate that these EWSs are effective for tipping point detection and robust against false alarms due to nonstationary noise, using idealized models for two key elements of the Earth system that are prone to tipping: the Atlantic Meridional Overturning Circulation and Arctic sea-ice loss.

54 ENVIRONMENTAL SCIENCES

The NASA/MSFC Global Reference Atmospheric Model: 1999 Version (GRAM-99)

The latest version of Global Reference Atmospheric Model (GRAM-99) is presented and discussed. GRAM-99 uses either (binary) Global Upper Air Climatic Atlas (GUACA) or (ASCII) Global Gridded Upper Air Statistics (GGUAS) CD-ROM data sets, for 0-27 km altitudes. As with earlier versions, GRAM-99 provides complete geographical and altitude coverage for each month of the year. GRAM-99 uses a specially-developed data set, based on Middle Atmosphere Program (MAP) data, for 20-120 km altitudes, and NASA's 1999 version Marshall Engineering Thermosphere (MET-99) model for heights above 90 km. Fairing techniques assure smooth transition in overlap height ranges (20-27 km and 90-120 km). GRAM-99 includes water vapor and 11 other atmospheric constituents (O3, N2O, CO, CH4, CO2, N2, O2, O, A, He and H). A variable-scale perturbation model provides both large-scale (wave) and small-scale (stochastic) deviations from mean values for thermodynamic variables and horizontal and vertical wind components. The small-scale perturbation model includes improvements in representing intermittency ("patchiness"). A major new feature is an option to substitute Range Reference Atmosphere (RRA) data for conventional GRAM climatology when a trajectory passes sufficiently near any RRA site. A complete user's guide for running the program, plus sample input and output, is provided. An example is provided for how to incorporate GRAM-99 as subroutines in other programs (e.g., trajectory codes).

Justus, C. G.

Comments to Irreversibility in Thermodynamics

The problem of irreversibility in thermodynamics was revisited and analyzed on the microscopic, stochastic, and macroscopic levels of description. It was demonstrated that Newtonian dynamics can be represented in the Reynolds form, a new phenomenological force with non-Lipschitz properties was introduced, and additional non- Lipschitz thermodynamical forces were incorporated into macroscopic models of transport phenomena.

thermodynamics irreversibility

Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of nonequilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. Here, these properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of the Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging Z 2 symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

Fluctuation theorems

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

VanOverbeke, Thomas J.

Thermodynamically consistent incorporation of the Langmuir adsorption model into compressible fluctuating hydrodynamics

For a gas–solid interfacial system where chemical species undergo reversible adsorption, we develop a mesoscopic stochastic modeling method that simulates both gas-phase hydrodynamics and surface coverage dynamics by coupling the Langmuir adsorption model with compressible fluctuating hydrodynamics. To this end, we derive a thermodynamically consistent mass–energy update scheme that accounts for how the mass and energy variables in the gas and surface subsystems should be updated according to the changes in the number of molecules of each species in each subsystem due to adsorption and desorption events. By performing a stochastic analysis for the ideal Langmuir model and the full hydrodynamic system, we analytically confirm that our mass–energy update scheme captures thermodynamic equilibrium predicted by equilibrium statistical mechanics. We find that an internal energy correction term is needed, which is attributed to the difference in the mean kinetic energy of gas molecules colliding with the surface from that computed from the Maxwell–Boltzmann distribution. By performing an equilibrium simulation study for an ideal gas mixture of CO and Ar, with CO undergoing reversible adsorption, we validate our overall simulation method and implementation.

Adsorption

A model for simulating random atmospheres as a function of latitude, season, and time

An empirical stochastic computer model was developed with the capability of generating random thermodynamic profiles of the atmosphere below an altitude of 99 km which are characteristic of any given season, latitude, and time of day. Samples of temperature, density, and pressure profiles generated by the model are statistically similar to measured profiles in a data base of over 6000 rocket and high-altitude atmospheric soundings; that is, means and standard deviations of modeled profiles and their vertical gradients are in close agreement with data. Model-generated samples can be used for Monte Carlo simulations of aircraft or spacecraft trajectories to predict or account for the effects on a vehicle's performance of atmospheric variability. Other potential uses for the model are in simulating pollutant dispersion patterns, variations in sound propagation, and other phenomena which are dependent on atmospheric properties, and in developing data-reduction software for satellite monitoring systems.

Campbell, J. W.

Growth Control and Disease Mechanisms in Computational Embryogeny

This paper presents novel approach to applying growth control and diseases mechanisms in computational embryogeny. Our method, which mimics fundamental processes from biology, enables individuals to reach maturity in a controlled process through a stochastic environment. Three different mechanisms were implemented; disease mechanisms, gene suppression, and thermodynamic balancing. This approach was integrated as part of a structural evolutionary model. The model evolved continuum 3-D structures which support an external load. By using these mechanisms we were able to evolve individuals that reached a fixed size limit through the growth process. The growth process was an integral part of the complete development process. The size of the individuals was determined purely by the evolutionary process where different individuals matured to different sizes. Individuals which evolved with these characteristics have been found to be very robust for supporting a wide range of external loads.

Genetic algorithm

Statistics and thermodynamics of fracture

A probabilistic model of the fracture processes unifying the phenomenological study of long term strength of materials, fracture mechanics and statistical approaches to fracture is briefly outlined. The general framework of irreversible thermodynamics is employed to model the deterministic side of the failure phenomenon. The stochastic calculus is used to account for thg failure mechanisms controlled by chance; particularly, the random roughness of fracture surfaces.

Chudnovsky, A.

Improving noisy free-energy measurements by adding more noise

Estimating free-energy differences using nonequilibrium work relations, such as the Jarzynski equality, is hindered by poor convergence when work fluctuations are large. For systems governed by overdamped Langevin dynamics, we propose the counterintuitive approach of adding noise in order to increase the precision of such calculations. Here, by introducing additional stochastic fluctuations to the system and rescaling its potential energy accordingly, we leave the thermodynamics of the system unchanged while increasing its relaxation rate. For a given time-dependent protocol this modification reduces the dissipated reduced work, leading to more accurate free-energy estimates. The method is designed to be used in experiment, and we illustrate its operation using computer simulations applied to two model systems. However, the regime of applicability of this strategy is likely limited, because it requires control of the system's potential energy in a way that is feasible in only a few experimental settings.

Whitelam, Stephen [Lawrence Berkeley National Labo

Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. I. Stochastic Fragmentation with Optical-depth-dependent Rate and Universal Fragment Mass

Fragmentation in a gravitationally unstable accretion disk can be an important pathway for forming stellar/planetary companions. To characterize quantitatively the condition for and outcome of fragmentation under realistic thermodynamics, we perform global 3D simulations of gravitationally unstable disks at various cooling rates and cooling types, including the first global simulations of gravitational instability that employ full radiation transport. We find that fragmentation is a stochastic process, with the fragment generation rate per disk area p frag showing an exponential dependence on the parameter β ≡ Ω K t cool , where Ω K is the Keplerian rotation frequency, and t cool is the average cooling timescale. Compared to a prescribed constant β, radiative cooling in the optically thin/thick regime makes p frag decrease slower/faster in β; the critical β corresponding to ∼1 fragment per orbit is ≈3, 5, and 2 for constant β, optically thin, and optically thick cooling, respectively. The distribution function of the initial fragment mass is remarkably insensitive to disk thermodynamics. Regardless of cooling rate and optical depth, the typical initial fragment mass is m frag ≈ 40M tot h 3 , with M tot being the total (star+disk) mass and h = H/R being the disk aspect ratio. Applying this result to typical Class 0/I protostellar disks, we find m frag ∼ 20M J , suggesting that fragmentation more likely forms brown dwarfs. Given the finite width of the m frag distribution, forming massive planets is also possible.

gravitational instability

Stochastic fluctuations and the relaxation time in transient relativistic fluids

We argue that the ratio between the shear viscosity and the shear relaxation time, η/τ π , should be defined as a thermodynamic quantity obtained from the equal-time symmetric correlator of the shear-stress tensor. In kinetic theory, we show that this ratio does not depend on the type of interaction. Similarly, an exact expression for this ratio is obtained for holographic gauge theories. We also determine how stochastic fluctuations change η/τ π in transient relativistic hydrodynamics and show that thermal fluctuations do not spoil causality and stability.

Denicol, Gabriel S. [Universidade Federal Fluminen

Double simple-harmonic-oscillator formulation of the thermal equilibrium of a fluid interacting with a coherent source of phonons

A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.

Defacio, B.

Thermal Expansion from Stochastic Nonlinear Acoustic Fields

The methods of stochastic mechanics are applied to nonlinear acoustic fields generated by random acoustic radiation sources associated with oscillating lattice sites in nonlinear lattices. The assumption of stochastically independent zero-point and temperature-dependent acoustic fields leads to expressions of the thermodynamic internal and Helmholtz free energies per unit mass in terms of modal energies per unit mass that account for the nonlinearity of the propagation modes. The thermodynamic state functions canonically transform to the familiar results of a system of quantized, simple harmonic oscillators in the linear field limit. The thermal expansion coefficient, derived from the Helmholtz free energy per unit mass, is obtained as a sum of the zero-point modal nonlinearity parameters, weighted by temperature-dependent, modal heat capacities. The relationship is fully anharmonic, in contrast to commonly used quasi-harmonic models, and predicts with excellent agreement the experimentally observed null thermal expansion of vitreous silica at the ‘cross-over’ temperature corresponding to the balance between long wavelength modes that contribute negative nonlinearity parameters to the modal sum and short wavelength modes that contribute positive nonlinearity parameters.

Cantrell, John H., Jr.

Real-Time KMC Simulation of Vacancy-Mediated Intermixing in Au@Ag Octahedral Core–Cubic Shell Nanocrystals with Ab Initio-Guided Kinetics

Utilization of core–shell rather than monometallic nanocrystals (NCs) facilitates fine-tuning of NC properties for applications. However, compositional evolution via intermixing can degrade these properties prompting recent experimental studies. We develop an atomistic-level stochastic model for vacancy-mediated intermixing exploiting a formalism which allows incorporation at an ab initio density functional theory level of not just the thermodynamics of vacancy formation, but also relevant diffusion barriers for a vast number of possible local environments (in the core and in the shell, at the interface, and in the intermixed phase). This facilitates a predictive treatment and comprehensive understanding of intermixing on the relevant time scale (e.g., 10 1 –10 3 s). In contrast, previous modeling at the atomistic level utilized only unrealistic generic prescriptions of barriers or employed simplified continuum treatments. For Au@Ag octahedral core–cubic shell NCs, our modeling not only captures the experimentally observed rate or time scale for intermixing of ~100 s at 450 °C for 60 nm NCs, but also elucidates the underlying rate controlling processes and the effective intermixing barrier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Some Thermodynamic Considerations on the Physical and Quantum Nature of Space and Time

It is suggested that the Planck h = m(sub k)c Lambda(sub k) and the Boltzmann k = m(sub k)c nu(sub k)Constants have stochastic foundation. It is further suggested that a body of fluid at equilibrium is composed of a spectrum of molecular clusters (energy levels) the size of which are governed by the Maxwell-Boltzmann distribution function. Brownian motions are attributed to equilibrium between suspensions and molecular clusters. Atomic (molecular) transition between different size atomic- (molecular-) clusters (energy levels) is shown to result in emission/absorption of energy in accordance with Bohr's theory of atomic spectra. Physical space is identified as a tachyonic fluid that is Dirac's stochastic ether or de Broglie's hidden thermostat. Compressibility of physical space, in accordance with Planck's compressible ether, is shown to result in the Lorentz-Fitzgerald contraction, thus providing a causal explanation of relativistic effect in accordance with the perceptions of Poincare and Lorentz. The invariant Schrodinger equation is derived from the invariant Bernoulli equation for incompressible potential flow. Following Heisenberg a temporal uncertainty relation is introduced as Delta(nu(sub Beta)) Delta(Rho(sub Beta)) > = k.

Sohrab, Siavash H.

Revisiting a Drag Partition Model For Canopy-Like Roughness Elements

Turbulent flows over a large surface area (S) covered by n obstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter area A and a shelter volume V. The individual sizes of A and V without any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element to n/S elements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducing A or V with each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction in A and V only when the ratio of n/S is small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughout S. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities.

canopy turbulence

The CO/SiO radiative instability in cool star atmospheres revisited

We revisit the formation of radiative instabilities in cool star atmospheres and compare our results with those given by Muchmore, Nuth, & Stencel. We have considered the combined influence of CO and SiO molecules and have computed models for a grid of effective temperatures and geometrical dilution factors for the stellar radiation. Our results are based on the analysis of the energy balance of gas elements with prescribed thermodynamic properties. Our results show that radiative instabilities are most likely primarily caused by CO, whereas SiO is expected to play only a minor role, except when the CO density is reduced compared to Local Thermodynamic Equilibrium (LTE) values or the CO band can be assumed to be optically thick. The onset of radiative instabilities is expected to be strongly modified when dynamic phenomena such as stochastic shocks are present. Our results provide strong evidence that dust formation can most likely occur via a radiative instability alone. Therefore, we present a revised version of the Muchmore et al. dust formation paradigm, which also considers hydrodynamic cooling. The new paradigm is particularly relevant in cases where dust is formed relatively close to the stellar photosphere.

Cuntz, M.