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Nonstoichiometric zirconium niobium carbide thermodynamic properties, deriving components activity equations from statistical considerations based on pairwise interaction energies
The PARC2D Navier-Stokes Code was modified to compute the performance parameters for rocket engine nozzles. The perfect gas code was applied to the SSME engine nozzle for inviscid, laminar and turbulent flow. Inviscid computations compare well with Rocketdyne computations. Performance degradation due to the boundary layers is very reasonable. Application of the code to nontraditional nozzle geometries and to low Reynolds nozzles is demonstrated. Modification of the code for equilibrium H2/O2 chemistry is described. Thermodynamic and equilibrium constants are determined from statistical mechanics and the transport properties from exact kinetic theory, using collison integrals determined from appropriate intermolecular potentials. The equilibrium code was used to compute the SSME flowfield. Modifications of the flowfield due to the change of composition are described.
Arctic sea ice responds to and drives Arctic climate change. The interactions between Arctic sea ice and clouds represent a mechanism through which sea ice can drive climate change. We composite active remote sensing satellite cloud properties for ice-free, marginal ice zone (MIZ), and ice-covered surfaces during MIZ crossing events to investigate the influence of the transition from an ice-covered to an ice-free surface on low-level clouds. We demonstrate that the event-based methodology controls for large-scale meteorological factors and isolates the sea ice effect on clouds. We find larger cloud fraction and total water content below ~1.5 km over ice-free relative to ice-covered surfaces during non-summer months, indicating a low-level cloud sensitivity to Arctic sea ice decline. During summer, results show larger cloud fraction and water content over ice-free surfaces, however the differences are statistically indistinguishable. Evidence is provided that atmospheric thermodynamic profile differences cause the cloud property differences, namely that ice-free footprints are warmer, moister, have more positive surface turbulent fluxes and are less stable than their ice-covered counterparts. Ice-free and ice-covered surface cloud property differences scale with surface temperature differences such that cloud property differences are only found in the presence of a surface temperature difference. We conclude that surface temperature differences modulate the cloud response to sea ice loss through influences on surface turbulent fluxes and lower tropospheric stability. The results imply a positive non-summer sea ice-cloud feedback and that up to a 0.02 cloud fraction and 0.05 g m 3 total water content increase in fall are due to the observed sea ice decline.
Arctic sea ice responds to and drives Arctic climate change. The interactions between Arctic sea ice and clouds represent a mechanism through which sea ice can drive climate change. We composite active remote sensing satellite cloud properties for ice-free, marginal ice zone (MIZ), and ice-covered surfaces during MIZ crossing events to investigate the influence of the transition from an ice-covered to an ice-free surface on low-level clouds. We demonstrate that the event-based methodology controls for large-scale meteorological factors and isolates the sea ice effect on clouds. We find larger cloud fraction and total water content below ~1.5 km over ice-free relative to ice-covered surfaces during non-summer months, indicating a low-level cloud sensitivity to Arctic sea ice decline. During summer, results show larger cloud fraction and water content over ice-free surfaces, however the differences are statistically indistinguishable. Evidence is provided that atmospheric thermodynamic profile differences cause the cloud property differences, namely that ice-free footprints are warmer, moister, have more positive surface turbulent fluxes and are less stable than their ice-covered counterparts. Ice-free and ice-covered surface cloud property differences scale with surface temperature differences such that cloud property differences are only found in the presence of a surface temperature difference. We conclude that surface temperature differences modulate the cloud response to sea ice loss through influences on surface turbulent fluxes and lower tropospheric stability. The results imply a positive non-summer sea ice-cloud feedback and that up to a 0.02 cloud fraction and 0.05 g m 3 total water content increase in fall are due to the observed sea ice decline.
It is shown by quantum statistics that under certain stated conditions the entropy of coherent radiation is zero and it is still negligible for multimode laser operation. This makes possible gas kinetic processes which, to a small extent, have already been observed or even utilized, but which can be greatly enhanced by an optimized choice of molecular structures and radiation conditions. Radiative cooling of gases is discussed in detail. The conditions for maximum heat withdrawal are derived, and it is proposed that the processes of cooling and relaxation heating can be sufficiently separated in time to achieve certain effects and thermodynamic cycles. One of these is the complete conversion, possible in principle, of coherent radiation into work. This concept is based on a heat pump process followed by heat-to-work conversion, the heat rejected being just equal to that withdrawn by radiation. The conditions for complete conversion turn out to be the same as for maximum heat withdrawal. The feasibility of these processes depends on the degree to which practical conditions can be met, and on the validity of certain assumptions which have to await experimental verification.
This study examines variability in marine low cloud properties derived from semi-global observations by the Tropical Rainfall Measuring Mission (TRMM) satellite, as linked to the aerosol index (AI) and lower-tropospheric stability (LTS). AI is derived from the Moderate Resolution Imaging Spectroradiometer (Terra MODIS) sensor and the Goddard Chemistry Aerosol Radiation and Transportation (GOCART) model, and is used to represent column-integrated aerosol concentrations. LTS is derived from the NCEP/NCAR reanalysis, and represents the background thermodynamic environment in which the clouds form. Global statistics reveal that cloud droplet size tends to be smallest in polluted (high-AI) and strong inversion (high-LTS) environments. Statistical quantification shows that cloud droplet size is better correlated with AI than it is with LTS. Simultaneously, the cloud liquid water path (CLWP) tends to decrease as AI increases. This correlation does not support the hypothesis or assumption that constant or increased CLWP is associated with high aerosol concentrations. Global variability in corrected cloud albedo (CCA), the product of cloud optical depth and cloud fraction, is very well explained by LTS, while both AI and LTS are needed to explain local variability in CCA. Most of the local correlations between AI and cloud properties are similar to the results from the global statistics, while weak anomalous aerosol-cloud correlations appear locally in the regions where simultaneous high (low) AI and low (high) LTS compensate each other. Daytime diurnal cycles explain additional variability in cloud properties. CCA has the largest diurnal cycle in high-LTS regions. Cloud droplet size and CLWP have weak diurnal cycles that differ between clean and polluted environments. The combined results suggest that investigations of marine low cloud radiative forcing and its relationship to hypothesized aerosol indirect effects must consider the combined effects of aerosols, thermodynamics, and the diurnal cycle.
Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H 2 O and D 2 O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations—with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a “corresponding-states-like” rescaling for water properties in three classical water models that all exhibit a liquid–liquid transition and critical point, the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H 2 O and D 2 O is investigated here. Utilizing previously published data and equations-of-state for H 2 O and D 2 O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid–liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water’s anomalies.
We report a Bidirectional Electrode Control Arm Assembly (BECAA) for precisely manipulating dust clouds levitated above the powered electrode in RF plasmas. The reported techniques allow the creation of perfectly 2D dust layers by eliminating off-plane particles by moving the electrode from outside the plasma chamber without altering the plasma conditions. Here, the tilting and moving of electrodes using BECAA also allows the precise and repeatable elimination of dust particles one by one to achieve any desired number of grains N without trial and error. Simultaneously acquired top and side view images of dust clusters show that they are perfectly planar or 2D. A demonstration of clusters with N = 1–28 without changing the plasma conditions is presented to show the utility of BECAA for complex plasma and statistical physics experimental design. Demonstration videos and 3D printable part files are available for easy reproduction and adaptation of this new method to repeatably produce 2D clusters in existing RF plasma chambers.
Unitary 𝑡-designs are distributions on the unitary group whose first 𝑡 moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate 𝑡-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate 𝑡-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.
The results of studies regarding the effect of rainfall about aircraft are briefly reviewed. It is found that performance penalties on airfoils have been identified in subscale tests. For this reason, it is of great importance that scaling laws be dveloped to aid in the extrapolation of these data to fullscale. The present investigation represents an attempt to develop scaling laws for testing subscale airfoils under heavy rain conditions. Attention is given to rain statistics, airfoil operation in heavy rain, scaling laws, thermodynamics of condensation and/or evaporation, rainfall and airfoil scaling, aspects of splash back, film thickness, rivulets, and flap slot blockage. It is concluded that the extrapolation of airfoil performance data taken at subscale under simulated heavy rain conditions to fullscale must be undertaken with caution.
A statistical solution for the problem of non-LTE radiative transfer in the millions of atomic transitions responsible for line blanketing is proposed which takes into account the influence of scattering on the atomic populations. A multifrequency/multigray algorithm is used to analyze the thermal equilibrium. Although CO is shown to cool the upper atmosphere to a boundary temperature of 2640 K, the molecule has little influence in the region of the solar temperature minimum.
The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.
Thomas-Fermi approximation applied to calculation of equations of state and thermodynamic functions at high pressure from differential equations of statistical atom model
Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).
A model describing the evaportion of an isolated drop of a multicomponent fuel containing hundreds of species has been developed. The model is based on Continuous Thermodynamics concepts wherein the composition of a fuel is statistically described using a Probability Distribution Function (PDF).
Combining multiple optical resonators or engineering dispersion of complex media has provided an effective method for demonstrating topological physics controlling photons in unprecedented ways such as unidirectional light propagation and spatially localized modes between an interface or on a corner. Further, adding nonlinear responses to those topological photonic systems has enabled achieving diverse phases of photons in both space and time, allowing for more functionalities in photonic devices that provide a new playground for studying dynamic features of nonlinear topological systems. However, most methods for describing nonlinear topological photonic systems rely on linear topological theories, making it challenging to accurately characterize the topology of nonlinear systems. Thus, substantial efforts have focused on rigorously describing nonlinear topological phases and developing effective tools to analyze nonlinear topological effects. Meanwhile, coupled multimode optical waveguides with nonlinear dynamic responses provide an excellent platform for the statistical description of photons, opening a new paradigm called “optical thermodynamics”. This review will introduce the basic concepts of nonlinear topological photonics and the recent development of theoretical approaches focusing on data-driven approaches for creating phase diagrams as well as the spectral localizer framework and the pseudospectrum method for understanding optical nonlinearities in topological systems. In addition, the new concept of optical thermodynamics will be introduced with some recent theoretical works.
The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. Here, we derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.
The Community Climate Model (CCM) is a comprehensive three-dimensional global atmospheric model assembled at the National Center for Atmospheric Research. Detailed comparisons are made between the climate simulated by a seasonal version of CCM, namely CCM1, at 12 level, R15 spectral resolution, and that revealed by ECMWF operational analyses over 1980-86 truncated to a similar resolution. A variety of circulation statistics are presented in order to reveal the spatial character and seasonality of CCM1 biases in temperature, winds, and wave flux quantities. The biases revealed for CCM1 are similar in many respects to those found in other climate models run at similar resolution. Results of this study are then presented, discussing temperature biases and thermodynamic balances, wind fields, zonal mean wave diagnostics, stationary waves, and local eddy statistics. The major findings are then summarized.