Variational study of the Holstein polaron

The paper deals with the ground and the first excited state of the polaron in the one dimensional Holstein model. Various variational methods are used to investigate both the weak coupling and strong coupling case, as well as the crossover regime between them. Two of the methods, which are presented here for the first time, introduce interesting elements to the understanding of the nature of the polaron. Reliable numerical evidence is found that, in the strong coupling regime, the ground and the first excited state of the self-trapped polaron are well described within the adiabatic limit. The lattice vibration modes associated with the self-trapped polarons are analyzed in detail, and the frequency softening of the vibration mode at the central site of the small polaron is estimated. It is shown that the first excited state of the system in the strong coupling regime corresponds to the excitation of the soft phonon mode within the polaron. In the crossover regime, the ground and the first excited state of the system can be approximated by the anticrossing of the self-trapped and the delocalized polaron state. In this way, the connection between the behavior of the ground and the first excited state is qualitatively explained.Comment: 11 pages, 4 figures, PRB 65, 14430

Comparison of Coupled Radiative Flow Solutions with Project Fire 2 Flight Data

A nonequilibrium, axisymmetric, Navier-Stokes flow solver with coupled radiation has been developed for use in the design or thermal protection systems for vehicles where radiation effects are important. The present method has been compared with an existing now and radiation solver and with the Project Fire 2 experimental data. Good agreement has been obtained over the entire Fire 2 trajectory with the experimentally determined values of the stagnation radiation intensity in the 0.2-6.2 eV range and with the total stagnation heating. The effects of a number of flow models are examined to determine which combination of physical models produces the best agreement with the experimental data. These models include radiation coupling, multitemperature thermal models, and finite rate chemistry. Finally, the computational efficiency of the present model is evaluated. The radiation properties model developed for this study is shown to offer significant computational savings compared to existing codes

Evaluation of Hypervelocity Carbon Dioxide Blunt Body Experiments in an Expansion Tube Facility

This work represents efforts to study high-enthalpy carbon dioxide flows in anticipation of the upcoming Mars Science Laboratory (MSL) and future missions. The current study extends the previous presentation of experimental results by the comparison now with axisymmetric simulations incorporating detailed thermochemical modeling. The work is motivated by observed anomalies between experimental and numerical studies in hypervelocity impulse facilities. In this work, experiments are conducted in the Hypervelocity Expansion Tube (HET) which, by virtue of its flow acceleration process, exhibits minimal freestream dissociation in comparison to reflected shock tunnels. This simplifies the comparison with computational result as freestream dissociation and considerable thermochemical excitation can be neglected. Shock shapes of the Laboratory aeroshell and spherical geometries are compared with numerical simulations. In an effort to address surface chemistry issues arising from high-enthalpy carbon dioxide ground-test based experiments, spherical stagnation point and aeroshell heat transfer distributions are also compared with simulation. The shock stand-off distance has been identified in the past as sensitive to the thermochemical state and as such, is used here as an experimental measureable for comparison with CFD and two different theoretical models. For low-density, small-scale experiments it is seen that models based upon assumptions of large binary scaling values are unable to match the experimental and numerical results. Very good agreement between experiment and CFD is seen for all shock shapes and heat transfer distributions fall within the non-catalytic and super-catalytic solutions

Experimental and Numerical Investigation of Hypervelocity Carbon Dioxide Flow over Blunt Bodies

This paper represents ongoing efforts to study high-enthalpy carbon dioxide flows in anticipation of the upcoming Mars Science Laboratory and future missions. The work is motivated by observed anomalies between experimental and numerical studies in hypervelocity impulse facilities. In this study, experiments are conducted in the hypervelocity expansion tube that, by virtue of its flow acceleration process, exhibits minimal freestream dissociation in comparison with reflected shock tunnels, simplifying comparison with simulations. Shock shapes of the laboratory aeroshell at angles of attack of 0, 11, and 16 deg and spherical geometries are in very good agreement with simulations incorporating detailed thermochemical modeling. Laboratory shock shapes at a 0 deg of attack are also in good agreement with data from the LENS X expansion tunnel facility, confirming results are facility-independent for the same type of flow acceleration. The shock standoff distance is sensitive to the thermochemical state and is used as an experimental measurable for comparison with simulations and two different theoretical models. For low-density small-scale experiments, it is seen that models based upon assumptions of large binary scaling values do not match the experimental and numerical results. In an effort to address surface chemistry issues arising in high-enthalpy groundtest experiments, spherical stagnation point and aeroshell heat transfer distributions are also compared with the simulation. Heat transfer distributions over the aeroshell at the three angles of attack are in reasonable agreement with simulations, and the data fall within the noncatalytic and supercatalytic solutions

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code

Electromagnetic Reduction of Plasma Density During Atmospheric Reentry and Hypersonic Flights

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76341/1/AIAA-32147-259.pd

Transition Within a Hypervelocity Boundary Layer on a 5-Degree Half-Angle Cone in Air/CO_2 Mixtures

Laminar to turbulent transition on a smooth 5-degree half angle cone at zero angle of attack is investigated computationally and experimentally in hypervelocity flows of air, carbon dioxide, and a mixture of 50% air and carbon dioxide by mass. Transition N factors above 10 are observed for air flows. At comparable reservoir enthalpy and pressure, flows containing carbon dioxide are found to transition up to 30% further downstream on the cone than flows in pure air in terms of x-displacement, and up to 38% and 140%, respectively, in terms of the Reynolds numbers calculated at edge and reference conditions

Spectroscopic Measurements in the Shock Relaxation Region of a Hypervelocity Mach Reflection

We examine the spatial temperature profile in the non-equilibrium relaxation region behind a stationary shock wave. The normal shock wave is established through a Mach reflection configuration from an opposing wedge arrangement for a hypervelocity air Mach 7.42 freestream. Schlieren images confirm that the shock configuration is steady and the location is repeatable. Emission spectroscopy is used to identify dissociated species and to obtain vibrational temperature measurements using the NO and OH A-X band sequences. Temperature measurements are presented at selected locations behind the normal shock. LIFBASE is used as the simulation spectrum software for OH temperature-fitting, however the need to access higher vibrational and rotational levels for NO leads to the use of an in-house developed algorithm. For NO, results demonstrate the contribution of higher vibrational and rotational levels to the spectra at the conditions of this study. Very good agreement is achieved between the experimentally measured NO vibrational temperatures and calculations performed using a state-resolved, one-dimensional forced harmonic oscillator thermochemical model