Diamond growth in a novel low pressure flame

Diamond growth using a new low-pressure combustion technique is reported. A large-area hydrogen/oxygen flame is used as the source of atomic hydrogen. Methane diluted in hydrogen is injected into the flame near a heated silicon substrate, on which diamond crystallites nucleate and grow. This technique is potentially capable of large-area film growth, since atomic hydrogen can be generated uniformly over arbitrarily large areas

Building a CCD Spectrograph for Educational or Amateur Astronomy

We discuss the design of an inexpensive, high-throughput CCD spectrograph for a small telescope. By using optical fibers to carry the light from the telescope focus to a table-top spectrograph, one can minimize the weight carried by the telescope and simplify the spectrograph design. We recently employed this approach in the construction of IntroSpec, an instrument built for the 16-inch Knowles Telescope on the Harvard College campus.Comment: 17 pages including 7 figures, PASP, accepted (higher resolution figures at http://cfa-www.harvard.edu/~sheila/introspec.ps.gz

Influence of thermochemistry on Mach reflection in hypersonic flow

Real gas thermochemistry can significantly impact the aerodynamics of hypersonic systems. For example, shock stand-off distance in front of a blunt body has been shown to depend on the degree of chemical dissociation. High temperature effects can also alter shock-shock interaction phenomena, but the degree of the modification and its consequences can be challenging to predict. Sanderson et al. experimentally investigated oblique shock impingment on a bow shock (Edney type IV configuration) in a flow with significant gas dissociation. Previous studies had suggested significant increase in heat transfer at jet impingement due to real gas effects, however, experiments showed no dependence of peak heat transfer rate on stagnation enthalpy. The influence of nonequilibrium gas chemistry on Mach and regular shock reflection has been investigated in a number of numerical studies. Burtschell et al. numerically investigated a wedge geometry located in a Mach 7 free stream, a setup similar to that used in the present experimental work. Mach stem height and hysteresis behavior was examined. Burtschell et al. found a strong dependence of transition angles, Mach stem height and location on the gas flow model. For a given wedge angle, the inclusion of real gas chemistry led to a significant decrease in Mach stem height. Chemical-vibration coupling, however, slightly increased the height of the Mach stem. Direct Monte-Carlo simulations of a shock reflection with and without real gas effects carried out by Gimelschein et al. also found a substantial effect on Mach stem height and transition angle. However, an experimental study in dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon could detect no effect on the transition condition due to finite relaxation length at the conditions of the experiment. In the present work, we experimentally investigate a Mach reflection generated by two opposing wedges in a Mach 7.1 free stream. The main goal of this work is to determine directly what kinds of real gas effects occur behind a normal shock in a Mach reflection configuration for a previously selected run condition. Experiments are carried out in an expansion tube facility which is capable of simulating high enthalpy hypersonic flight conditions, and a significant degree of vibrational excitation and chemical dissociation are expected behind the normal shock. In high enthalpy gas flows, emission spectroscopy can be used to characterize the test gas composition and thermodynamic state. As impulse facilities, expansion tubes produce a challenging experimental environment for probe measurements with issues such as short test times, high temperatures and velocities, and diaphragm fragmentation. The non-intrusive nature of spectroscopy makes it an attractive technique for determining flow field properties in impulse facilities. Spectrally resolved studies have been previously used as a means towards characterizing high-enthalpy run conditions. Work completed at the X1 and X2 superorbital expansion tube facilities used emission spectroscopy to measure electron number density behind a bow shock and to identify sources of visible radiation. Time-resolved spectral methods were used in the JX1 expansion tube facility to determine the useful test time. Using the CARS technique, temperature profiles were determined for a hypervelocity blunt body flow field using the T3 shock tunnel facility. Using the free piston shock tube/tunnel facility TCM2, laser spectroscopy was used for species identification and shock front temperature profile diagnostics and spontaneous Raman spectroscopy was used to analyze the self-luminosity of nitrogen hypersonic flows for varying enthalpy conditions. In the current experiments, asymmetric wedges are used to generate a Mach stem, with a free shear layer at each triple point. Imaged spectroscopic measurements behind the Mach stem are presented. The spectra confirms flow dissociation and verifies the appropriateness of a run condition which in the future is to be used towards investigating high-temperature effects upon shear layer structure in hypersonic flow

NO and OH Spectroscopic Vibrational Temperature Measurements in a Post-Shock Relaxation Region

In this paper, spatial temperature profiles are examined in the nonequilibrium relaxation region behind a stationary shock wave in a hypervelocity air Mach 7.42 freestream. The normal shock wave is established through a Mach reflection from an opposing wedge arrangement in an expansion tube facility. Schlieren images confirm that the shock configuration is steady and the location is repeatable. Emission spectroscopy is used to identify dissociated species and to make vibrational temperature measurements using both the nitric oxide and the hydroxyl radical 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 an existing state-resolved, three-dimensional forced-harmonic oscillator thermochemical model. The measured NO vibrational temperatures are significantly higher than the OH temperatures

Expansion Tube Investigation of Shock Stand-Off Distances in High-Enthalpy CO_2 Flow Over Blunt Bodies

The shock standoff distance in front of a blunt body is sensitive to the thermochemical state of the free stream. Recently, experimental and numerical studies have reported significantly different bow shock profiles in high-enthalpy carbon dioxide flows, a discrepancy that may result from non-equilibrium processes during flow acceleration in ground-based facilities. In this work, an expansion tube is used to create a Mach 5.7 carbon dioxide flow, matching the stagnation enthalpy and the velocity of previous studies. Images of shock layers are obtained for spherical geometries and a scaled model of the Mars Science Lander. Different sphere diameters are used in order to access non-equilibrium and equilibrium stagnation line shock profiles predicted by theory. Mars Science Lander profiles at zero angle of attack are in good agreement with available data from the LENS X expansion tunnel facility, confirming results are facility-independent for the same type of flow acceleration, and indicating the flow velocity is a suitable first-order matching parameter for comparative testing. Heat transfer measurements on the Mars Science Lander are also presented for the three different angle of attacks, and the results are consistent with previous studies. Initial results from a proposed organo-metallic based emission spectroscopy technique for bow shock layer interrogation are also presented

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Reexamination of the long-range Potts model: a multicanonical approach

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value $\sigma_c(q)$ separating the first- and second-order regimes to two-digit precision within the range $3 \leq q \leq 9$. We offer convincing numerical evidence supporting $\sigma_c(q)Comment: 18 pages, 18 figure

Classical phase transitions in a one-dimensional short-range spin model

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure

Yang-Lee Zeros of the Q-state Potts Model on Recursive Lattices

The Yang-Lee zeros of the Q-state Potts model on recursive lattices are studied for non-integer values of Q. Considering 1D lattice as a Bethe lattice with coordination number equal to two, the location of Yang-Lee zeros of 1D ferromagnetic and antiferromagnetic Potts models is completely analyzed in terms of neutral periodical points. Three different regimes for Yang-Lee zeros are found for Q>1 and 0<Q<1. An exact analytical formula for the equation of phase transition points is derived for the 1D case. It is shown that Yang-Lee zeros of the Q-state Potts model on a Bethe lattice are located on arcs of circles with the radius depending on Q and temperature for Q>1. Complex magnetic field metastability regions are studied for the Q>1 and 0<Q<1 cases. The Yang-Lee edge singularity exponents are calculated for both 1D and Bethe lattice Potts models. The dynamics of metastability regions for different values of Q is studied numerically.Comment: 15 pages, 6 figures, with correction

Fisher zeros of the Q-state Potts model in the complex temperature plane for nonzero external magnetic field

The microcanonical transfer matrix is used to study the distribution of the Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne0$ which has only a non-physical critical point (the Fisher edge singularity), the $Q>2$ Potts models have physical critical points for $H_q<0$ as well as the Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model is discussed, and the critical line of the three-state Potts ferromagnet is determined. For $H_q>0$ we investigate the edge singularity for finite lattices and compare our results with high-field, low-temperature series expansion of Enting. For $3\le Q\le6$ we find that the specific heat, magnetization, susceptibility, and the density of zeros diverge at the Fisher edge singularity with exponents $\alpha_e$, $\beta_e$, and $\gamma_e$ which satisfy the scaling law $\alpha_e+2\beta_e+\gamma_e=2$.Comment: 24 pages, 7 figures, RevTeX, submitted to Physical Review