Untersuchungen zum Existenzbereich einer BOLTZMANN-Verteilung im Argonbogenplasma

Using as plasma source a wall stabilized argon arc working within a restricted parameter range (inner tube diameter = 7 mm, pressure = 30–120 Torr, current = 5-20 A)) the existence of a Boltzmann equilibrium between spectral energy levels is checked by comparing measured occupation number densities of higher excited levels (N_{m, exp}) with the corresponding number densities calculated under the assumption of Boltzmann equilibrium (N_{m, calc}). The methods for determination of the quantities N_{m, exp'} T_g (2300–5405°K), T_e (7170–9950°K) and N_e (0.33 – 2.4 × 10¹⁵ cm^?3) needed for this comparison are described. It can be shown within the limit of experimental error that a Boltzmann equilibrium exists at least for electron densities of N_e > 3 · 10¹⁴ cm^?3. The problem of energy balance of that type of arcs used in these experiments is discussed.     

Dynamic Topology Reconfiguration of Boltzmann Machines on Quantum Annealers

Boltzmann machines have useful roles in deep learning applications, such as generative data modeling, initializing weights for other types of networks, or extracting efficient representations from high-dimensional data. Most Boltzmann machines use restricted topologies that exclude looping connectivity, as such connectivity creates complex distributions that are difficult to sample. We have used an open-system quantum annealer to sample from complex distributions and implement Boltzmann machines with looping connectivity. Further, we have created policies mapping Boltzmann machine variables to the quantum bits of an annealer. These policies, based on correlation and entropy metrics, dynamically reconfigure the topology of Boltzmann machines during training and improve performance.     

Lattice Boltzmann simulation of flow around two,three and four circular cylinders in close proximity

Cross-flows around two, three and four circular cylinders in tandem, side-by-side, isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5D, where D is the identical circular cylinder diameter. The wake patterns, pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases. The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures, which are interesting, complex and useful for practical applications. This study provides a useful database to validate the simplicity, accuracy and robustness of the Lattice Boltzmann method.

     

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of Ωt of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at three points (triads) and allow the explicit removal of pressure fluctuations. We first extend the formalism to anisotropic rotating turbulence with ‘production’, in the presence of mean velocity gradients in the rotating frame. Second, we compare the spectral approach at three points to the two-point approach directly performed in physical space, in which we consider the transport of the scalar second-order structure function ?(δq)²?. This calls into play componental third-order correlations ?(δq)²δu?(r) in axisymmetric turbulence. This permits to discuss inhomogeneous anisotropic effects from spatial decay, shear, or production, as in the central region of a rotating round jet. We show that the above-mentioned important statistical quantities can be estimated from experimental planar particle image velocimetry, and that explicit passage relations systematically exist between one- and two-point statistics in physical and spectral space for second-order tensors, but also sometimes for third-order tensors that are involved in the dynamics.     

Excitation Temperature Measurement of Ar + N2 RF Plasma by Spectroscopic Method

The mixed gas (Ar + N₂) plasma has been generated by a 6 KW, 10.3 MHz radio frequency oscillator. The flame got extinguished if N₂ exceeded more than 20% of Ar. The Boltzmann plot using spectral intensities of Ar I and NI lines in the wavelength range 4000–4510 Å have been used to determine the excitation temperature. The results show that excitation equilibrium between two species exist since the temperatures are found to be nearly same for both species.     

Solar wind driven electrostatic instabilities with generalized (r,q) distribution function

Using Boltzmann–Vlasov kinetic model, a currentless ion acoustic instability driven by stream of solar wind plasma is studied in a non‐thermal distributed electrons and ions. The non‐thermal distribution considered here is the generalized distribution which has low energetic flat‐top and velocity power law tail at higher energies. The instability threshold is found to be affected and depends upon the spectral indices r and q . It is found that the growth rate increases with the decrease in the value of r and increase with q . Moreover, such kinetic instability has also been discussed for three species electron–ion–dust plasma using the generalized (r, q) distribution function. Such case is of interest when the solar wind is streaming through the cometary plasma in the presence of interstellar dust and excites electrostatic instabilities. The dispersion properties and growth rates for ion‐acoustic and dust‐acoustic mode are calculated analytically and plotted for different values of the spectral indices r and q .     

Optimal Decay Estimates on the Linearized Boltzmann Equation with Time Dependent Force and their Applications

Although the decay in time estimates of the semi-group generated by the linearized Boltzmann operator without forcing have been well established, there is no corresponding result for the case with general external force. This paper is mainly concerned with the optimal decay estimates on the solution operator in some weighted Sobolev spaces for the linearized Boltzmann equation with a time dependent external force. No time decay assumption is made on the force. The proof is based on both the energy method through the macro-micro decomposition and the L ^p -L ^q estimates from the spectral analysis. The decay estimates thus obtained are applied to the study on the global existence of the Cauchy problem to the nonlinear Boltzmann equation with time dependent external force and source. Precisely, for space dimension n ≥ 3, the global existence and decay rates of solutions to the Cauchy problem are obtained under the condition that the force and source decay in time with some rates. This time decay restriction can be removed for space dimension n ≥ 5. Moreover, the existence and asymptotic stability of the time periodic solution are given for space dimension n ≥ 5 when the force and source are time periodic with the same period.     

On a class of operators related to second-order differential equations

In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential equation. The spectral properties of differential operators generated by these differential expressions are investigated. In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which the case of maximal deficiency indices is realized. Dedicated to the memory of B. M. Levitan     

Infrared diode laser absorption features of N2O and CO2 in a laval nozzle

Design and operation of a pulsed Laval nozzle and the characterization of molecular flow through such a nozzle using IR tunable diode laser (TDL) is the central theme of this work. The results here deal with He diluted N₂O and CO₂ gaseous systems. Boltzmann type plots of the spectral intensity data of both N₂O and CO₂ show non-linear behaviour. We have attempted to understand this non-linear behaviour of Boltzmann plots in terms of (1) instability in the jet and (2) a two-temperature model for the flowing gas, a cold central core and a hot boundary layer close to the nozzle walls. The model based on jet instability represents the data somewhat poorer than the two-temperature model. The parameters derived from fitting our experimental data to the former model could be used to calculate the thermodynamic parameters only through further approximations. Measured absorption line profile of the P(15) line of the v ₂ band of N₂O as a function of axial distance from the nozzle exit gradually shifts from a Lorentzian to a Gaussian type. Velocity distribution of N₂O molecules in a Laval nozzle is determined by differentiating the absorption line profile of the P(15) line (v ₀=576.235 cm^–1) of the v ₂ band of N₂O. Translational temperature of N₂O molecules is determined from the observed spectral profiles.     

Analysis of Spectral Temperature of Participant Protons in p + 12C Interactions at 4.2 GeV/c Using UrQMD Model

The transverse momentum spectra of protons participated in the collision processes calculated using UrQMD model simulations have been compared with the p_T spectra of participant protons, obtained experimentally in interactions of protons beam with carbon nuclei at momenta of 4.2 GeV/c. Spectral temperatures of participant protons obtained in the experimental and UrQMD model simulated interactions of protons beam with carbon nuclei have been calculated by fitting both spectra with four different fitting functions i.e. Hagedorn Thermodynamic, Boltzmann distribution, Gaussian and exponential functions. These functions are used commonly for describing the hadrons spectra and their spectral temperatures. The most suitable fitting functions among these four functions have also been recommended.