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Entropy-Robust Estimation Procedures for Randomized Models and Measurement Noises
Published in Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov, Entropy Randomization in Machine Learning, 2023
Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov
Here k=1.38·10−23 denotes the Boltzmann constant. The statistical weight of the macrostate (ΔQ,T) is measured by the number of all possible microstates (combinations) that make up this macrostate. Recall that these terms apply to the so-called (mono- or polyatomic) gas model, which considers a system (macrosystem) of very many indistinguishable particles (molecules). The space of the system's macrostates consists of m nonintersecting subsets with given capacities G1,…,Gm (i.e., the number of states that can be occupied by the particles). Behaving stochastically, the particles are distributed in a random way over the states in these subsets, with the same probability and independently of each other. Let each particle be uniquely labeled, and list the resulting subsets for all labeled particles; in fact, this list is the system's microstate. Of course, the list under consideration is of a huge volume. The sublists with the same number of particles Nk in the kth subset can be extracted. The number of particles Nk is an element of the system's macrostate N={N1,…,Nm}. The number of elements in a sublist (the number of microstates that induce a given macrostate) is called its statistical weight Z=Z(Nk).
Plasma synthesis of ammonia by asymmetric electrode arrangement
Published in Materials and Manufacturing Processes, 2023
F. Baharlounezhad, M.A. Mohammadi, M.S. Zakerhamidi
where is the intensity of the spectral line, is the wavelength of the emitted light, which is the probability per second that an atom in state j spontaneously emits in a random direction and is de-excited to state i, is the statistical weight of the energy level, is transition probability, is Boltzmann constant, is plasma electron temperature, is energy level of the upper state for emission and c is a constant value. To create the Boltzmann plot, is plotted against in eV, using Table 1 data.[69,70]
High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models
Published in Molecular Physics, 2022
Vladimir Tyuterev, Sergey Tashkun, Michael Rey, Andrei Nikitin
Another important subject concerns the line intensity calculations. Infrared line intensities Inm for the transition n → m corresponding to the wavenumber νnm are defined by in standard spectroscopic units cm−1/(molecule ×cm−2). Here, c2=hc/k with k the Boltzmann constant, g(Cn) and En are the nuclear spin statistical weight and the energy of the lower state. Q(T) is the partition function [338], and I0 is the isotopic abundance of the considered molecular species. The line strength of a dipole-allowed ro-vibrational transition n → m is defined as in the absence of an external field, where the summation is over all magnetic sub-levels of the initial and the final states. Here, the dipole moment components of µ are given in the laboratory-fixed frame (LFF) and |n>, |m> are eigenfunctions of the full nuclear motion Hamiltonian.
The Investigation of Corrosion Behaviors of Type 316L Stainless Steel in Stagnating Liquid Lithium
Published in Fusion Science and Technology, 2020
Zongbiao Ye, Wenyao Yang, Lei Shu, Zhijun Wang, Qiancheng Liu, Qiang Yan, Jianjun Wei, Kun Zhang, Fujun Gou
where I(i) =emission rate density of photonsn(i) =concentration of excited atomsK(i),j =Einstein coefficientg(i),j, E(I),j =statistical weight factor and transition energy, respectivelyk, T =Boltzmann constant and plasma temperature, respectively.