Boltzmann-like

The central hypothesis of the knowledge-based approach [16, 17] is that pairwise contacts follow an exponential Boltzmann-like distribution [33] according to its interaction energy... 

Einkelstein AV, Badretdinov A, Gutin AM. Why do protein architectures have Boltzmann-like statistics Proteins 1995 23 142-50. 

A critical point in the retrieving of the number of nuclear reactions in laser-solid experiments is that there is no control on the spectrum of the electrons accelerated in the interaction, as well as the acceleration mechanism is uncertain and difficult to fit in a predictable scheme. In most cases, the electron energy distribution is assumed to be Boltzmann-like and deconvolutions are performed starting from this assumption. 

As known from nuclear physics, a direct extension of quantal mean-field is delicate [36]. Fortunately enough, in the high excitation regime, where semi-classical approximations are likely to become acceptable, Boltzmann-like kinetic equations, offer an efficient alternative. They thus have been extensively used in nuclear physics for describing heavy-ion collisions (VUU,... 

Thus, the density operator, which is Boltzmann-like at initial time, remains so at any time, that is,... 

As a consequence, the density operator of the H-bond bridge that was Boltzmann-like at the initial time, cannot remain the same as time evolves. Its time-dependent... 

A useful extension of this method consists in assuming that the membrane acquires a Boltzmann-like distribution of type (B.5) even for an arbitrary, nonharmonic potential /( ), which has a minimum at u = 0 [24,25]. When an external pressure Peat is applied to the undulating membrane, the relevant statistical potential is the enthalpy hill) = /(ii) + pextu and the membrane distribution is provided by ... 

The assumption of linear steady-state and, hence, the application of linear thermodynamics methods allows the application of the Prigogine theorem, then one obtains the Boltzmann-like distribution of subsystems (micropores with their walls) in energy ... 

Finally, Richardson and his students have recently reported a study of excited state energy distribution between dissimilar carbonyl molecules produced from 1,2-dioxetanes [15] (Richardson et al., 1979). The location of the excitation energy on one or the other of the carbonyl products, as determined by trapping with olefins, appears to approach a Boltzmann-like distribution determined by the carbonyl triplet energies. 

Advanced Monte Carlo algorithms, developed in other fields (e.g., for electron transport studies in solids), automatically switch from a kinetic Boltzmann-like to a diffusive ( Brownian motion-like ) description, depending on the local background medium conditions, in order to improve statistical performance at high collisionality. 

The scaling factor A, is chosen to satisfy Eq. (23). The number of time slices is N, and Q is the number of degrees of freedom in a single time slice. The code in MOIL is producing complete trajectories in any of the steps following the dynamics of Eqs. (22) and (23). The trajectories so obtained have the Boltzmann-like weight for a trajectory, expected from formula (21). 

Deserno M. A Monte-Carlo approach to Poisson-Boltzmann like free energy functionals. Physica A, 2000 278 405. 

The distribution function for energy Q is given by the Boltzmann-like formula... 

Several studies have attempted to quantify differences in the density of scatterpoints. All of them make explieit or implicit use of Boltzmann distributions. One form of the argument pertains to molecules which may assume two (or more) different structures, e.g. the C2 -endo and C3 -endo conformations of furanose [18]. The ratio of the probabilities P, for finding one or the other struetures is assumed to follow a Boltzmann-like distribution... 

Rather than review the development of hot atom kinetic theory here, the reader is directed to several recent approaches and the references therein (43- 8). While there continues to be debate over the initial relaxation of the hot atom velocity distribution and the conditions imder which a Maxwell-Boltzmann-like temperature profile for reaction can be established, the general dynamical features of at least one very important high energy reaction, F + H2 HF + H, have been described consistent with experimental results. 

If the OH product state distributions are, for example, averaged over the A-doublet states, the rotational state distributions become smooth Boltzmann-like distributions, reflecting the rotational energy content in the parent molecule. 

It has been recognized for some time that a fully microscopic treatment of the dynamics of fluids is feasible at low densities. For dilute gases methods based on density expansion prove to be useful and a Boltzmann-like equation can be used to calculate time correlation functions. " The notion that microscopic or kinetic theory calculations could be formulated for dense fluids is much more recent. The difficulty with dense systems is that there is no small parameter in the problem. Consequently a direct density expansion where one computes the first few corrections to the low-density result is not likely to give useful results. At first sight things are worse than this because the first few density corrections are not only mathematically exhausting, but the... 

Borrowing from tbe LBM, one can rewrite Eq. (13) as a Boltzmann-like equation by expanding a time-dependent term... 

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