On the Fourier-Transformed Boltzmann Equation with Brownian Motion by Yong-Kum Cho, Eunsil Kim

“…We establish a global existence theorem, and uniqueness and stability of solutions of the Cauchy problem for the Fourier-transformed Fokker-Planck-Boltzmann equation with singular Maxwellian kernel, which may be viewed as a kinetic model for the stochastic time-evolution of characteristic functions governed by Brownian motion and collision dynamics.…”
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A construction of the general relativistic Boltzmann equation by P. Dolan, A. C. Zenios

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Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity by Shi-you Lin

“…The Cauchy problem of the nonlinear spatially homogeneous Boltzmann equation without angular cutoff is studied. By using analytic techniques, one proves the Gevrey regularity of the C∞ solutions in non-Maxwellian and strong singularity cases.…”
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Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel by Daixin Wang, Shaoyong Lai

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Boundary Layers and Shock Profiles for the Broadwell Model by Niclas Bernhoff

“…In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.…”
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Thermal axion production at hard and soft momenta by Killian Bouzoud, Jacopo Ghiglieri

“…Upon solving the Boltzmann equation, we find that this theory uncertainty translates to an uncertainty of order 0.002 for the contribution to N eff prior to the QCD crossover. …”
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Large Time Behavior of the Vlasov-Poisson-Boltzmann System by Li Li, Shuilin Jin, Li Yang

“…To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). …”
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Numerical Analysis of Oxygen Adsorption on SnO2 Surface Using Slab Geometry by Weronika Izydorczyk

“…In particular, the evolution of depletion layer was investigated by solving Poisson-Boltzmann equation for SnO2 slab geometry grains. On this basis, the surface energy barrier dependence on layer thickness (30–500 nm) was obtained. …”
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A Multicoefficient Slip-Corrected Reynolds Equation for Micro-Thin Film Gas Lubrication by Eddie Yin-Kwee Ng, Ningyu Liu

“…In comparison with other conventional slip models, it is found that the current results have a better agreement with the solution obtained from the linearized Boltzmann equation and direct simulation of Monte Carlo method (DSMC).…”
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Giant high-order nonlinear and nonreciprocal electrical transports induced by valley flipping in Bernal bilayer graphene by Yuelin Shao, Xi Dai

“…Then we study the electrical transport of the one-pocket state by solving the Boltzmann equation. We find that the valley polarization could be easily flopped by an in-plane electrical field, which will lead to hysteresis loop in the direct current (DC) I-V curves. …”
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The Effect of Scattering of Phonons, Size and Grain Boundary on Electrical Properties for Ruthenium Nano Metals by Reda F. Hanon Almajedi, May A. S. Mohammed, Haider FA. Abdul Amir

“…The study's equation, derived from these two models, considers surface scattering and metal resistance to determine an experimental thickness that depends on metal resistivity. The Boltzmann Equation can be utilized to solve this equation. …”
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Unsteady Electroosmotic Flow of Jeffrey Fluid in a Circular Microchannel under the Combined Action of Vertical Magnetic Field, External Electric Field, and Pressure at High Zeta Po... by Meirong Ren, Tiange Zhang, Jifeng Cui, Xiaogang Chen, Bixia Wu

“…The numerical solutions of the potential and velocity distributions are obtained by solving the nonlinear Poisson-Boltzmann equation, the constitutive equation of the Jeffrey fluid, and the Cauchy momentum equation applying the Chebyshev spectral method and the finite difference method. …”
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Modeling Urban Growth and Form with Spatial Entropy by Yanguang Chen

“…First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. …”
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The Effect of Nuclear Elastic Scattering on Temperature Equilibration Rate of Ions in Fusion Plasma by M. Mahdavi, R. Azadifar, T. Koohrokhi

“…Using the extracted nuclear elastic scattering differential cross-section from experimental data, solving the Boltzmann equation, and also taking into account the mobility of the background particles, temperature equilibration rate between two different ions in a fusion plasma is calculated. …”
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Analytical Solutions for Electroosmotic Flow and Heat Transfer Characteristics of Nanofluids in Circular Cylindrical Microchannels with Slip-Dependent Zeta Potential Considering Th... by Zouqing Tan, Xiangcheng Ren

“…The linearized Poisson–Boltzmann equation, along with the momentum and energy conservation equations, is solved analytically to obtain the electrical potential field, velocity field, temperature distribution, and Nusselt number for both slip-dependent (SD) and slip-independent (SI) zeta potentials. …”
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Thermal performance and MHD peristaltic flow of hybrid nanofluid (Au-Ta/Blood) in an asymmetric conduit with electro-osmosis and shape factor effects by K. Thirunavukarasan, G. Sucharitha

“…The Debye-Hückel approximation is employed to estimate the Poisson-Boltzmann equation. The lubrication approximation is used to reduce the complexity of dimensionless equations. …”
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How NaCl addition destabilizes ionic liquid micellar suspension until phase separation by Dufrêche, Jean-François, Plazanet, Marie, Meyer, Gautier, Billard, Isabelle

“…A simple theory based on the Poisson–Boltzmann equation and with charge regulation is proposed. …”
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Research on Deep-Site Failure Mechanism of High-Steep Slope under Active Fault Creeping Dislocation by Yang Liu, Kaiwen Zhang, Denghang Tian, Liming Qu, Yang Liu

“…The development of the upper envelope curve in the plastic zone of the overlying soil satisfies the Boltzmann equation with a first-order exponential growth, while the development of the lower envelope curve satisfies the Gauss equation with a second-order exponential growth. …”
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A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method by Qiaojie Li, Zhoushun Zheng, Shuang Wang, Jiankang Liu

“…The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. …”
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Coscattering in next-to-minimal dark matter and split supersymmetry by F. Brümmer

“…We present a procedure to numerically solve the full momentum-dependent Boltzmann equations in coscattering, which allows for a precise calculation of the dark matter relic density including the effects of early kinetic decoupling. …”
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