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This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
A dispersion relation for a commonly used hybrid model of plasma physics is developed, which combines fully kinetic ions and a massless-electron fluid description. Although this model and variations of it have been used to describe plasma…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
A low pressure discharge sustained in molecular hydrogen with help of the electron cyclotron resonance heating at a frequency of 2.45 GHz is simulated using a fully electromagnetic implicit charge- and energy-conserving…
Plasma, which constitutes 99\% of the visible matter in the universe, is characterized by a wide range of waves and instabilities that play a pivotal role in space physics, astrophysics, laser-plasma interactions, fusion research, and…
For theoretical gas dynamics, the flow regimes are classified according to the Knudsen number. For computational fluid dynamics (CFD), the numerical flow field is the projection of the physical flow field onto the discrete space and time,…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
Thermally excited waves in a Plasma crystal were numerically simulated using a Box_Tree code. The code is a Barnes_Hut tree code proven effective in modeling systems composed of large numbers of particles. Interaction between individual…
Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
The properties of linear instabilities in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Inst., 62, 2875 (1991)] are studied both through analytic calculations and solving numerically a system of linearized collisional plasma fluid…
Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
During substructure formation in magnetized astrophysical plasma, dissipation of magnetic energy facilitated by magnetic reconnection affects the system dynamics by heating and accelerating the ejected plasmoids. Numerical simulations are a…
Fast reconnection in magnetically dominated plasmas is widely invoked in models of dissipation in pulsar winds, gamma-ray flares in the Crab nebula, and to explain the radio nanoshots of pulsars. When current sheets evolve reaching a…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve…
Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…