Critical Mass Phenomenon Research Articles

Critical mass phenomenon for a chemotaxis kinetic model with spherically symmetric initial data

The goal of this paper is to exhibit a critical mass phenomenon occurring in a model for cell self-organization via chemotaxis. The very well-known dichotomy arising in the behavior of the macroscopic Keller–Segel system is derived at the kinetic level, being closer to microscopic features. Indeed, under the assumption of spherical symmetry, we prove that solutions with initial data of large mass blow-up in finite time, whereas solutions with initial data of small mass do not. Blow-up is the consequence of a momentum computation and the existence part is derived from a comparison argument. Spherical symmetry is crucial within the two approaches. We also briefly investigate the drift-diffusion limit of such a kinetic model. We recover partially at the limit the Keller–Segel criterion for blow-up, thus arguing in favour of a global link between the two models.

High energy pulsed inductive thruster modeling operating with ammonia propellant

Numerical modeling of the pulsed inductive thruster operating with ammonia propellant at high energy levels, utilized a time-dependent, two-dimensional, and axisymmetric magnetohydrodynamics code to provide bilateral validation of experiment and theory and offer performance insights for improved designs. The power circuit model was augmented by a plasma voltage algorithm that accounts for the propellant’s time-dependent resistance and inductance to properly account for plasma dynamics and was verified using available analytic solutions of two idealized plasma problems. Comparisons of the predicted current waveforms to experimental data exhibited excellent agreement for the initial half-period, essentially capturing the dominant acceleration phase. Further validation proceeded by comparisons of the impulse for three different energy levels, 2592, 4050, and 4608J and a wide range of propellant mass values. Predicted impulse captured both trends and magnitudes measured experimentally for nominal operation. Interpretation of the modeling results in conjunction to experimental observations further confirm the critical mass phenomenon beyond which efficiency degrades due to elevated internal energy mode deposition and anomalous operation.

Modeling and Performance Analysis of the Pulsed Inductive Thruster

Numerical modeling of the pulsed inductive thruster exercising a time-dependent, two-dimensional, axisymmetric magnetohydrodynamics code provides bilateral validation of the thruster's measured performance and the code's capability of capturing the pertinent physical processes. Computed impulse values for helium and argon propellants demonstrate excellent correlation to the experimental data for a range of energy levels and propellant-mass values. Quantitative energy deposition analysis confirms the thruster's approximately constant-efficiency operation and captures the experimentally observed, critical-mass phenomenon. An idealized model produced a simple impulse expression for this energy range that expands the validity of the aforementioned insights to other propellants and corroborates the thruster's singular operation with ammonia propellant. The simple impulse expression produced compares well with experimental trends and can be used to guide design and optimization of operating conditions.