Related papers: A geometric approach to constructing quasi-isodyna…
A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
A systematic theory of the asymptotic expansion of the magnetohydrodynamic (MHD) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared to the vacuum and the…
A new optimized quasihelically symmetric configuration is described that has the desir-able properties of improved energetic particle confinement, reduced turbulent transportby 3D shaping, and non-resonant divertor capabilities. The…
A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with…
Square contingency tables are traditionally analyzed with a focus on the symmetric structure of the corresponding probability tables. We view probability tables as elements of a simplex equipped with the Aitchison geometry. This perspective…
A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for…
Quasi-isometries are mappings on graphs, with distance-distortions parameterized by a multiplicative factor and an additive constant. The distance-distortions of quasi-isometries are in a general form that captures a wide range of…
A representation of the static MHD equilibrium system in coordinates connected with magnetic surfaces is suggested. It is used for producing families of non-trivial 3D exact solutions of isotropic and anisotropic plasma equilibria in…
We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…
We give the generalization of the method of the space-time description of particle creation by a gravitational field for a scalar field with nonconformal coupling to the curvature. The space-time correlation function is obtained for a…
Two-dimensional Maxwell-Vlasov equilibria with finite electric fields, axial ("toroidal") plasma flow and isotropic pressure are constructed in plane geometry by using the quasineutrality condition to express the electrostatic potential in…
We present a perturbative method for constructing approximate invariants of motion directly from the equations of discrete-time symplectic systems. This framework offers a natural nonlinear extension of the classic Courant-Snyder (CS)…
Microinstabilities exhibit a rich variety of behavior in stellarators due to the many degrees of freedom in the magnetic geometry. It has recently been found that certain stellarators (quasi-isodynamic ones with maximum-$J$ geometry) are…
The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…
In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary…
High-order harmonic generation in gas targets is a widespread scheme used to produce extreme ultraviolet radiation, however, it has a limited microscopic efficiency. Macroscopic enhancement of the produced radiation relies on…
A quasisymmetry is a special symmetry that enhances the ability of a magnetic field to trap charged particles. Quasisymmetric magnetic fields may allow the realization of next generation fusion reactors (stellarators) with superior…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which…