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Abstract When compressed, certain lattices undergo phase transitions that may allow nuclei to gain sig- nificant kinetic energy. To explore the dynamics of this phenomenon, we develop a methodology to study Coulomb coupled N-body systems constrained to a sphere, as in the Thomson problem. We initialize N total Boron nuclei as point particles on the surface of the sphere, allowing them to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove Nrm particles, forcing the system to rearrange into a new equilibrium. With this model, we consider the Thomson problem as a dynamical system, providing a framework to explore how non-zero temperature affects structural imperfections in Thomson minima. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of N and Nrm. For certain values of N , we find an order of magnitude energy gain when increasing Nrm from 1 to 6. The model may help to design a lattice that maximizes the energy output. 

High-power lasers are at the forefront of science in many domains. While their fields are still far from reaching the Schwinger limit, they have been used in extreme regimes, to successfully accelerate particles at high energies, or to reproduce phenomena observed in astrophysical settings. However, our understanding of laser–plasma interactions is limited by numerical simulations, which are very expensive to run as short temporal and spatial scales need to be resolved explicitly. Under such circumstances, a non-collisional approach to model laser–plasma interactions becomes numerically expensive. Even a collisional approach, modeling the electrons and ions as independent fluids, is slow in practice. In both cases, the limitation comes from a direct computation of electron motion. In this work, we show how the generalized Ohm's law captures collisional absorption phenomena through the macroscopic interactions of laser fields, electron flows, and ion dynamics. This approach replicates several features usually associated with explicit electron motion, such as cutoff density, reflection, and absorption. As the electron dynamics are now solved implicitly, the spatial and temporal scales of this model fit well between multi-fluid and standard magnetohydrodynamics scales, enabling the study of a new class of problems that would be too expensive to solve numerically with other methods. 

Young stellar objects (YSOs) are protostars that exhibit bipolar outflows fed by accretion disks. Theories of the transition between disk and outflow often involve a complex magnetic field structure thought to be created by the disk coiling field lines at the jet base; however, due to limited resolution, these theories cannot be confirmed with observation and thus may benefit from laboratory astrophysics studies. We create a dynamically similar laboratory system by driving a$$\sim$$1 MA current pulse with a 200 ns rise through a$$\approx$$2 mm-tall Al cylindrical wire array mounted to a three-dimensional (3-D)-printed, stainless steel scaffolding. This system creates a plasma that converges on the centre axis and ejects cm-scale bipolar outflows. Depending on the chosen 3-D-printed load path, the system may be designed to push the ablated plasma flow radially inwards or off-axis to make rotation. In this paper, we present results from the simplest iteration of the load which generates radially converging streams that launch non-rotating jets. The temperature, velocity and density of the radial inflows and axial outflows are characterized using interferometry, gated optical and ultraviolet imaging, and Thomson scattering diagnostics. We show that experimental measurements of the Reynolds number and sonic Mach number in three different stages of the experiment scale favourably to the observed properties of YSO jets with$$Re\sim 10^5\unicode{x2013}10^9$$and$$M\sim 1\unicode{x2013}10$$, while our magnetic Reynolds number of$$Re_M\sim 1\unicode{x2013}15$$indicates that the magnetic field diffuses out of our plasma over multiple hydrodynamical time scales. We compare our results with 3-D numerical simulations in the PERSEUS extended magnetohydrodynamics code. 

This paper shows analytically and numerically that a vortex plate coupled to a neutral density filter can deliver a true optical spatial derivative when placed at the focal plane of a 2flens pair. This technique turns any intensity or phase variations of coherent light into an intensity that is proportional to the square of the norm of the initial variation gradient. Since the optical derivative removes the uniform background, it is possible to measure the mode numbers of spatial phase gradients or fluctuations optically, without using any interferometer. 

Radial basis functions are typically used when discretization schemes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in solving many types of differential equations. However, the weights of the interpolated solution, used in the linear superposition of basis functions to interpolate the solution, and the actual value of the solution are completely different. In fact, these weights mix the value of the solution with the geometrical location of the nodes used to discretize the equation. In this paper, we used nodal radial basis functions, which are interpolants of the impulse function at each node inside the domain. This transformation allows to solve a linear hyperbolic partial differential equation using series expansion rather than the explicit computation of a matrix inverse. This transformation effectively yields an implicit solver which only requires the multiplication of vectors with matrices. Because the solver requires neither matrix inverse nor matrix-matrix products, this approach is numerically more stable and reduces the error by at least two orders of magnitude, compared to solvers using radial basis functions directly. Further, boundary conditions are integrated directly inside the solver, at no extra cost. The method is locally conservative, keeping the error virtually constant throughout the computation.