Wire, hybrid, and laser-cut X-pinches as Talbot-Lau backlighters for electron density diagnostics

Talbot-Lau X-ray Deflectometry (TXD) enables refraction-based imaging for high-energy-density physics (HEDP) experiments, and thus, it has been studied and developed with the goal of diagnosing plasmas relevant to Inertial Confinement and Magnetic Liner Inertial Fusion. X-pinches, known for reliably generating fast (~1 ns), small (~1 µm) x-ray sources, were driven on the compact current driver GenASIS (~200 kA, 150 ns) as a potential backlighter source for TXD. Considering that different X-pinch configurations have characteristic advantages and drawbacks as x-ray generating loads, three distinct copper X-pinch configurations were studied: the wire X-pinch, the hybrid X-pinch, and the laser-cut X-pinch. The Cu K-shell emission from each configuration was characterized and analyzed regarding the specific backlighter requirements for an 8 keV TXD system: spatial and temporal resolution, number of sources, time of emission, spectrum, and reproducibility. Recommendations for future experimental improvements and applications are presented. The electron density of static objects was retrieved from Moiré images obtained through TXD. This allowed to calculate the mass density of static samples within 4% of the expected value for laser-cut X-pinches, which were found to be the optimal X-pinch configuration for TXD due to their high reproducibility, small source size (≤5 µm), short duration (~1 ns FWHM), and up to 10^6 W peak power near 8 keV photon energy. Plasma loads were imaged through TXD for the first-time using laser-cut X-pinch backlighting. Experimental images were compared with simulations from the X-ray Wave-Front Propagation code, demonstrating that TXD can be a powerful x-ray refraction-based diagnostic for dense Z-pinch loads. Future plans for Talbot-Lau Interferometry diagnostics in the pulsed-power environment are described.

Front propagation and arrival times in networks with application to neurodegenerative diseases

Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key question is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying system; the Lambert time, obtained by considering the interaction of two nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher-Kolmogorov-Petrovsky-Piskunov equation as a paradigm for the dynamics and show that each method provides different insight and time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution valid in the entire domain and the correct ordering of arrival regions over large regions of parameters and initial conditions.

A mesoscopic analysis of a localized shear band propagation effect on the deformation and fracture of coated materials

The numerical simulations of the deformation and fracture in an iron boride coating – steel substrate composition are presented. The dynamic boundary-value problem is solved numerically by the finite-difference method. A complex geometry of the borided coating – steel substrate interface is taken into account explicitly. To simulate the mechanical behavior of the steel substrate, use is made of an isotropic strain hardening model including a relation for shear band propagation. Local regions of bulk tension are shown to arise near the interface even under simple uniaxial compression of the composition and in so doing they determine the mesoscale mechanisms of fracture. The interrelation between plastic deformation in the steel substrate and cracking of the borided coating is studied. Stages of shear band front propagation attributable to the interface complex geometry have been revealed. The coating cracking pattern, location of the fracture onset regions and the total crack length are found to depend on the front velocity in the steel substrate.

Parameters of temperature disturbance triggering the propagation of the quench front on an extremely overheated surface

The results of computational experiments simulating the triggering of the quench front propagation on the superheated vertically oriented metal plates are presented. The plates are quenched by a gravitationally flowing down liquid nitrogen film. The temperature of the test samples at the beginning of the process was higher than the critical temperature and the Leidenfrost temperature, which means that direct long-term liquid-solid contact is impossible. For this reason, the front is initially motionless. As a result of numerical simulation, a dynamic pattern of the quench front propagation on a high-temperature surface was obtained. Analysis of the results allowed to find the realistic values of heat sink into the cooling medium, as well as the parameters of the local temperature disturbance, its spatial extent and amplitude, at which the conditions are created for triggering the process of quench front propagation on the high-temperature surface. Direct comparison of the numerical simulations results with experimental data on the velocity, geometry of the quench front and on the dynamical pattern of the process confirmed the reliability of the results obtained.

An Alternative Algorithm for Simulating Flash Flood

Most of the approaches in numerical modeling techniques are based on the Eulerian coordinate system. This approach faces difficulty in simulating flash flood front propagation. This paper shows an alternative method that implements a numerical modeling technique based on the Lagrangian coordinate system to simulate the water of debris flow. As for the interaction with the riverbed, the simulation uses an Eulerian coordinate system. The method uses the conservative and momentum equations of water and sediment mixture in the Lagrangian form. Source terms represent deposition and erosion. The riverbed in the Eulerian coordinate system interacts with the flow of the mixture. At every step, the algorithm evaluates the relative position of moving nodes of the flow part to the fixed nodes of the riverbed. Computation of advancing velocity and depth uses the riverbed elevation, slope data, and the bed elevation change computation uses the erosion or deposition data of the flow on the moving nodes. Spatial discretization is implementing the Galerkin method. Furthermore, temporal discretization is implementing the forward difference scheme. Test runs show that the algorithm can simulate downward, upward, and reflected backward 1-D flow cases. Two-D model tests and comparisons with SIMLAR software show that the algorithm works in simulating debris flow.

Multidimensional computational models of gas combustion in heterogeneous porous medium

The processes of filtration gas combustion in heterogeneous porous medium is studying. The presence of two opposite modes of front propagation made it possible to stabilize the combustion front in a composite porous medium with piecewise constant porosity. A feature of this study is the presentation of the original model not in the traditional form of a system of parabolic equations, but in the form of integral conservation laws in terms of the temperature of the porous medium, the total gas enthalpy, and the mass of gas mixture, and the fluxes corresponding to these functions.

Implementation of planar 3D hydraulic fracture model in rock with layered compressive stress

Plane 3D model of hydraulic fracture propagation is implemented. Fluid flow inside the fracture, leak-of, rock deformation and breaking are taken into account. Asymptotic solution for tip of semi-infinite plane fracture is used to set boundary conditions for fluid flow problem and to calculate fracture front propagation velocity. Elastic and fluid flow equations are united in one system of nonlinear equations and solved simultaneously by Newton method with analytically calculated Jacoby matrix. The implemented model may be used as a start point for testing various methods of solution of “hydrodynamic-elasticity” problem and improving their convergence speed. Also model can be used for developed hydraulic fracture simulation.

Determination of Adsorption-Retention Constants and Inaccessible Pore Volume for High-Molecular Polymers

The application of chemical enhanced oil recovery methods is based mainly on data from experiments. Determining the adsorption constants without destroying the sample remains a relevant problem. It is necessary for accurate data. The determination of filtration parameters of high-molecular polymers in a porous medium using special model is considered in this paper. The aim of the investigation is the solution of inverse problem of polymer transport with adsorption. The key data for this are the characteristic times of the polymer front propagation, water and rock densities, porosity, and initial polymer concentration. The solutions of the direct problem and the inverse problem from the characteristic form of equations are obtained. The algorithm of interpretation of adsorption-retention parameters and inaccessible pore volume form non-destructive experimental studies is developed. Comparison of the calculated values of the inaccessible pore volume with the results of laboratory studies leads to an error within 10%. The practical application of the algorithm was carried out using the data obtained in previously conducted experiments.