arXiv subjects

Shay I. Heizler

Publications and source records attributed to Shay I. Heizler.

At least 19 recordsLinked to original sources

arXiv2024

The non-equilibrium Marshak wave problem in non-homogeneous media

We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion approximation in the supersonic regime. The solutions constitute a generalization of the non-equilibrium nonlinear solutions that were developed recently for homogeneous media. Self-similar solutions are constructed for a power law time dependent surface temperature, a spatial power law density profile and a material model with power law temperature and density dependent opacities and specific energy density. The extension of the problem to non-homogeneous media enables the existence of similarity solutions for a general power law specific material energy. It is shown that the solutions exist for specific values of the temporal temperature drive and spatial density exponents, which depend on the material exponents. We also illustrate how the similarity solutions take various qualitatively different forms which are analyzed with respect to various parameters. Based on the solutions, we define a set of non-trivial benchmarks for supersonic non-equilibrium radiative heat transfer. The similarity solutions are compared to gray diffusion simulations as well as to detailed implicit Monte-Carlo and discrete-ordinate transport simulations in the optically-thick regime, showing a great agreement, which highlights the benefit of these solutions as a code verification test problem.

astro-ph.HE↗

arXiv2024

An accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation

We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions for homogeneous media, to include general collisional properties, including birth-death events and linearly anisotropic scattering. This is done by introducing an exact scaling law relating the Green function of the pure-scattering case with the general collision case, which is verified using deterministic and Monte-Carlo simulations. Importantly, the effective diffusion coefficient is identified by inspecting the transport solution at long times.

cond-mat.stat-mech↗

arXiv2023

Frequency-dependent Discrete Implicit Monte-Carlo Scheme for the Radiative Transfer Equation

This work generalizes the discrete implicit Monte-Carlo (DIMC) method for modeling the radiative transfer equation from a gray treatment to an frequency-dependent one. The classic implicit Monte-Carlo (IMC) algorithm, that has been used for several decades, suffers from a well-known numerical problem, called teleportation, where the photons might propagate faster than the exact solution due to the finite size of the spatial and temporal resolution. The Semi-analog Monte-Carlo algorithm proposed the use of two kinds of particles, photons and material particles that are born when a photon is absorbed. The material particle can `propagate' only by transforming into a photon, due to black-body emission. While this algorithm produces a teleportation-free result, it is noisier results compared to IMC due to the discrete nature of the absorption-emission process. In a previous work [Steinberg and Heizler, ApJS, 258:14 (2022)], proposed a gray version of DIMC, that makes use of two kinds of particles, and therefore has teleportation-free results, but also uses the continuous absorption algorithm of IMC, yielding smoother results. This work is a direct frequency-dependent (energy-dependent) generalization of the DIMC algorithm. We find in several one and two dimensional benchmarks, that the new frequency-dependent DIMC algorithm yields teleportation-free results on one hand, and smooth results with IMC-like noise level.

physics.comp-ph↗

arXiv2022

Supersonic-subsonic transition region in radiative heat flow via self-similar solutions

We study the radiative hydrodynamics flow of radiation-driven heat waves in hot dense plasmas, using approximate self-similar solutions. Specifically, we have focused on the intermediate regime between pure radiative supersonic flow and the pure subsonic regime. These two regimes were investigated both using exact self-similar solutions and numerical simulations, however, most of the study used numerical simulations, mainly because the radiative heat wave and the shock regions are not self-similar altogether. In a milestone work [J. Garnier et al., Phys. Plas., 13, 092703 (2006)], it was found that for a specific power law dependency temperature profile, a unique exact self-similar solution exists, that is valid for all physical regimes. In this work we approximate Garnier's exact solution for a general power-law temperature-dependency, using simple analytical considerations. This approximate solution yields a good agreement compared to numerical simulations for the different thermodynamic profiles within the expected range of validity. In addition, we offer an approximate solution for the energies absorbed in the matter, again, for a general power-law temperature profile. Our approximate self-similar solution for the energy yields very good results comparing to exact numerical simulations for both gold and $\mathrm{Ta_2O_5}$. We also set a comparison of our self-similar solutions with the results of an experiment for radiation temperature measurement in a hohlraum in low-density foams that is addressed directly, to the intermediate regime, yielding a good agreement and similar trends. The different models as well as the numerical simulations are powerful tools to analyze the supersonic-subsonic transition region.

physics.plasm-ph↗

arXiv2022

A New Discrete Implicit Monte Carlo Scheme for Simulating Radiative Transfer Problems

We present a new algorithm for radiative transfer-based on a statistical Monte Carlo approach-that does not suffer from teleportation effects, on the one hand, and yields smooth results, on the other hand. Implicit Monte Carlo (IMC) techniques for modeling radiative transfer have existed from the 1970s. When they are used for optically thick problems, however, the basic algorithm suffers from "teleportation" errors, where the photons propagate faster than the exact physical behavior, due to the absorption-blackbody emission processes. One possible solution is to use semianalog Monte Carlo, in its new implicit form (ISMC), which uses two kinds of particles, photons and discrete material particles. This algorithm yields excellent teleportation-free results, but it also produces noisier solutions (relative to classic IMC), due to its discrete nature. Here, we derive a new Monte Carlo algorithm, Discrete Implicit Monte Carlo (DIMC), which also uses the idea of two kinds of discrete particles, and thus does not suffer from teleportation errors. DIMC implements the IMC discretization and creates new radiation photons for each time step, unlike ISMC. Using the continuous absorption technique, DIMC yields smooth results like classic IMC. One of the main elements of the algorithm is the avoidance of the explosion of the particle population, by using particle merging. We test the new algorithm on 1D and 2D cylindrical problems, and show that it yields smooth, teleportation-free results. We finish by demonstrating the power of the new algorithm on a classic radiative hydrodynamic problem-an opaque radiative shock wave. This demonstrates the power of the new algorithm for astrophysical scenarios.

astro-ph.IM↗

arXiv2022

Multi-Frequency Implicit Semi-analog Monte-Carlo (ISMC) Radiative Transfer Solver in Two-Dimensions (without Teleportation)

We study the multi-dimensional radiative transfer phenomena using the ISMC scheme, in both gray and multi-frequency problems. Implicit Monte-Carlo (IMC) schemes have been in use for five decades. The basic algorithm yields teleportation errors, where photons propagate faster than the correct heat front velocity. Recently [Poëtte and Valentin, J. Comp. Phys., 412, 109405 (2020)], a new implicit scheme based on the semi-analog scheme was presented and tested in several one-dimensional gray problems. In this scheme, the material energy of the cell is carried by material-particles, and the photons are produced only from existing material particles. As a result, the teleportation errors vanish, due to the infinite discrete spatial accuracy of the scheme. We examine the validity of the new scheme in two-dimensional problems, both in Cartesian and Cylindrical geometries. Additionally, we introduce an expansion of the new scheme for multi-frequency problems. We show that the ISMC scheme presents excellent results without teleportation errors in a large number of benchmarks, especially against the slow classic IMC convergence.

physics.comp-ph↗

arXiv2021

Radiation drive temperature measurements in aluminium via radiation-driven shock waves: Modeling using self-similar solutions

We study the phenomena of radiative-driven shock waves using a semi-analytic model based on self similar solutions of the radiative hydrodynamic problem. The relation between the hohlraum drive temperature $T_{\mathrm{Rad}}$ and the resulting ablative shock $D_S$ is a well-known method for the estimation of the drive temperature. However, the various studies yield different scaling relations between $T_{\mathrm{Rad}}$ and $D_S$, based on different simulations. In [T. Shussman and S.I. Heizler, Phys. Plas., 22, 082109 (2015)] we have derived full analytic solutions for the subsonic heat wave, that include both the ablation and the shock wave regions. Using this self-similar approach we derive here the $T_{\mathrm{Rad}}(D_S)$ relation for aluminium, using the detailed Hugoniot relations and including transport effects. By our semi-analytic model, we find a spread of $\approx 40$eV in the $T_{\mathrm{Rad}}(D_S)$ curve, as a function of the temperature profile's duration and its temporal profile. Our model agrees with the various experiments and the simulations data, explaining the difference between the various scaling relations that appear in the literature.

physics.plasm-ph↗

arXiv2021

Multi-Group Discontinuous Asymptotic $P_1$ Approximation in Radiative Marshak Waves Experiments

We study the propagation of radiative heat (Marshak) waves, using modified $P_1$-approximation equations. In relatively optically-thin media the heat propagation is supersonic,~i.e. hydrodynamic motion is negligible, and thus can be described by the radiative transfer Boltzmann equation, coupled with the material energy equation. However, the exact thermal radiative transfer problem is still difficult to solve and requires massive simulation capabilities. Hence, there still exists a need for adequate approximations that are comparatively easy to carry out. Classic approximations, such as the classic diffusion and classic $P_1$, fail to describe the correct heat wave velocity, when the optical depth is not sufficiently high. Therefore, we use the recently developed discontinuous asymptotic $P_1$ approximation, which is a time-dependent analogy for the adjustment of the discontinuous asymptotic diffusion for two different zones. This approximation was tested via several benchmarks, showing better results than other common approximations, and has also demonstrated a good agreement with a main Marshak wave experiment and its Monte-Carlo gray simulation. Here we derive energy expansion of the discontinuous asymptotic $P_1$ approximation in slab geometry, and test it with numerous experimental results for propagating Marshak waves inside low density foams. The new approximation describes the heat wave propagation with good agreement. Furthermore, a comparison of the simulations to exact implicit Monte-Carlo slab-geometry multi-group simulations, in this wide range of experimental conditions, demonstrates the superiority of this approximation to others.

physics.plasm-ph↗

arXiv2020

Asymptotic $P_N$ Approximation in Radiative Transfer Problems

We study the validity of the time-dependent asymptotic $P_N$ approximation in radiative transfer of photons. The time-dependent asymptotic $P_N$ is an approximation which uses the standard $P_N$ equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic $P_N$ approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision ($ω_{\mathrm{eff}}$) can be larger than one due to inner or outer radiation sources and the coefficients of the closure must be extended for these cases. Our approximation is tested against a well-known radiative transfer benchmark. It yields excellent results, with almost correct particle velocity that controls the radiative heat-wave fronts.

physics.comp-ph↗

arXiv2020

The Time-Dependent Asymptotic $P_N$ Approximation for the Transport Equation

In this study a spatio-temporal approach for the solution of the time-dependent Boltzmann (transport) equation is derived. Finding the exact solution using the Boltzmann equation for the general case is generally an open problem and approximate methods are usually used. One of the most common methods is the spherical harmonics method (the $P_N$ approximation), when the exact transport equation is replaced with a closed set of equations for the moments of the density, with some closure assumption. Unfortunately, the classic $P_N$ closure yields poor results with low-order $N$ in highly anisotropic problems. Specifically, the tails of the particle's positional distribution as attained by the $P_N$ approximation, are inaccurate compared to the true behavior. In this work we present a derivation of a linear closure that even for low-order approximation yields a solution that is superior to the classical $P_N$ approximation. This closure, is based on an asymptotic derivation, both for space and time, of the exact Boltzmann equation in infinite homogeneous media. We test this approximation with respect to the one-dimensional benchmark of the full Green function in infinite media. The convergence of the proposed approximation is also faster when compared to (classic or modified) $P_N$ approximation.

physics.comp-ph↗

arXiv2020

Key to understanding supersonic radiative Marshak waves using simple models and advanced simulations

This article studies the propagation of supersonic radiative Marshak waves. These waves are radiation dominated, and play an important role in inertial confinement fusion and in astrophysical and laboratory systems. For that reason, this phenomenon has attracted considerable experimental attention in recent decades in several different facilities. The present study integrates the various experimental results published in the literature, demonstrating a common physical base. A new simple semi-analytic model is derived and presented along with advanced radiative hydrodynamic implicit Monte Carlo direct numerical simulations, which explain the experimental results. This study identifies the main physical effects dominating the experiments, notwithstanding their different apparatuses and different physical regimes.

physics.comp-ph↗

arXiv2018

Modeling of Supersonic Radiative Marshak waves using Simple Models and Advanced Simulations

We study the problem of radiative heat (Marshak) waves using advanced approximate approaches. Supersonic radiative Marshak waves that are propagating into a material are radiation dominated (i.e. hydrodynamic motion is negligible), and can be described by the Boltzmann equation. However, the exact thermal radiative transfer problem is a nontrivial one, and there still exists a need for approximations that are simple to solve. The discontinuous asymptotic $P_1$ approximation, which is a combination of the asymptotic $P_1$ and the discontinuous asymptotic diffusion approximations, was tested in previous work via theoretical benchmarks. Here we analyze a fundamental and typical experiment of a supersonic Marshak wave propagation in a low-density $\mathrm{SiO_2}$ foam cylinder, embedded in gold walls. First, we offer a simple analytic model, that grasps the main effects dominating the physical system. We find the physics governing the system to be dominated by a simple, one-dimensional effect, based on the careful observation of the different radiation temperatures that are involved in the problem. The model is completed with the main two-dimensional effect which is caused by the loss of energy to the gold walls. Second, we examine the validity of the discontinuous asymptotic $P_1$ approximation, comparing to exact simulations with good accuracy. Specifically, the heat front position as a function of the time is reproduced perfectly in compare to exact Boltzmann solutions.

physics.comp-ph↗

arXiv2018

The Discontinuous Asymptotic Telegrapher's Equation ($P_1$) Approximation

Modeling the propagation of radiative heat-waves in optically thick material using a diffusive approximation is a well-known problem. In optically thin material, classic methods, such as classic diffusion or classic $P_1$, yield the wrong heat wave propagation behavior, and higher order approximation might be required, making the solution harder to obtain. The asymptotic $P_1$ approximation [Heizler, {\em NSE} 166, 17 (2010)] yields the correct particle velocity but fails to model the correct behavior in highly anisotropic media, such as problems that involve sharp boundary between media or strong sources. However, the solution for the two-region Milne problem of two adjacent half-spaces divided by a sharp boundary, yields a discontinuity in the asymptotic solutions, that makes it possible to solve steady-state problems, especially in neutronics. In this work we expand the time-dependent asymptotic $P_1$ approximation to a highly anisotropic media, using the discontinuity jump conditions of the energy density, yielding a modified discontinuous $P_1$ equations in general geometry. We introduce numerical solutions for two fundamental benchmarks in plane symmetry. The results thus obtained are more accurate than those attained by other methods, such as Flux-Limiters or Variable Eddington Factor.

physics.comp-ph↗

arXiv2017

Hindrances to precise recovery of cellular forces in fibrous biopolymer networks

How cells move through the three-dimensional extracellular matrix (ECM) is of increasing interest in attempts to understand important biological processes such as cancer metastasis. Just as in motion on flat surfaces, it is expected that experimental measurements of cell-generated forces will provide valuable information for uncovering the mechanisms of cell migration. However, the recovery of forces in fibrous biopolymer networks may suffer from large errors. Here, within the framework of lattice-based models, we explore possible issues in force recovery by solving the inverse problem: how can one determine the forces cells exert to their surroundings from the deformation of the ECM? Our results indicate that irregular cell traction patterns, the uncertainty of local fiber stiffness, the non-affine nature of ECM deformations and inadequate knowledge of network topology will all prevent the precise force determination. At the end, we discuss possible ways of overcoming these difficulties.

physics.bio-ph↗

arXiv2017

3D-2D transition in mode-I fracture microbranching in a perturbed hexagonal close-packed lattice

Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the instability and calculating the dynamics post-instability within the linear elastic framework is difficult and controversial. The experimental results give several indications that the microbranching phenomenon is basically a three-dimensional phenomenon. Nevertheless, the theoretical effort has been focused mostly in two-dimensional modeling. In this work we study the microbranching instability using three-dimensional atomistic simulations, exploring the difference between the 2D and 3D models. We find that the basic 3D fracture pattern shares similar behavior with the 2D case. Nevertheless, we exhibit a clear 3D-2D transition as the crack velocity increases, while as long as the microbranches are sufficiently small, the behavior is pure 3D-behavior, while at large driving, as the size of the microbranches increases, more 2D-like behavior is exhibited. In addition, in 3D simulations, the quantitative features of the microbranches, separating the regimes of steady-state cracks (mirror) and post-instability (mist-hackle) are reproduced clearly, consistent with the experimental findings.

cond-mat.stat-mech↗

arXiv2016

Self-similar solution of the subsonic radiative heat equations using a binary equation of state

Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in order to investigate the effect of the equation of state (EOS) on the propagation of radiation driven shocks. We find that using a single ideal gas EOS for both regions, as used in previous works, yields large errors in describing the shock wave. We use the fact that the solution is composed of two different self-similar solutions, one for the ablation region and one for the shock, and apply two ideal gas EOS (binary-EOS), one for each region, by fitting a detailed tabulated EOS to power laws at different regimes. By comparing the semi-analytic solution with a numerical simulation using a full EOS, we find that the semi-analytic solution describes both the heat and the shock regions well.

physics.plasm-ph↗

arXiv2015

Full self-similar solutions of the subsonic radiative heat equations

We study the phenomenon of diffusive radiative heat waves (Marshak waves) under general boundary conditions. In particular, we derive full analytic solutions for the subsonic case, that include both the ablation and the shock wave regions. Previous works in this regime, based on the work of [R. Pakula and R. Sigel, Phys. Fluids. 443, 28, 232 (1985)], present self-similar solutions for the ablation region alone, since in general, the shock region and the ablation region are not self-similar together. Analytic results for both regions were obtained only for the specific case in which the ratio between the ablation front velocity and the shock velocity is constant. In this work, we derive a full analytic solution for the whole problem in general boundary conditions. Our solution is composed of two different self-similar solutions, one for each region, that are patched at the heat front. The ablative region of the heat wave is solved in a manner similar to previous works. Then, the pressure at the front, which is derived from the ablative region solution, is taken as a boundary condition to the shock region, while the other boundary is described by Hugoniot relations. The solution is compared to full numerical simulations in several representative cases. The numerical and analytic results are found to agree within $1\%$ in the ablation region, and within $2-5\%$ in the shock region. This model allows better prediction of the physical behavior of radiation induced shock waves, and can be applied for high energy density physics experiments.

cond-mat.stat-mech↗

arXiv2015

Microbranching in mode-I fracture using large scale simulations of amorphous and perturbed lattice models

We study the high-velocity regime mode-I fracture instability when small microbranches start to appear near the main crack, using large scale simulations. Some of the features of those microbranches have been reproduced qualitatively in smaller scale studies (using ${\cal O}(10^4)$ atoms) on both a model of an amorphous materials (via the continuous random network model) and using perturbed lattice models. In this study, larger scale simulations (${\cal O}(10^6)$ atoms) were performed using multi-threading computing on a GPU device, in order to achieve more physically realistic results. First, we find that the microbranching pattern appears to be converging with the lattice width. Second, the simulations reproduce the growth of the size of a microbranch as a function of the crack velocity, as well as the increase of the amplitude of the derivative of the electrical resistance RMS with respect to the time as a function of the crack velocity. In addition, the simulations yield the correct branching angle of the microbranches, and the power law governing the shape of the microbranches seems to be lower than one, so that the side cracks turn over in the direction of propagation of the main crack as seen in experiment.

cond-mat.stat-mech↗