相关论文: The adjoint neutron transport equation and the sta…

This paper presents a novel stochastic method for modeling the transport of Delayed Neutron Precursors (DNPs) in liquid nuclear fuel. The method incorporates advection and diffusion effects into the Monte Carlo solution of the neutron…

Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…

Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an…

The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied…

The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [9, 27]), the NTE has had a somewhat scattered treatment in mathematical…

This paper proposes a new equation from continuous adjoint theory to compute the gradient of quantities governed by the Transport Theory of light. Unlike discrete gradients ala autograd, which work at the code level, we first formulate the…

Over the last decade, ingenuous developments in Monte Carlo methods have enabled the unbiased estimation of adjoint-weighted reactor parameters expressed as bilinear forms, such as kinetics parameters and sensitivity coefficients. A…

This paper provides an initial description of the Method of Simultaneous Solutions, a Monte Carlo approach that simultaneously solves multiple Boltzmann-transport-like phenomena. Here, it is used to simultaneously solve the neutron…

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In…

This paper synergizes the roles of adjoint in various disciplines of mathematics, sciences, and engineering. Though the materials developed and presented are not new -- as each or some could be found in (or inferred from) publications in…

In this paper the simplified double-spherical harmonics SDPN, approximation of the neutron transport equation is proposed. The SDPN equations are derived from the multi-group DPN equations for N=1,2,3 (comparable to the SP3, SP5, and SP7…

For a number of applications like low-source reactor start-up or neutron coincidence counting it is necessary to take into account the stochastic nature of neutron transport and go beyond the average neutron density, which is solution of a…

Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…

The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…

The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…

In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…

We study the unique continuation property for the neutron transport equation and for a simplified model of the Fokker-Planck equation in a bounded domain with absorbing boundary condition. An observation estimate is derived. It depends on…

We present a method to compute transport coefficients in molecular dynamics. Transport coefficients quantify the linear dependencies of fluxes in non-equilibrium systems subject to small external forcings. Whereas standard non-equilibrium…

There seems to exist significant similarities between a reactor system and a supply chain from collection to delivery. In the reactor case, neutrons are continuously produced and absorbed in nuclear fuel. In a supply system case, items are…