scholarly journals A Closed-form Solution for Source-term Emission of Xenon Isotopes from Underground Nuclear Explosions

2021 ◽  
Author(s):  
Yunwei Sun ◽  
Charles Carrigan ◽  
William Cassata ◽  
Yue Hao ◽  
Souheil Ezzedine ◽  
...  
Keyword(s):  
Closed Form ◽  
Radioactive Decay ◽  
Closed Form Solution ◽  
Compartment Model ◽  
Form Solution ◽  
Isotopic Ratios ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Xenon Isotopes ◽  
Value Decomposition

AbstractIsotopic ratios of radioactive xenons sampled in the subsurface and atmosphere can be used to detect underground nuclear explosions (UNEs) and civilian nuclear reactors. Disparities in the half-lives of the radioactive decay chains are principally responsible for time-dependent concentrations of xenon isotopes. Contrasting timescales, combined with modern detection capabilities, make the xenon isotopic family a desirable surrogate for UNE detection. However, without including the physical details of post-detonation cavity changes that affect radioxenon evolution and subsurface transport, a UNE is treated as an idealized system that is both closed and well mixed for estimating xenon isotopic ratios and their correlations so that the spatially dependent behavior of xenon production, cavity leakage, and transport are overlooked. In this paper, we developed a multi-compartment model with radioactive decay and interactions between compartments. The model does not require the detailed domain geometry and parameterization that is normally needed by high-fidelity computer simulations, but can represent nuclide evolution within a compartment and migration among compartments under certain conditions. The closed-form solution to all nuclides in the series 131–136 is derived using analytical singular-value decomposition. The solution is further used to express xenon ratios as functions of time and compartment position.

scholarly journals Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Gian Luigi Gragnani ◽  
Maurizio Diaz Mendez
Keyword(s):  
Closed Form ◽  
Cross Sections ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Computation Time ◽  
Shape Reconstruction ◽  
Form Solution ◽  
Scattering Data ◽  
Equivalent Sources ◽  
Value Decomposition

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

Sign in / Sign up

Export Citation Format

Share Document