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In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z‐pinch like implosion that can be used in the development and evaluation of shock‐hydrodynamics algorithms that are intended to be used in Z‐pinch simulations. The model uses a J × B Lorentz force, motivated by a 0‐D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi‐physics aspects of a proposed combined radiation hydrodynamics (rad‐hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre‐fill plasma effects. In this work, a high‐resolution flux‐corrected‐transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock‐hydrodynamic studies. The presented results include an asymptotic solution based on a limiting‐case thin‐shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre‐fill and a set of perturbed liner geometries that excite a hydro‐magnetic like Rayleigh–Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self‐convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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The falsification of a hybrid system aims at finding trajectories that violate a given safety property. This is a challenging problem, and the practical applicability of current falsification algorithms still suffers from their high time complexity. In contrast to falsification, verification algorithms aim at providing guarantees that no such trajectories exist. Recent symbolic reachability techniques are capable of efficiently computing linear constraints that enclose all trajectories of the system with reasonable precision. In this paper, we leverage the power of symbolic reachability algorithms to improve the scalability of falsification techniques. Recent approaches to falsification reduce the problem to a nonlinear optimization problem. We propose to reduce the search space of the optimization problem by adding linear state constraints obtained with a reachability algorithm. An empirical study of how varying abstractions during symbolic reachability analysis affect the performance of solving a falsification problem is presented. In addition, for solving a falsification problem, we propose an alternating minimization algorithm that solves a linear programming problem and a non-linear programming problem in alternation finitely many times. We showcase the efficacy of our algorithms on a number of standard hybrid systems benchmarks demonstrating the performance increase and number of falsifyable instances. 相似文献
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While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called ‘verification theorems’ and ‘viscosity solutions’ provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest. 相似文献
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Metrological justification of reflection hologram interferometry with respect to residual stresses determination by means of blind hole drilling 总被引:2,自引:1,他引:1
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Marten Van Dijk Dwaine Clarke Blaise Gassend G. Edward Suh Srinivas Devadas 《Designs, Codes and Cryptography》2006,39(2):253-273
We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation
using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base
protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend
them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols
provide a speedup of
over the square-and-multiply algorithm, where k is the bitlength of the exponent.
One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential
schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would
like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform
variable-base variable- exponent exponentiation, which also has this feature.
Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of
work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller.
Our protocols are unconditionally secure. 相似文献