An accurate approximation for the highly efficient sampling of polar scattering angle of electron elastic single-scattering events

In single-event Monte Carlo electron transport simulations, elastic scattering events dominate the changes in electron trajectories due to collisions. Classically, the polar scattering angle due to an elastic collision can be sampled efficiently from the screened Rutherford cross section. However, the screened Rutherford cross section fails for both high Z materials and when the incident electron energy becomes too low. Alternatively, improved simulation accuracy for electrons in all energy ranges and through all materials may be obtained by sampling directly from differential data derived from partial-wave-expansion method (PWEM) calculations based on theoretical atomic potential models. While sampling directly from wave calculations will yield simulation results to the best known physical accuracy, it comes at the cost of simulation time. This is due to a sampling process that is typically more involved when compared with using the screened Rutherford cross section. In this work we present a relationship capable of reproducing the moments of the differential cross section derived from PWEM calculations, resulting in good preservation of forward and backscattering peaks. The relationship is directly invertible and is as easily sampled as the Rutherford cross section. Most important, the data presented in this paper in combination with this relationship produce Monte Carlo simulation results which are comparable with those using the exact differential cross section from PWEM calculations for elements Z = 1 to 96 and for incident electron energies from 300,000 down to 50 eV.     

Stochastic automata-based estimators for adaptively compressing files with nonstationary distributions.

This correspondence shows that learning automata techniques, which have been useful in developing weak estimators, can be applied to data compression applications in which the data distributions are nonstationary. The adaptive coding scheme utilizes stochastic learning-based weak estimation techniques to adaptively update the probabilities of the source symbols, and this is done without resorting to either maximum likelihood, Bayesian, or sliding-window methods. The authors have incorporated the estimator in the adaptive Fano coding scheme and in an adaptive entropy-based scheme that "resembles" the well-known arithmetic coding. The empirical results obtained for both of these adaptive methods are obtained on real-life files that possess a fair degree of nonstationarity. From these results, it can be seen that the proposed schemes compress nearly 10% more than their respective adaptive methods that use maximum-likelihood estimator-based estimates.     

The use of an electrothermal plasma gun to simulate the extremely high heat flux conditions of a tokamak disruption

Disruption damage conditions for future large tokamaks like ITER are nearly impossible to simulate on current tokamaks. The electrothermal plasma source SIRENS has been designed, constructed, and operated to produce high density (> 10²⁵/m³), low temperature (1–3 eV) plasma formed by the ablation of the insulator with currents of up to 100 kA (100 s pulse length) and energies up to 15 kJ. The source heat fluence (variable from 0.2 to 7 MJ/m²) is adequate for simulation of the thermal quench phase of plasma disruption in future fusion tokamaks. Different materials have been exposed to the high heat flux in SIRENS, where comparative erosion behavior was obtained. Vapor shield phenomena has been characterized for different materials, and the energy transmission factor through the shielding layer is obtained. The device is also equipped with a magnet capable of producing a parallel magnetic field (up to 16 T) over a 8 msec pulse length. The magnetic field is produced to decrease the turbulent energy transport through the vapor shield, which provides further reduction of surface erosion (magnetic vapor shield effect).     

Model-based cognitive diagnosis

This paper considers the problem of cognitive diagnosis as an instance of general diagnosis, as studied in artificial intelligence. Cognitive diagnosis is the process of inferring a cognitive state from observations of performance. It is thus a key component of any system which attempts to build a dynamic model of the user of that system. Many issues in cognitive diagnosis, previously discussed informally, are mapped onto formal techniques, with consequent increased clarity and rigour. But it is concluded that the general theories for diagnosis must be broadened to fully encompass the problems of cognitive diagnosis.     

Dynamics of Flexible Multibody Systems Using Virtual Work and Linear Graph Theory

By combining linear graph theory with the principle of virtualwork, a dynamic formulation is obtained that extends graph-theoreticmodelling methods to the analysis of flexible multibody systems. Thesystem is represented by a linear graph, in which nodes representreference frames on rigid and flexible bodies, and edges representcomponents that connect these frames. By selecting a spanning tree forthe graph, the analyst can choose the set of coordinates appearing inthe final system of equations. This set can include absolute, joint, orelastic coordinates, or some combination thereof. If desired, allnon-working constraint forces and torques can be automaticallyeliminated from the dynamic equations by exploiting the properties ofvirtual work. The formulation has been implemented in a computerprogram, DynaFlex, that generates the equations of motion in symbolicform. Three examples are presented to demonstrate the application of theformulation, and to validate the symbolic computer implementation.     

Polynomial enumeration of multidimensional lattices

Denoting the nonnegative (resp. signed) integers byN (resp.Z) and the real numbers byR, letK R ^m andf: R ^m R. Thenf is astoring function (resp.packing function) onK wheneverf|(Z ^m K) is an injection into (resp. bijection onto)N. Unit translations g_m of some P. Chowla [1961] polynomials are packing functions on the correspondingN ^m , and all compositions of these polynomials yield further packing functions on variousN ^r . We study this accessible family of packing functions, using standard properties ofordered trees to classify all those compositions, up to a simple equivalence, which define polynomial packing functions on eachN ^m . The numberc(m) of equivalence classes is an exponentially growing function for largem, whence the uniqueness conjecture of our prior two-dimensional work has no counterpart for largerm. We obtain the admissible degrees for composition polynomials inm variables; we describe the tre structures for all such polynomials with extremal degrees. Them-variable polynomials of least degree form a rather irregular numbera(m) of equivalence classes. Density considerations give some degree constraints on ageneral polynomial packing function whose domainK is the topological closure of a nonvoid open cone.     

Electrochemical investigtion of solubility and chemical diffusion of lithium in aluminum

The solubility of lithium in aluminum and the chemical diffusion coefficient in this solid solution have been investigated as a function of temperature between 400 and 600°C using the electrochemical cell: (-)A1, “LiAl”/LiCl-KCl(eut.)/Al(Li)(+) The solubility limit of lithium in aluminum was found to decrease from 13.8 at. pct at 595°C to 8.0 at. pct at 395°C, in good agreement with data previously reported by other investigators using different techniques. The chemical diffusion coefficient has been measured by two different electrochemical transient techniques. The data can be represented by the relation: 1 $$\tilde D = 0.155\exp (--\Delta H/RT)cm^2 /s$$ where ΔH is 119.2 kJ/mol. This electrochemical technique has also been used to obtain values of the composition dependence of the Gibbs free energy of mixing and the enhancement factor d lna_Li/dlnX_Li which relates the chemical diffusion coefficient and the self diffusion coefficients within the Li-Al solid solution.     

Space-time tradeoffs for linear recursion

A linear recursive procedure is one each of whose executions activates at most one invocation of itself. When linear recursion cannot be replaced by iteration, it is usually implemented with a stack of size proportional to the depth of recursion. In this paper we analyze implementations of linear recursion which permit large reductions in storage space at the expense of a small increase in computation time. For example, if the depth of recursion isn, storage space can be reduced to \(\sqrt n \) at the cost of a constant factor increase in running time. The problem is treated by abstracting any implementation of linear recursion as the pebbling of a simple graph, and for this abstraction we exhibit the optimal space-time tradeoffs.