Journal of Nuclear Engineering and Radiation Science, 2021
Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are know... more Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are known to be optimized multilayered composites. This paper is a simplified short inroad to the complex problem of optimizing the design of such shields when they attenuate a neutron beam to extremise certain quality criteria, in plane geometry, subject to equality and inequality constraints. In the equality constraints, the interfacial polychromatic neutron fluxes are solutions to course-mesh finite-difference holonomic state equations. The set of these interfacial fluxes act as state variables,while the set of layer thicknesses, or their poisoning (by added neutron absorbers) concentrations are decision variables. The entire procedure is then demonstrated to be reducible to standard Kuhn-Tucker semi-linear programming that may also lead robustly to an optimal sequence for these layers.
By making use of miniature 239Pu and 235U fission chambers and an accelerator-based neutron sourc... more By making use of miniature 239Pu and 235U fission chambers and an accelerator-based neutron source, the 239Pu/235U neutron fission rate ratio profile has been measured in the region of a plane interface between a tank containing ordinary water and a tank containing an aqueous solution of boric acid. The reported preliminary results indicate an approximately 8 mm shift of the central point of the fission rate ratio profile towards the poisoned side of the system and an accompanying larger shift in the 235U Cd ratio profile towards the unpoisoned side.
We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in ... more We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in the evaluation of integrals of piecewise continuous differentiable functions. A Romberg symmetrized integration method, with randomized intervals, is developed for various possible applications. Integration error bounds are derived statistically for the pertaining Richardson extrapolations. Symmetrized-to-conventional integral ratio computations are suggested as a means to reduce these error bounds.
Abstract. We demonstrate how symmetrized Riemann integration recently introduced in [3] can be em... more Abstract. We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in the evaluation of integrals of piecewise continuous differentiable functions. A Romberg symmetrized integration method, with randomized intervals, is developed for various possible applications. Integration error bounds are derived statistically for the pertaining Richardson extrapolations. Symmetrized-to-conventional integral ratio computations are suggested as a means to reduce these error bounds.
Haidar, N. H. S., On Sampled Fourier Sums,Digital Signal Processing6 (1996), 179–184.The band lim... more Haidar, N. H. S., On Sampled Fourier Sums,Digital Signal Processing6 (1996), 179–184.The band limiting approximation for duration-limited signals is operationally studied in the frequency-sampled and frequency-time bisampled forms. Error bounds are established and new convergence proofs are given for the sampled Fourier sums.
Based on the continuity of functions of two variables, we provide a new qualitative proof of the ... more Based on the continuity of functions of two variables, we provide a new qualitative proof of the well known fast convergence of Fourier series representations of most continuous periodic functions. Our proof is based on a representation of this infinite Fourier series, even when it diverges, by a five-term, with 17 interpolation points, minimal harmonic series with a new minimal series interpolation (MSI) algorithm for an iterative approximant. A smoothing linear summation minimal series is also demonstrated to be constructible by the same algorithm.
This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean ha... more This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach.
ABSTRACT An integral equation of the Fredholm first kind is developed semi-analytically to quanti... more ABSTRACT An integral equation of the Fredholm first kind is developed semi-analytically to quantify the strategy of operating a nuclear power generating unit at reduced load in the (100–600) MW (e) range so as to break even its average (over the lifetime of the plant) power generation costs with the generation costs of a nuclear plant of a smaller size and with an identical plant availability curve. For the model of plant constant availability, the integral equation may be reduced to a transcendental relation between the reduced-load-operation time, the annual fixed charge rate of plant capital costs, its availability figure, the rate of load reduction and the plant lifetime.
Journal of Nuclear Engineering and Radiation Science
The technique of composite region coupling by a neutron source at a common boundary of different ... more The technique of composite region coupling by a neutron source at a common boundary of different regions, that has been introduced in [1], has allowed for an additive separation of variables (ASOV) neutron-density 3D wave analytical solution to the posing four-regional boundary value problem (BVP) of neutron cancer therapy (NCT). The three employable mutually orthogonal neutron beams, which may have different pulse shapes, have distinct modulation frequencies ω, ϖ, w^ and distinct relative time delays ε, ε^. By employing this solution, we demonstrate in this paper how the therapeutic utility index and the ballistic index for this kind of dynamical NCT form a nonlinear optimization problem. As an extension of a result obtained recently, [2], for a certain lower-dimensional setup, a Pareto optimal control vector ω*=(ω*, ϖ* ε*, w^*,ε^*) is identified for this 3D problem. Both of these two indices are demonstrated to be remarkably periodically discontinuous in ε or ε^, even in the neigh...
Journal of Nuclear Engineering and Radiation Science, 2021
Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are know... more Compact neutronic shields for mobile nuclear reactors or accelerator-based neutron beams are known to be optimized multilayered composites. This paper is a simplified short inroad to the complex problem of optimizing the design of such shields when they attenuate a neutron beam to extremise certain quality criteria, in plane geometry, subject to equality and inequality constraints. In the equality constraints, the interfacial polychromatic neutron fluxes are solutions to course-mesh finite-difference holonomic state equations. The set of these interfacial fluxes act as state variables,while the set of layer thicknesses, or their poisoning (by added neutron absorbers) concentrations are decision variables. The entire procedure is then demonstrated to be reducible to standard Kuhn-Tucker semi-linear programming that may also lead robustly to an optimal sequence for these layers.
By making use of miniature 239Pu and 235U fission chambers and an accelerator-based neutron sourc... more By making use of miniature 239Pu and 235U fission chambers and an accelerator-based neutron source, the 239Pu/235U neutron fission rate ratio profile has been measured in the region of a plane interface between a tank containing ordinary water and a tank containing an aqueous solution of boric acid. The reported preliminary results indicate an approximately 8 mm shift of the central point of the fission rate ratio profile towards the poisoned side of the system and an accompanying larger shift in the 235U Cd ratio profile towards the unpoisoned side.
We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in ... more We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in the evaluation of integrals of piecewise continuous differentiable functions. A Romberg symmetrized integration method, with randomized intervals, is developed for various possible applications. Integration error bounds are derived statistically for the pertaining Richardson extrapolations. Symmetrized-to-conventional integral ratio computations are suggested as a means to reduce these error bounds.
Abstract. We demonstrate how symmetrized Riemann integration recently introduced in [3] can be em... more Abstract. We demonstrate how symmetrized Riemann integration recently introduced in [3] can be employed in the evaluation of integrals of piecewise continuous differentiable functions. A Romberg symmetrized integration method, with randomized intervals, is developed for various possible applications. Integration error bounds are derived statistically for the pertaining Richardson extrapolations. Symmetrized-to-conventional integral ratio computations are suggested as a means to reduce these error bounds.
Haidar, N. H. S., On Sampled Fourier Sums,Digital Signal Processing6 (1996), 179–184.The band lim... more Haidar, N. H. S., On Sampled Fourier Sums,Digital Signal Processing6 (1996), 179–184.The band limiting approximation for duration-limited signals is operationally studied in the frequency-sampled and frequency-time bisampled forms. Error bounds are established and new convergence proofs are given for the sampled Fourier sums.
Based on the continuity of functions of two variables, we provide a new qualitative proof of the ... more Based on the continuity of functions of two variables, we provide a new qualitative proof of the well known fast convergence of Fourier series representations of most continuous periodic functions. Our proof is based on a representation of this infinite Fourier series, even when it diverges, by a five-term, with 17 interpolation points, minimal harmonic series with a new minimal series interpolation (MSI) algorithm for an iterative approximant. A smoothing linear summation minimal series is also demonstrated to be constructible by the same algorithm.
This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean ha... more This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach.
ABSTRACT An integral equation of the Fredholm first kind is developed semi-analytically to quanti... more ABSTRACT An integral equation of the Fredholm first kind is developed semi-analytically to quantify the strategy of operating a nuclear power generating unit at reduced load in the (100–600) MW (e) range so as to break even its average (over the lifetime of the plant) power generation costs with the generation costs of a nuclear plant of a smaller size and with an identical plant availability curve. For the model of plant constant availability, the integral equation may be reduced to a transcendental relation between the reduced-load-operation time, the annual fixed charge rate of plant capital costs, its availability figure, the rate of load reduction and the plant lifetime.
Journal of Nuclear Engineering and Radiation Science
The technique of composite region coupling by a neutron source at a common boundary of different ... more The technique of composite region coupling by a neutron source at a common boundary of different regions, that has been introduced in [1], has allowed for an additive separation of variables (ASOV) neutron-density 3D wave analytical solution to the posing four-regional boundary value problem (BVP) of neutron cancer therapy (NCT). The three employable mutually orthogonal neutron beams, which may have different pulse shapes, have distinct modulation frequencies ω, ϖ, w^ and distinct relative time delays ε, ε^. By employing this solution, we demonstrate in this paper how the therapeutic utility index and the ballistic index for this kind of dynamical NCT form a nonlinear optimization problem. As an extension of a result obtained recently, [2], for a certain lower-dimensional setup, a Pareto optimal control vector ω*=(ω*, ϖ* ε*, w^*,ε^*) is identified for this 3D problem. Both of these two indices are demonstrated to be remarkably periodically discontinuous in ε or ε^, even in the neigh...
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Papers by Nassar Haidar