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Publications and source records attributed to Mihaila, Bogdan.
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Here, we discuss the stability properties of the solutions of the general nonlinear Schrödinger equation in 1 + 1 dimensions in an external potential derivable from a parity-time ($ \newcommand{\PT}{\mathcal{PT}} \PT$ ) symmetric superpotential $W(x)$ that we considered earlier in Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation $ \{i \, \partial_t + \partial_x^2 - V(x) + g \vert \psi(x, t) \vert ^{2\kappa} \} \, \psi(x, t) = 0 \>, $ for arbitrary nonlinearity parameter κ, where $g= \pm1$ and V is the well known Pöschl–Teller potential which we allow to be repulsive as well as attractive. Using energy landscape methods, linear stability analysis as well as a time dependent variational approximation, we derive consistent analytic results for the domains of instability of these new exact solutions as a function of the strength of the external potential and κ. For the repulsive potential we show that there is a translational instability which can be understood in terms of the energy landscape as a function of a stretching parameter and a translation parameter being a saddle near the exact solution. In this case, numerical simulations show that if we start with the exact solution, the initial wave function breaks into two pieces traveling in opposite directions. If we explore the slightly perturbed solution situations, a 1% change in initial conditions can change significantly the details of how the wave function breaks into two separate pieces. For the attractive potential, changing the initial conditions by 1% modifies the domain of stability only slightly. For the case of the attractive potential and negative g perturbed solutions merely oscillate with the oscillation frequencies predicted by the variational approximation.
We discuss the stability properties of the solutions of the general nonlinear Schrödinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (${ \mathcal P }{ \mathcal T }$) symmetric superpotential $W(x)$ that we considered earlier, Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation $\{{\rm{i}}\,{\partial }_{t}+{\partial }_{x}^{2}-{V}^{-}(x)+| \psi (x,t){| }^{2\kappa }\}\,\psi (x,t)=0,$ for arbitrary nonlinearity parameter κ. We study the bound state solutions when ${V}^{-}(x)\,=(1/4-{b}^{2}){\text{sech}}^{2}(x)$, which can be derived from two different superpotentials $W(x)$, one of which is complex and ${ \mathcal P }{ \mathcal T }$ symmetric. Using Derrick's theorem, as well as a time dependent variational approximation, we derive exact analytic results for the domain of stability of the trapped solution as a function of the depth b 2 of the external potential. We compare the regime of stability found from these analytic approaches with a numerical linear stability analysis using a variant of the Vakhitov–Kolokolov (V–K) stability criterion. The numerical results of applying the V–K condition give the same answer for the domain of stability as the analytic result obtained from applying Derrick's theorem. Our main result is that for $\kappa \gt 2$ a new regime of stability for the exact solutions appears as long as $b\gt {b}_{{\rm{crit}}}$, where ${b}_{{\rm{crit}}}$ is a function of the nonlinearity parameter κ. In the absence of the potential the related solitary wave solutions of the NLSE are unstable for $\kappa \gt 2$.
Currently, the proposed processing path for low enriched uranium – 10 wt. pct. molybdenum alloy (LEU-10Mo) monolithic fuel plates for high power research and test reactors includes hot isostatic pressing (HIP) to bond the aluminum cladding that encapsulates the fuel foil. Initial HIP experiments were performed at Idaho National Laboratory (INL) on approximately ¼ scale “mini” fuel plate samples using a HIP can design intended for these smaller experimental trials. These experiments showed that, with the addition of a co-rolled zirconium diffusion barrier on the LEU-10Mo alloy fuel foil, the HIP bonding process is a viable method for producing monolithic fuel plates. Further experimental trials at Los Alamos National Laboratory (LANL) effectively scaled-up the “mini” can design to produce full-size fuel prototypic plates. This report summarizes current efforts at LANL to produce a HIP can design that is further optimized for higher volume production runs. The production-optimized HIP can design goals were determined by LANL and Babcock & Wilcox (B&W) to include maintaining or improving the quality of the fuel plates produced with the baseline scaled-up mini can design, while minimizing material usage, improving dimensional stability, easing assembly and disassembly, eliminating machining, and significantly reducing welding. The initial small-scale experiments described in this report show that a formed-can approach can achieve the goals described above. Future work includes scaling the formed-can approach to full-size fuel plates, and current progress toward this goal is also summarized here.
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Ceramic nuclear fuel pellets represent the fuel of choice for most of the civilian nuclear reactors worldwide. Therefore, it is reasonable to expect the use of ceramic uranium-oxide pellets will continue for many years to come, because an extensive infrastructure is in place to support this strategic component of the energy industry, the technology is well-established and profitable, and the manufacturing process is flexible with the potential to support fuel reprocessing within the existing infrastructure. A better understanding of the properties of the starting materials, improving the control of the processes that are used to fabricate fuel pellets and understanding how the properties of these pellets change in service, represent important aspects that are being studied via experiments, models and simulations. A close integration of these approaches is essential if we are to find new ways to optimize both the fuel composition and structure for the purpose of improving performance and reducing costs.
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The purpose of this project is to: (1) Directly observe phase transformations and microstructure evolution using proton (and synchrotron x-ray) radiography and tomography; (2) Constrain phase-field models for microstructure evolution; (3) Experimentally control microstructure evolution during processing to enable co-design; and (4) Advance toward the MaRIE vision. Understand microstructure evolution and chemical segregation during solidification {yields} solid-state transformations in Pu-Ga.
We use experimentation and finite element modeling to study a Hot Isostatic Press (HIP) manufacturing process for U-10Mo Monolithic Fuel Plates. Finite element simulations are used to identify the material properties affecting the process and improve the process geometry. Accounting for the high temperature material properties and plasticity is important to obtain qualitative agreement between model and experimental results. The model allows us to improve the process geometry and provide guidance on selection of material and finish conditions for the process strongbacks. We conclude that the HIP can must be fully filled to provide uniform normal stress across the bonding interface.
Abstract Not Provided
The AMP (Advanced MultiPhysics) Nuclear Fuel Performance code is a new, three-dimensional, multi-physics tool that uses state-of-the-art solution methods and validated nuclear fuel models to simulate the nominal operation and anticipated operational transients of nuclear fuel. The AMP Nuclear Fuel Performance code leverages existing validated material models from traditional fuel performance codes and the Scale/ORIGEN-S spent-fuel characterization code to provide an initial capability that is shown to be sufficiently accurate for a single benchmark problem and anticipated to be accurate for a broad range of problems. The thermomechanics-chemical foundation can be solved in a time-dependent or quasi-static approach with any variation of operator-split or fully-coupled solutions at each time step. The AMP Nuclear Fuel Performance code provides interoperable interfaces to leading computational mathematics tools, which will simplify the integration of the code into existing parallel code suites for reactor simulation or lower-length-scale coupling. A baseline validation of the AMP Nuclear Fuel Performance code has been performed through the modeling of an experiment in the Halden Reactor Project (IFA-432), which is the first validation problem incorporated in the FRAPCON Integral Assessment report.
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