Geometric Conditions for the Exact Observability of Schr\"{o}dinger Equations with Point Interaction and Inverse-Square Potentials on Half-Line

We provide necessary and sufficient conditions for the exact observability of the Schrodinger equations with point interaction and inverse-square potentials on half-line. The necessary and sufficient condition for these two cases are derived from two Logvinenko-Sereda type theorems for generalized Fourier transform. Specifically, the generalized Fourier transform associated to the Schr\"{o}dinger operators with inverse-square potentials on half-line are the well known Hankel transforms. We provide a necessary and sufficient condition for a subset $\Omega$ such that a function with its Hankel transform supporting in a given interval can be bounded, in $L^{2}$-norm, from above by its restriction to the set $\Omega$, with constant independent of the position of the intervalComment: arXiv admin note: text overlap with arXiv:2003.11263, arXiv:2007.04096 by other author

Observability and unique continuation inequalities for the Schr\"{o}dinger equations with inverse-square potentials

This paper is inspired by Wang, Wang and Zhang's work [ Observability and unique continuation inequalities for the Schr\"odinger equation. J. Eur. Math. Soc. 21, 3513--3572 (2019)], where they present several observability and unique continuation inequalities for the free Schr\"{o}dinger equation in $\mathbb{R}^{n}$. We extend all such observability and unique continuation inequalities for the Schr\"{o}dinger equations on half-line with inverse-square potentials. Technically, the proofs essentially rely on the representation of the solution, a Nazarov type uncertainty principle for the Hankel transform and an interpolation inequality for functions whose Hankel transform have compact support.Comment: 45 page

Design strategies for optimizing high burnup fuel in pressurized water reactors

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2003.Includes bibliographical references (p. 254-264).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.This work is focused on the strategy for utilizing high-burnup fuel in pressurized water reactors (PWR) with special emphasis on the full array of neutronic considerations. The historical increase in batch-averaged discharge fuel burnup, from ~30 MWd/kg in the 1970s to ~50 MWd/kg today, was achieved mainly by increasing the reload fuel enrichment to allow longer fuel cycles: from an average of 12 months to about 18 months. This also reduced operating costs by improving the plant capacity factor. Recently, because of limited spent fuel storage capacity, increased core power output and the search for increased proliferation resistance, achieving burnup in the 70 to 100 MWd/kg range has attracted considerable attention. However the implications of this initiative have not been fully explored; hence this work defines the practical issues for high-burnup PWR fuels based on neutronic, thermal hydraulic and economic considerations as well as spent fuel characteristics. In order to evaluate the various high burnup fuel design options, an improved MCNP-ORIGEN depletion program called MCODE was developed. A standard burnup predictor-corrector algorithm is implemented, which distinguishes MCODE from other MCNP-ORIGEN linkage codes. Using MCODE, the effect of lattice design (moderation effect) on core design and spent fuel characteristics is explored. Characterized by the hydrogen-to-heavy-metal ratio (H/HM), the neutron spectrum effect in UO2/H2O lattices is investigated for a wide range of moderation, from fast spectra to over-thermalized spectra. It is shown that either wetter or very dry lattices are preferable in terms of achievable burnup potential to those having an epithermal spectrum. Wet lattices are the preferred high burnup approach due to improved proliferation resistance. The constraint of negative moderator temperature coefficient (MTC) requires that H/HM values (now at 3.4) remain below ~6.0 for PWR lattices. Alternative fuel choices, including the conventional solid pellets, central-voided annular pellets, Internally- & eXternally-cooled Annular Fuel (IXAF), and different fuel forms are analyzed to achieve a wetter lattice. Although a wetter lattice has higher burnup potential than the reference PWR lattice, the requirement of a fixed target cycle energy production necessitates higher initial fuel enrichments to compensate for the loss of fuel mass in a wetter lattice. Practical issues and constraints for the high burnup fuel include neutronic reactivity control, heat transfer margin, and fission gas release. Overall the IXAF design appears to be the most promising approach to realization of high burnup fuel. High-burnup spent fuel characteristics are compared to the reference spent fuel of 33 MWd/kg, representative of most of the spent fuel inventory. Although an increase of decay power and radioactivity per unit mass of initial heavy metal is immediately observed, the heat load (integration of decay power over time) per unit electricity generation decreases as the fuel discharge burnup increases. The magnitude of changes depends on the time after discharge. For the same electricity production, not only the mass and volume of the spent fuel are reduced, but also, to a lesser extent, the total heat load of the spent fuel. Since the heat load in the first several hundred years roughly determines the capital cost of the repository, a high burnup strategy coupled with adequate cooling time, may provide a cost-reduction approach to the repository. High burnup is beneficial to enhancing the proliferation resistance. The plutonium vector in the high-burnup spent fuel is degraded, hence less attractive for weapons. For example, the ratio of Pu-238 to Pu-239 increases with burnup to the 2.5 power. However, the economic benefits are uncertain. Under the current economic conditions, the PWR fuel burnup appears to have a shallow optimum discharge burnup between 50 and 80 MWd/kg. The actual minimum is influenced by the financing costs as well as the cost of refueling shutdowns. Since the fuel cycle back-end benefits will accrue to the federal government, the current economic framework, such as the waste fee based on the electricity produced rather than volume or actinide content, does not create an incentive for utilities to increase burnup. Different schemes exist for fuel management of high burnup PWR cores. For the conventional core design, a generalized enrichment-burnup correlation (applicable between 3 w/o and 20 w/o) was produced based on CASMO/SIMULATE PWR core calculations. Among retrofit cores, increasing the number of fuel batches is preferred over increasing the cycle length due to nuclear fuel cycle economic imperatives. For future core designs, a higher power-density core is a very attractive option to cut down the busbar cost. The IXAF concept possesses key design characteristics that provide the necessary thermal margins at high core power densities. In this regard, the IXAF fuel deserves further investigation to fully exploit its high burnup capability.by Zhiwen Xu.Ph.D

Molecular Detection of Porcine Torovirus in Piglets with Diarrhea in Southwest China

Porcine torovirus (PToV) was detected from intestinal samples of piglets with diarrhea from 20 farms in southwest China. The total prevalence of PToV was 45% (9 out of 20 farms); it was the first detection of PToV in China, and also the study analyzed the phylogenetic relationships between the Chinese PToV and PToV reference strains as well as other representative toroviruses. Genetic and phylogenetic analysis showed the existence of genetic diversity among geographically separated PToV. Statistical analysis of the PToV positive rate as well as a survey for other enteric pathogens in diarrheic pigs suggests that PToV may play a role as a causative agent of severe diarrhea in piglets

Dual-terminal event triggered control for cyber-physical systems under false data injection attacks

summary:This paper deals with the problem of security-based dynamic output feedback control of cyber-physical systems (CPSs) with the dual-terminal event triggered mechanisms (DT-ETM) under false data injection (FDI) attacks. Considering the limited attack energy, FDI attacks taking place in transmission channels are modeled as extra bounded disturbances for the resulting closed-loop system, thus enabling $H_{\infty}$ performance analysis with a suitable $\varrho$ attenuation level. Then two buffers at the controller and actuator sides are skillfully introduced to cope with the different transmission delays in such a way to facilitate the subsequent security analysis. Next, a dynamic output feedback security control (DOFSC) model based on the DT-ETM schemes under FDI attacks is well constructed. Furthermore, novel criteria for stability analysis and robust stabilization are carefully derived by exploiting Lyapunov-Krasovskii theory and LMIs technique. Finally, an illustrative example is provided to show the effectiveness of the proposed method