On the Variance of the Length of the Longest Common Subsequences in Random Words With an Omitted Letter

We investigate the variance of the length of the longest common subsequences of two independent random words of size $n$, where the letters of one word are i.i.d. uniformly drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m\}$, while the letters of the other word are i.i.d. drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m, \alpha_{m+1}\}$, with probability $p > 0$ to be $\alpha_{m+1}$, and $(1-p)/m > 0$ for all the other letters. The order of the variance of this length is shown to be linear in $n$.Comment: 19 page

Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations

In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small perturbation of a positive constant state. We first show the asymptotic stability of solutions to the Cauchy problem near the stationary state provided that the initial perturbation is sufficiently small. Moreover the convergence rates are obtained by combining the $L^p$-$L^q$ estimates for the linearized equations with time-weighted estimate.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1006.3606 by other author

Darcy's law and diffusion for a two-fluid Euler-Maxwell system with dissipation

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous justification of diffusion phenomena in fluid plasma at the linear level. Precisely, motivated by the classical Darcy's law for the nonconductive fluid, we first give a heuristic derivation of the asymptotic equations of the Euler-Maxwell system in large time. It turns out that both the density and the magnetic field tend time-asymptotically to the diffusion equations with diffusive coefficients explicitly determined by given physical parameters. Then, in terms of the Fourier energy method, we analyze the linear dissipative structure of the system, which implies the almost exponential time-decay property of solutions over the high-frequency domain. The key part of the paper is the spectral analysis of the linearized system, exactly capturing the diffusive feature of solutions over the low-frequency domain. Finally, under some conditions on initial data, we show the convergence of the densities and the magnetic field to the corresponding linear diffusion waves with the rate $(1+t)^{-5/4}$ in $L^2$ norm and also the convergence of the velocities and the electric field to the corresponding asymptotic profiles given in the sense of the geneneralized Darcy's law with the faster rate $(1+t)^{-7/4}$ in $L^2$ norm. Thus, this work can be also regarded as the mathematical proof of the Darcy's law in the context of collisional fluid plasma.Comment: 46 pages. The paper was modified according to referees' reports. Main modifications: Title, definition of the asymptotic profile (1.5)-(1.8), the statement of Theorem 1.1 where the assumption that |x| B_0 is L^1_x etc was removed, and some other corrected typos or minor mistakes pointed out in the report. The comments by anonymous reviewers are quite appreciated

Post-CHF Heat Transfer Experiments and Modeling at Subcooled and Low-quality Conditions

During postulated large break loss of coolant accidents (LB-LOCAs) in a water-cooled nuclear reactor, the reactor is expected to shut down but the fuel cladding temperature would still increase due to the release of the stored energy in the fuel and decay energy of fission products. To prevent the cladding from overheating, the Emergency Core Cooling System will start up to inject makeup water into the reactor core, during which post-critical heat flux (post-CHF) flow regimes could dominate the heat transfer from the cladding to the coolant. The heat transfer characteristics in the post-CHF flow regimes are important for reactor design and safety. In this research, a Post-CHF Heat Transfer (PCHT) test facility was designed and constructed to perform high-pressure (up to 1,000 psi or 6.8 MPa) post-CHF heat transfer experiments at high mass fluxes (up to 2,000 kg/m2-s) with large inlet subcooling values (up to 50 ºC). A COMSOL multiphysics model was developed to inform the test section design. All the instrumentation in the test facility to measure the temperature, pressure, pressure differential, flow rate, void fraction, and flow topology have been tested to ensure their functionality. Shakedown tests have been performed in the test facility, including hydrostatic leak test, pressure control test, subcooled boiling test, hot patch test, gamma densitometer test, and X-ray radiography system test. Reflooding and dry patch tests have been performed to study the wall heat transfer characteristics in the post-CHF flow regimes. In the reflooding tests, the quench curve indicates that the wall temperature has a rapid decrease in the quenched region, during which the heat (stored energy) release from the test section plays a significant role in the total wall heat flux to the fluid. Based on the convective heat transfer coefficient profile, it is believed that inverted annular film boiling (IAFB) regime exists right downstream of the quench front. In the dry patch tests, the convective heat transfer coefficient for the dry patches is larger than those calculated by three heat transfer correlations for IAFB in the literature, especially for conditions of relatively low wall superheats, which indicates that the motion of the dry patch along the heated surface enhances the heat transfer. In addition to the experimental study, some closure models in the two-fluid model for the IAFB regime are benchmarked and improved. A correlation for the liquid-side Nusselt number is developed based on a parametric study performed in this research. A laminar vapor film model and nine existing correlations for the interfacial friction factor are evaluated based on the IAFB experimental data. The comparisons suggest that the interfacial friction factor in the smooth IAFB region is primarily dependent on the gas Reynold number and vapor film thickness and that in the wavy IAFB region, it is dominantly affected by the interfacial waves. To predict the flow regime transition from IAFB to ISFB, a correlation for the critical Weber number is proposed as a function of two non-dimensional parameters, i.e., the Reynolds number and subcooling number. In summary, this research presents a number of original contributions to the field. The PCHT test facility with its unique test capabilities brings many benefits to the community and can assist in further nuclear reactor safety improvement. The improved post-CHF closure models could be used in reactor system analysis to improve the IAFB modeling.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162896/1/qingqliu_1.pd

Earning Maximization with Quality of Charging Service Guarantee for IoT Devices

Resonant Beam Charging (RBC) is a promising Wireless Power Transfer (WPT) technology to provide long-range, high-power, mobile and safe wireless power for the Internet of Things (IoT) devices. The Point-to-Multipoint (PtMP) RBC system can charge multiple receivers simultaneously similar to WiFi communications. To guarantee the Quality of Charging Service (QoCS) for each receiver and maximize the overall earning in the PtMP RBC service, we specify the Charging Pricing Strategy (CPS) and develop the High Priority Charge (HPC) scheduling algorithm to control the charging order and power allocation. Each receiver is assigned a priority, which is updated dynamically based on its State of Charging (SOC) and specified charging power. The receivers with high priorities are scheduled to be charged in each time slot. We present the pseudo code of the HPC algorithm based on quantifying the receiver's SOC, discharging energy and various relevant parameters. Relying on simulation analysis, we demonstrate that the HPC algorithm can achieve better QoCS and earning than the Round-Robin Charge (RRC) scheduling algorithm. Based on the performance evaluation, we illustrate that the methods to improve the PtMP RBC service are: 1) limiting the receiver number within a reasonable range and 2) prolonging the charging duration as long as possible. In summary, the HPC scheduling algorithm provides a practical strategy to maximize the earning of the PtMP RBC service with each receiver's QoCS guarantee

An Efficient Anonymous Authentication Scheme for Internet of Vehicles

Internet of Vehicles (IoV) is an intelligent application of IoT in smart transportation, which can make intelligent decisions for passengers. It has drawn extensive attention to improve traffic safety and efficiency and create a more comfortable driving and riding environment. Vehicular cloud computing is a variant of mobile cloud computing, which can process local information quickly. The cooperation of the Internet and vehicular cloud can make the communication more efficient in IoV. In this paper, we mainly focus on the secure communication between vehicles and roadside units. We first propose a new certificateless short signature scheme (CLSS) and prove the unforgeability of it in random oracle model. Then, by combining CLSS and a regional management strategy we design an efficient anonymous mutual quick authentication scheme for IoV. Additionally, the quantitative performance analysis shows that the proposed scheme achieves higher efficiency in terms of interaction between vehicles and roadside units compared with other existing schemes

MDBV: Monitoring Data Batch Verification for Survivability of Internet of Vehicles

Along with the development of vehicular sensors and wireless communication technology, Internet of Vehicles (IoV) is emerging that can improve traffic efficiency and provide a comfortable driving environment. However, there is still a challenge how to ensure the survivability of IoV. Fortunately, this goal can be achieved by quickly verifying real-time monitoring data to avoid network failure. Aggregate signature is an efficient approach to realize quick data verification quickly. In this paper, we propose a monitoring data batch verification scheme based on an improved certificateless aggregate signature for IoV, named MDBV. The size of aggregated verification message is remain roughly constant even as the increasing number of vehicles in MDBV. Additionally, MDBV is proved to be secure in the random oracle model assuming the intractability of the computational Diffie-Hellman problem. In consideration of the network survivability and performance, the proposed MDBV can decrease the computation overhead and is more suitable for IoV

Adaptive Resonant Beam Charging for Intelligent Wireless Power Transfer

As a long-range high-power wireless power transfer (WPT) technology, resonant beam charging (RBC) can transmit Watt-level power over long distance for the devices in the internet of things (IoT). Due to its open-loop architecture, RBC faces the challenge of providing dynamic current and voltage to optimize battery charging performance. In RBC, battery overcharge may cause energy waste, thermal effects, and even safety issues. On the other hand, battery undercharge may lead to charging time extension and significant battery capacity reduction. In this paper, we present an adaptive resonant beam charging (ARBC) system for battery charging optimization. Based on RBC, ARBC uses a feedback system to control the supplied power dynamically according to the battery preferred charging values. Moreover, in order to transform the received current and voltage to match the battery preferred charging values, ARBC adopts a direct current to direct current (DC-DC) conversion circuit. Relying on the analytical models for RBC power transmission, we obtain the end-to-end power transfer relationship in the approximate linear closed-form of ARBC. Thus, the battery preferred charging power at the receiver can be mapped to the supplied power at the transmitter for feedback control. Numerical evaluation demonstrates that ARBC can save 61% battery charging energy and 53%-60% supplied energy compared with RBC. Furthermore, ARBC has high energy-saving gain over RBC when the WPT is unefficient. ARBC in WPT is similar to link adaption in wireless communications. Both of them play the important roles in their respective areas.Comment: 12 pages, 24 figures, IEEE Internet of Things Journa

Fundamental Tradeoffs in Communication and Trajectory Design for UAV-Enabled Wireless Network

The use of unmanned aerial vehicles (UAVs) as aerial communication platforms is of high practical value for future wireless systems such as 5G, especially for swift and on-demand deployment in temporary events and emergency situations. Compared to traditional terrestrial base stations (BSs) in cellular network, UAV-mounted aerial BSs possess stronger line-of-sight (LoS) links with the ground users due to their high altitude as well as high and flexible mobility in three-dimensional (3D) space, which can be exploited to enhance the communication performance. On the other hand, unlike terrestrial BSs that have reliable power supply, aerial BSs in practice have limited on-board energy, but require significant propulsion energy to stay airborne and support high mobility. Motivated by the above new considerations, this article aims to revisit some fundamental tradeoffs in UAV-enabled communication and trajectory design. Specifically, it is shown that communication throughput, delay, and (propulsion) energy consumption can be traded off among each other by adopting different UAV trajectory designs, which sheds new light on their traditional tradeoffs in terrestrial communication. Promising directions for future research are also discussed.Comment: [ UAV-Enabled Aerial Base Station (BS) series, the fourth paper ] The other three technical works are "Common Throughput Maximization in UAV-Enabled OFDMA Systems with Delay Consideration", "Joint Trajectory and Communication Design for Multi-UAV Enabled Wireless Networks", "Capacity Characterization of UAV-Enabled Two-User Broadcast Channel

Preferential imbibition in a dual-permeability pore network

A deep understanding of two-phase displacement in porous media with permeability contrast is essential for the design and optimisation of enhanced oil recovery processes. In this paper, we investigate the forced imbibition behaviour in two dual-permeability geometries that are of equal permeability contrast. First, a mathematical model is developed for the imbibition in a pore doublet, which shows that the imbibition dynamics can be fully described by the viscosity ratio $\lambda$ and capillary number $Ca_m$ which creatively incorporates the influence of channel width and length. Through the finite difference solution of the mathematical model, a $\lambda-Ca_m$ phase diagram is established to characterise the imbibition preference in the pore doublet. We then investigate the imbibition process in a dual-permeability pore network using a well-established lattice Boltzmann method, focusing on the competition between the viscous and capillary forces. Like in the pore doublet, the preferential imbibition occurs in high permeability zone at high $Ca_{m}$ but in low permeability zone at low $Ca_{m}$. When $Ca_m$ is not sufficiently high, an oblique advancing pattern is observed which is attributed to non-trivial interfacial tension. Thanks to the newly defined capillary number, the critical $Ca_{m}$ curve on which the breakthrough simultaneously occurs in both permeability zones, is found to match perfectly with that from the pore doublet and it is the optimal condition for maximising the imbibition efficiency in the entire pore network.Comment: 11 figures, 21 page