A numerical study of flow over a confined backward-facing step

Numerical solutions using the SIMPLE algorithms for laminar flow over a backward-facing step are presented. Five differencing schemes were used: hybrid; quadratic upwind (QUICK); second-order upwind (SOUD); central-differencing and a novel scheme named second-order upwind biased (SOUBD). The SOUBD scheme is shown to be part of a family of schemes which include the central-differencing, SOUD and QUICK schemes for uniform grids. The results of the backward-facing step problem are presented and are compared with other numerical solutions and experimental data to evaluate the accuracy of the differencing schemes. The accuracy of the differencing schemes was ascertained by using uniform grids of various grid densities. The QUICK, SOUBD and SOUD schemes gave very similar accurate results. The hybrid scheme suffered from excessive diffusion except for the finest grids and the central-differencing scheme only converged for the finest grids.     

A Skorokhod Problem formulation and large deviation analysis of a processor sharing model

Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between different data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buffer content. More precisely, we show how to represent the map in terms of a Skorokhod Problem, and from this infer that the mapping is well defined (existence and uniqueness) and well behaved (Lipschitz continuity). As an elementary application we present some large deviation estimates for a many data source model. This revised version was published online in June 2006 with corrections to the Cover Date.     

Twisted cubics, bis

We consider the smooth compactification constructed in [12] for a space of varieties like twisted cubics. We show this compactification embeds naturally in a product of flag varieties.Partially supported by CNPq, Pronex (ALGA)     

Performance analysis of test scheduling schemes for a multi-access communications network

In this paper, we investigate the performance of two implementable test scheduling schemes for a multi-access communication channel whose components are subject to failure or malfunction. We relate the reliability of the system design, as reflected by system failure rate parameters, and the frequency at which the system (or nodal subsystem) is tested for failure detection, to the underlying key message delay and throughput performance. We derive queue-size distribution results for a discreteGeom ^(X)/D/1 system, representing the operation of the multi-access channel, or of a network node operating as a communications or queueing processor, which is maintained by a periodic or near periodic test scheduling scheme. Explicit formulas are presented for the system behavior as exhibited by the generating functions of the system queue-size distributions. The mean message delay is then calculated. The mean delay (or mean system size/workload performance index) can then be optimized by selecting the proper scheme parameters, under specified system (and component) failure conditions, noting that performing a test at too high a rate leads to inefficient system bandwidth utilization, while if tests are not carried out often enough, excessive message (or task) retransmissions and delays ensue.     

Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Part I. Derivation of different formulations and constant density limit

The paper presents various formulations of characteristics-based schemes in the framework of the artificial-compressibility method for variable-density incompressible flows. In contrast to constant-density incompressible flows, where the characteristics-based variables reconstruction leads to a single formulation, in the case of variable density flows three different schemes can be obtained henceforth labeled as: transport, conservative and hybrid schemes. The conservative scheme results in pseudo-compressibility terms in the (multi-species) density reconstruction. It is shown that in the limit of constant density, the transport scheme becomes the (original) characteristics-based scheme for incompressible flows, but the conservative and hybrid schemes lead to a new characteristics-based variant for constant density flows. The characteristics-based schemes are combined with second and third-order interpolation for increasing the computational accuracy locally at the cell faces of the control volume. Numerical experiments for constant density flows reveal that all the characteristics-based schemes result in the same flow solution, but they exhibit different convergence behavior. The multigrid implementation and numerical studies for variable density flows are presented in Part II of this study.     

Secret sharing schemes on access structures with intersection number equal to one

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, structures such that there is at most one participant in the intersection of any two different minimal qualified subsets. The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. In addition, bounds on the optimal information rate are provided for the non-ideal case.     

Cheating in Visual Cryptography

A secret sharing scheme allows a secret to be shared among a set of participants, P, such that only authorized subsets of P can recover the secret, but any unauthorized subset cannot recover the secret. In 1995, Naor and Shamir proposed a variant of secret sharing, called visual cryptography, where the shares given to participants are xeroxed onto transparencies. If X is an authorized subset of P, then the participants in X can visually recover the secret image by stacking their transparencies together without performing any computation. In this paper, we address the issue of cheating by dishonest participants, called cheaters, in visual cryptography. The experimental results demonstrate that cheating is possible when the cheaters form a coalition in order to deceive honest participants. We also propose two simple cheating prevention visual cryptographic schemes.     

Constrained radar waveform optimization for a cooperative radar-communication system

The coexistence of radar-sensing and communication systems research has received a surge of interest in recent times to tackle the issue of spectrum inadequacy. Designing an optimized radar waveform for a coexistence scenario has been a challenging task for accomplishing the convergence of radar-sensing and communication functionalities, without degrading the performance at either end. This paper proposes a novel global optimization-based Spatial Branch and Bound (SBnB) approach to optimize the phase coefficients of a Non-Linear Frequency Modulated (NLFM) waveform in a CRCS framework. In addition, the Modified-Power Ratio Constraint-Cramér–Rao Lower Bound (M-PRC-CRLB), a local optimization-based approach is proposed to optimize the phase coefficients of an NLFM waveform. The spectral energy distribution and auto-correlation characteristics of an NLFM waveform are comprehensively investigated for various values of polynomial order (N) and at different threshold Signal-to-Noise-Ratio (SNR) values. To compare the proposed waveform design approaches (M-PRC-CRLB, SBnB) with the existing waveform design approaches namely, Minimum Estimation Error Variance (MEEV) and PRC- CRLB, a Peak-to-Side-Lobe-Ratio (PSLR), and Integrated-Side-Lobe-Ratio (ISLR) are evaluated at various polynomial orders and threshold SNR values. Furthermore, the performance of a CRCS is assessed using the radar estimation rate and communication data rate. The simulation results reveal that the proposed optimized radar waveform design approaches provide improved performance compared to the existing radar waveform design approaches in terms of radar estimation rate. Further, the proposed global optimization-based SBnB approach achieves a comparable performance of the communication data rate. In addition, the proposed approaches accomplish enhanced spectral utilization, controlled side-lobe energy levels, reduced range-domain ambiguities, and a higher information rate in a CRCS.     

Intelligent resource allocation for transmission security on IRS-assisted spectrum sharing systems with OFDM

In this paper, intelligent reflecting surface (IRS) technology is employed to enhance physical layer security (PLS) for spectrum sharing communication systems with orthogonal frequency division multiplexing (OFDM). Aiming to improve the secondary users’ secrecy rates, a design problem for jointly optimizing the transmission beamforming of secondary base station (SBS), the IRS’s reflecting coefficient and the channel allocation is formulated under the constraints of the requirements of minimum data rates of primary users and the interference between users. As the scenario is highly complex, it is quite challenging to address the non-convexity of the optimization problem. Thus, a deep reinforcement learning (DRL) based approach is taken into consideration. Specifically, we use dueling double deep Q networks (D3QN) and soft Actor–Critic (SAC) to solve the discrete and continuous action space optimization problems, respectively, taking full advantage of the maximum entropy RL algorithm to explore all possible optimal paths. Finally, simulation results show that our proposed approach has a great improvement in security transmission rate compared with the scheme without IRS and OFDM, and our proposed D3QN-SAC approach is more effective than other approaches in terms of maximum security transmission rate.