Quasi-homomorphisms of quantum cluster algebras

In this paper, we study quasi-homomorphisms of quantum cluster algebras, which are quantum analogy of quasi-homomorphisms of cluster algebras introduced by Fraser. For a quantum Grassmannian cluster algebra $\mathbb{C}_q[{\rm Gr}(k,n)]$, we show that there is an associated braid group and each generator $\sigma_i$ of the braid group preserves the quasi-commutative relations of quantum Pl\"{u}cker coordinates and exchange relations of the quantum Grassmannian cluster algebra. We conjecture that $\sigma_i$ also preserves $r$-term ($r \ge 4$) quantum Pl\"{u}cker relations of $\mathbb{C}_q[{\rm Gr}(k,n)]$ and other relations which cannot be derived from quantum quantum Pl\"{u}cker relations (if any). Up to this conjecture, we show that $\sigma_i$ is a quasi-automorphism of $\mathbb{C}_q[{\rm Gr}(k,n)]$ and the braid group acts on $\mathbb{C}_q[{\rm Gr}(k,n)]$

Joint Secure Communication and Radar Beamforming: A Secrecy-Estimation Rate-Based Design

This paper considers transmit beamforming in dual-function radar-communication (DFRC) system, where a DFRC transmitter simultaneously communicates with a communication user and detects a malicious target with the same waveform. Since the waveform is embedded with information, the information is risked to be intercepted by the target. To address this problem, physical-layer security technique is exploited. By using secrecy rate and estimation rate as performance measure for communication and radar, respectively, three secrecy rate maximization (SRM) problems are formulated, including the SRM with and without artificial noise (AN), and robust SRM. For the SRM beamforming, we prove that the optimal beamformer can be computed in closed form. For the AN-aided SRM, by leveraging alternating optimization similar closed-form solution is obtained for the beamformer and the AN covariance matrix. Finally, the imperfect CSI of the target is also considered under the premise of a moment-based random phase-error model on the direction of arrival at the target. Simulation results demonstrate the efficacy and robustness of the proposed designs.Comment: 14 page

Numerical Simulation on Forced Convection Cooling of Horizontal Ionic Wind with Multi-electrodes

Enhancement ofheat transfer plays an important role in the cooling of electronic or refrigeration systems, and its characteristics could strongly affect the stability and performance of such systems. To enhance heat transfer, air cooling of forced convection remains one of the main solutions. For example, conventional rotary-fan air cooling is still dominant in many areas. However, with the increasing of heat generation in these systems, the limitation of the conventional rotary-fan air cooling is become more obvious. So, demands in novel air cooling technology become necessary, e.g., silent and high efficient air cooling. Recently, ionic wind, which has no moving part and is easily miniaturized, shows great potential in heat dissipation and attracts widespread attentions. In this work, ionic wind, which is produced by wire to plate configuration for forced convection enhancement of horizontal flow along the plate, is numerically investigated. Firstly, a multi-physic model, which accounts for electric field, charge distribution, fluid dynamics, and heat transfer phenomenon, is presented. Comparisons between the simulation and literature data are conducted. Results show that better agreements are achieved by the developed model. Secondly, influences of the emitting electrodes numbers are analyzed. Results show that multiple electrodes configuration has higher performance in terms of heat transfer coefficient than that of the single electrode. Investigations are also carried out on the influences of the distances between the emitting electrodes. Thirdly, effects of the main parameters of ionic wind, such as the inlet velocity, and voltage applied on the electrodes etc., are investigated. Finally, by using the multi-physic model of ionic wind, characteristics of the heat transfer are predicted. It is found that the maximum enhancement of average heat transfer coefficient could reach around 150 %