Radio frequency (RF) coaxial connectors are crucial in high-speed digital systems for data transmission. Connectors applied in harsh environments will be degraded over time, affecting the signal integrity. At present, a suitable equalization technology is of substantial value for enhancing the quality of high-speed signal transmission. However, there is limited research focusing on specific equalization designs for degraded connectors. In this current work, based on the theoretical analysis, simulations validation and experimental testing, an equivalent circuit model of the degraded connector was developed. Furthermore, an equalization structure consisting of series resistance and capacitance was proposed. The transmission loss caused by the connector degradation was compensated effectively using this method. Meanwhile, eye diagram characteristics were improved significantly at the receiver where zero timing jitter and an almost full eye opening were achieved. Equalization enhances the eye opening factor by over 50% compared to the uncompensated system. This paper integrates electrical contact theory with high-speed equalization design. Tools and guidance were provided through the proposed modeling techniques for studying equalization effects of this degraded connector system in designs and applications.

In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety A, we can construct a CM abelian variety B such that all non-trivial Hodge relations between the holomorphic periods of the product $A\times B$ are generated by monomial quadratic ones which are also explicit. Moreover, B splits over the Galois closure of the CM field associated with A.

Ultra-thin liquid sheets generated by impinging two liquid jets are crucial high-repetition-rate targets for laser ion acceleration and ultra-fast physics, and serve widely as barrier-free samples for structural biochemistry. The impact of liquid viscosity on sheet thickness should be comprehended fully to exploit its potential. Here, we demonstrate experimentally that viscosity significantly influences thickness distribution, while surface tension primarily governs shape. We propose a thickness model based on momentum exchange and mass transport within the radial flow, which agrees well with the experiments. These results provide deeper insights into the behaviour of liquid sheets and enable accurate thickness control for various applications, including atomization nozzles and laser-driven particle sources.

To meet the demands of laser-ion acceleration at a high repetition rate, we have developed a comprehensive diagnostic system for real-time and in situ monitoring of liquid sheet targets (LSTs). The spatially resolved rapid characterizations of an LST’s thickness, flatness, tilt angle and position are fulfilled by different subsystems with high accuracy. With the help of the diagnostic system, we reveal the dependence of thickness distribution on collision parameters and report the 238-nm liquid sheet generated by the collision of two liquid jets. Control methods for the flatness and tilt angle of LSTs have also been provided, which are essential for applications of laser-driven ion acceleration and others.

Here, we report the generation of MeV alpha-particles from H-11B fusion initiated by laser-accelerated boron ions. Boron ions with maximum energy of 6 MeV and fluence of 109/MeV/sr@5 MeV were generated from 60 nm-thick self-supporting boron nanofoils irradiated by 1 J femtosecond pulses at an intensity of 1019 W/cm2. By bombarding secondary hydrogenous targets with the boron ions, 3 × 105/sr alpha-particles from H-11B fusion were registered, which is consistent with the theoretical yield calculated from the measured boron energy spectra. Our results demonstrated an alternative way toward ultrashort MeV alpha-particle sources employing compact femtosecond lasers. The ion acceleration and product measurement scheme are referential for the studies on the ion stopping power and cross section of the H-11B reaction in solid or plasma.

Post-acceleration of protons in helical coil targets driven by intense, ultrashort laser pulses can enhance ion energy by utilizing the transient current from the targets’ self-discharge. The acceleration length of protons can exceed a few millimeters, and the acceleration gradient is of the order of GeV/m. How to ensure the synchronization between the accelerating electric field and the protons is a crucial problem for efficient post-acceleration. In this paper, we study how the electric field mismatch induced by current dispersion affects the synchronous acceleration of protons. We propose a scheme using a two-stage helical coil to control the current dispersion. With optimized parameters, the energy gain of protons is increased by four times. Proton energy is expected to reach 45 MeV using a hundreds-of-terawatts laser, or more than 100 MeV using a petawatt laser, by controlling the current dispersion.

Let $\mathcal {A} \rightarrow S$ be an abelian scheme over an irreducible variety over $\mathbb {C}$ of relative dimension $g$. For any simply-connected subset $\Delta$ of $S^{\mathrm {an}}$ one can define the Betti map from $\mathcal {A}_{\Delta }$ to $\mathbb {T}^{2g}$, the real torus of dimension $2g$, by identifying each closed fiber of $\mathcal {A}_{\Delta } \rightarrow \Delta$ with $\mathbb {T}^{2g}$ via the Betti homology. Computing the generic rank of the Betti map restricted to a subvariety $X$ of $\mathcal {A}$ is useful to study Diophantine problems, e.g. proving the geometric Bogomolov conjecture over char $0$ and studying the relative Manin–Mumford conjecture. In this paper we give a geometric criterion to detect this rank. As an application we show that it is maximal after taking a large fibered power (if $X$ satisfies some conditions); it is an important step to prove the bound for the number of rational points on curves (Dimitrov et al., Uniformity in Mordell–Lang for Curves, Preprint (2020), arXiv:2001.10276). Another application is to answer a question of André, Corvaja and Zannier and improve a result of Voisin. We also systematically study its link with the relative Manin–Mumford conjecture, reducing the latter to a simpler conjecture. Our tools are functional transcendence and unlikely intersections for mixed Shimura varieties.

In this paper we prove the mixed Ax–Schanuel theorem for the universal abelian varieties (more generally any mixed Shimura variety of Kuga type), and give some simple applications. In particular, we present an application for studying the generic rank of the Betti map.

We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-Schanuel conjecture and explain its relation with the logarithmic Ax theorem and the Ax-Lindemann theorem which we shall prove. All these bi-algebraic and transcendental results extend their counterparts for mixed Shimura varieties. In the end we briefly discuss the André–Oort and Zilber–Pink type problems for enlarged mixed Shimura varieties.