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Considering the ocean water's optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable (CV) quantum key distribution (QKD) based air-to-water channel. The effects of the absorption and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

In this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supported boundary conditions along other edges are developed, which makes the dynamic stiffness method (DSM) more applicable to engineering problems compared to existing works. The Wittrick–Williams algorithm of the DSM is applied with the explicit expressions of the J0 count for plate elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. Moreover, the present theory is applied for exact free vibration analysis within the whole frequency range of three built-up structures which are commonly encountered in engineering. The results show that the DSM gives exact results with as much as 100-fold computational efficiency advantage over the commercial finite element method. Besides, benchmark results are also provided.

Explicit solutions to vertical and horizontal displacements are derived for large deformation of a cantilever beam under point load at the free end by an improved homotopy analysis method (IHAM). Quadratic and cubic nonlinear differential equations are adopted to construct more proficient nonlinear equations for vertical and horizontal displacements respectively combined with their currently available nonlinear displacement equations. Higher-order nonlinear iterative homotopy equations are established to solve the vertical and horizontal displacements by combining simultaneous equations of the constructed nonlinear equations and the auxiliary linear equations. The convergence range of vertical displacement is extended by the homotopy-Páde approximation. The explicit solutions to the vertical and horizontal displacements are in favorable agreements with the respective exact solutions. The convergence ranges for a relative error of 1% by the improved homotopy analysis method for vertical and horizontal displacements increases by 60% and 7%, respectively. These explicit formulas are helpful in practical engineering design for very slender structures, such as high-rise buildings and long bridges.

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We investigate the composable security of unidimensional continuous variable quantum key distribution (UCVQKD), which is based on the Gaussian modulation of a single quadrature of the coherent-state of light, aiming to provide a simple implementation of key distribution compared to the symmetrically modulated Gaussian coherent-state protocols. This protocol neglects the necessity in one of the quadrature modulation in coherent-states and hence reduces the system complexity. To clarify the influence of finite-size effect and the cost of performance degeneration, we establish the relationship of the balanced parameters of the unmodulated quadrature and estimate the precise secure region. Subsequently, we illustrate the composable security of the UCVQKD protocol against collective attacks and achieve the tightest bound of the UCVQKD protocol. Numerical simulations show the asymptotic secret key rate of the UCVQKD protocol, together with the symmetrically modulated Gaussian coherent-state protocols.

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