PARAMETRIC FORMULATION OF THE FLOODABLE LENGTH CURVE: APPLICATION CASE TO OFFSHORE PATROL VESSELS

The residual buoyancy of vessels after damage has a fundamental role in their survivability and it is implemented through adequate ship internal subdivision. Traditionally the number and the position of transverse watertight bulkheads are selected for most ships early in the design phase by means of the “floodable length curve” coupled with the concept of “margin line”. However, for naval vessels, it is more and more common during the acquisition process to explore a wide domain of feasible ships, identified with the assistance of automated processes and assessed also in terms of capabilities, among which is survivability. The generation and the comparison of a considerable number of different ship configurations is very time consuming. Therefore recourse to a parametric expression of the floodable length curve is considered to be a very efficient approach and would thus enable characterisation of the ship, in terms of survivability performance. In this paper such an approach is presented, using an offshore patrol vessel (OPV) as the case study.

Fishnet four-point integrals: integrable representations and thermodynamic limits

We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.

Exact parametric causal mediation analysis for a binary outcome with a binary mediator

With reference to causal mediation analysis, a parametric expression for natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator, both modelled via a logistic regression. The proposed effect decomposition operates on the odds ratio scale and does not require the outcome to be rare. It generalizes the existing ones, allowing for interactions between both the exposure and the mediator and the confounding covariates. The derived parametric formulae are flexible, in that they readily adapt to the two different natural effect decompositions defined in the mediation literature. In parallel with results derived under the rare outcome assumption, they also outline the relationship between the causal effects and the correspondent pathway-specific logistic regression parameters, isolating the controlled direct effect in the natural direct effect expressions. Formulae for standard errors, obtained via the delta method, are also given. An empirical application to data coming from a microfinance experiment performed in Bosnia and Herzegovina is illustrated.

Stress Concentration Factors for Welded Plate T-Joints Subjected to Tensile, Bending and Shearing Loads

The paper deals with the problem of stress concentration at the weld toe of a plate T-joint subjected to axial, bending, and shearing loading modes. Theoretical stress concentration factors were obtained from numerical simulations using the finite element method for several thousand geometrical cases, where five of the most important geometrical parameters of the joint were considered to be independent variables. For each loading mode—axial, bending, and shearing—highly accurate closed form parametric expression has been derived with a maximum percentage error lower than 2% with respect to the numerical values. Validity of each approximating formula covers the range of dimensional proportions of welded plate T-joints used in engineering applications. Two limiting cases are also included in the solutions—when the weld toe radius tends to zero and the main plate thickness becomes infinite.

Robust Parametric Control of Lorenz System via State Feedback

This paper considers the parametric control to the Lorenz system by state feedback. Based on the solutions of the generalized Sylvester matrix equation (GSE), the unified explicit parametric expression of the state feedback gain matrix is proposed. The closed loop of the Lorenz system can be transformed into an arbitrary constant matrix with the desired eigenstructure (eigenvalues and eigenvectors). The freedom provided by the parametric control can be fully used to find a controller to satisfy the robustness criteria. A numerical simulation is developed to illustrate the effectiveness of the proposed approach.

Parametric Formulation of the Floodable Length Curve: Application Case to Offshore Patrol Vessels

The residual buoyancy of vessels after damage has a fundamental role in their survivability and it is implemented through adequate ship internal subdivision. Traditionally the number and the position of transverse watertight bulkheads are selected for most ships early in the design phase by means of the “floodable length curve” coupled with the concept of “margin line”. However, for naval vessels, it is more and more common during the acquisition process to explore a wide domain of feasible ships, identified with the assistance of automated processes and assessed also in terms of capabilities, among which is survivability. The generation and the comparison of a considerable number of different ship configurations is very time consuming. Therefore recourse to a parametric expression of the floodable length curve is considered to be a very efficient approach and would thus enable characterisation of the ship, in terms of survivability performance. In this paper such an approach is presented, using an offshore patrol vessel (OPV) as the case study.

Airfoil Optimization of Land-Yacht Robot Based on Hybrid PSO and GA

Airfoil optimization algorithm is studied and a hybrid PSO and GA method is proposed in this paper. After function test, it shows that algorithm is well in convergence performance, fast speed, and optimization capability. Then, the airfoil parametric expression theory is analyzed. A new airfoil is obtained after combining CFD and PSO-GA optimization. The aerodynamic of new airfoil is compared with the airfoil optimized by GA-PSO and basic airfoil NACA0018. The results indicate that new airfoil is better than the other two airfoils in lift coefficient, lift-drag ratio, and surface pressure. At last, wing-sail of new airfoil and NACA0018 wing-sail are designed and manufactured. Both of them are applied in land-yacht robot linear motion and steering motion experiment. For the linear motion, in the situation of wind speed being 15[Formula: see text]m/s and angle of attack being 5, running speed of robot with optimized new wing-sail is 1.853[Formula: see text]m/s. In steering motion, trajectory with new wing-sail is closer to the real situation and it gets more thrust. The experiments data verify that the simulation results are correct and PSO-GA algorithm is effective.

An anelliptic approximation for geometric spreading in transversely isotropic and orthorhombic media

The relative geometric spreading along the raypath contributes to the amplitude decay of the seismic wave propagation that needs to be considered for amplitude variation with offset or other seismic data processing methods that require the true amplitude processing. Expressing the P-wave geometric spreading factor in terms of the offset-traveltime-based parameters is a more practical and convenient way because these parameters can be estimated from the nonhyperbolic velocity analysis. We have developed an anelliptic approximation for the relative geometric spreading of P-wave in a homogeneous transversely isotropic medium with vertical symmetry axis (VTI) and an orthorhombic (ORT) medium under the acoustic anisotropy assumption. The coefficients in our approximation are only defined within the symmetry planes and computed from fitting with the exact parametric expression. For an ORT model, due to the symmetric behavior in different symmetry planes, the other coefficients in the approximation can be easily obtained by making corresponding changes in indices from the computed coefficients in one symmetry plane. From the numerical examples, we found that for a homogeneous VTI model, the anelliptic approximation is more accurate than the generalized nonhyperbolic moveout approximation form for larger offset. For a homogeneous ORT model, our anelliptic approximation is more accurate than its traveltime-based counterparts. Using the Dix-type equations for the effective parameters, our anelliptic form approximation is extended to a multilayered VTI and ORT models and has accurate results in both models.

An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that govern its performance as a basic constituent of flexure mechanisms. This paper presents a new modeling approach for obtaining insight into the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear, and torsion deformation. The approach is based on the use of a discretized version of a finite (i.e., nonlinear) strain spatial beam formulation for extracting analytical expressions that describe deformation and stiffness characteristics of a flexure strip in a parametric format. This particular way of closed-form modeling exploits the inherent finite-element assumptions on interpolation and also lends itself for numeric implementation. As a validating case study, a closed-form parametric expression is derived for the lateral support stiffness of a flexure strip and a parallelogram flexure mechanism. This captures a combined torsion–bending dictated geometrically nonlinear effect that undermines the support bearing stiffness when the mechanism moves in the intended degree of freedom (DoF). The analytical result is verified by simulations and experimental measurements.