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This paper employs a numerical approach to investigate the impact of liquidity shocks on European options in modeling markets. To accurately capture the behavior of European options under liquidity shocks, a coupled system of differential equations is employed, consisting of a degenerate parabolic equation and a diffusion-free equation. The primary focus is on developing and analyzing implicit-explicit methods for numerically simulating European option pricing, specifically considering the presence of liquidity shocks while ensuring the positivity of the solution. The paper also includes convergence analysis and establishes the discrete comparison principle for the developed methods. Numerical experiments are conducted using both uniform and nonuniform meshes to validate the theoretical findings, demonstrating the efficiency and accuracy of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a distributed bearing-based formation control scheme with finite-time convergency is proposed for multiple underactuated surface vessels (USVs). By virtue of the guide point-based model transformation method, the dimension of underactuated tracking error dynamics can be reduced from three to two. This allows us to convert the actuator model to a fully form that matches dimension-reduced tracking error dynamics. Further, to reduce the computation complexity, a finite-time recruited filter is designed according to first-order Levant differentiator. At meanwhile, auxiliary error compensation signals are introduced to address unknowns stemming from filter process and system dynamics. Since merely relative-distances and inner bearings are utilized in the proposed bearing-based formation approaches, the proposed control scheme provides a feasible solution to achieve formation control under body-fixed frame. Finally, theoretical analysis and numerical simulations are presented to demonstrate the efficacy. • Bearing-based finite-time formation control. • Underactuated surface vessels. • Levant differentiator. • Command filtered backstepping with error compensation signals and compensated errors. [ABSTRACT FROM AUTHOR]

What are the geometrical and mechanical properties ruling bistability of Kresling origami metamaterials? How can we tune the magnitude of their axial-torsional coupling? Complete answers to these compelling questions cannot be found in the scientific literature, as the intertwining between bistability, axial-torsional coupling and an other significant behaviour, namely transverse dilation/contraction, remains mostly uninvestigated. This contribution aims at shedding light on this intertwining, through the use of a discrete model of Kresling origami that takes into account folding resistance. The present study is mostly computational and involves both pre- and post-critical analyses. It is based on displacement controlled tests — shearing and axial shortening/lengthening. Single-storey Kresling origami's are first considered, preliminarly to multiple-storey tubes, where buckling is observed. Several parameters are taken into account such as the number of storeys, stretching and folding stiffnesses, and – for shearing tests – the prescribed displacement direction in the transversal plane. The ultimate goal of the paper is to provide evidence that can be useful in the construction of homogenised continuum models of Kresling origami metamaterials. • We present some numerical simulation concerning metamaterials based on Kresling tube pattern. • Numerical analyses of some selected tests clarifies the mechanical behaviour of metamaterials based on Kresling pattern. • Numerical simulations address the homogenised model of Kresling tubes. [ABSTRACT FROM AUTHOR]

• Mechanical response characteristics of beam-column substructures exposed to fire are analyzed. • Explicit calculation formulas for determining the collapse resistance are derived in detail. • Proposed theoretical calculated formulas agree well with these from numerical simulations. • Error analysis is conducted to reveal deviation reasons between theoretical model and numerical simulations. This paper provides a simplified analytical model for the restrained steel beam-column substructure under a fire-induced progressive collapse scenario, which is applied to predict the collapse resistance of substructures under fire. The simplified model is formulated for axially and rotationally restrained two-span steel beam-column substructures under column-loss scenarios and involves rigid and semi-rigid connections. The response characteristics of restrained substructures exposed to fire under column-loss scenarios in each response stage are elaborately analyzed. A "negative" catenary stage, in consideration of the unique negative axial force effects induced by the temperature thermal expansion, was first introduced in the five-stage simplified model for restrained substructures exposed to fire against progressive collapse. Subsequently, the explicit calculation formulas for determining the vertical loads and deflection of both rigid and semi-rigid joint substructures exposed to fire were derived in a quantified way, based on rigid-plastic mechanisms and restraint coefficient methods. In addition, the corresponding numerical simulation analysis on a restrained two-span steel beam-column substructure with different end constraints and fire conditions was carried out to verify the applicability and reliability of established theoretical formulas. Comparisons of vertical load-deflection relationships between the calculation formulas and corresponding numerical simulation shows good accuracy. For more accurate prediction results, the error analysis was further conducted, and several theoretical formulas were modified, which were verified to be accurate and reliable after correction. With derived resistance functions, the resistance of steel beam-column substructures in fire-induced progressive collapse scenarios can be predicted. [ABSTRACT FROM AUTHOR]