Seasonal variability of the mixed layer depth determined using an improved maximum angle method in the Arctic basins

To investigate the spatiotemporal variations in the mixed layer depth(MLD)in the Arctic basins,a new criterion to determine the MLD,called the improved maximum angle method(IMAM),was developed.A total of 45123 potential density profiles collected using Ice-Tethered Profilers(ITPs)in the Arctic basins during 2005-2021 were used to demonstrate the method’s effectiveness.By comparing the results obtained by the fixed threshold method(FTM),percentage threshold method(PTM),and maximum gradient method(MGM)for profiles in the Canada Basin,Makarov Basin,and Eurasian Basin,we determined that the quality index(1.0 for perfect identification of the MLD)of the IMAM regarding the assessment of the MLD determination method reached 0.94,which is much greater than those of other criteria.Moreover,two types of the density profiles were identified based on the mixed layer development stage.The MLDs of the typical profiles determined using the IMAM were found to have better consistency with the original definition.By utilizing the new mixed layer criterion,the seasonal variations and regional differences in the MLD in the Arctic basins were analyzed.Spatially,the summer and winter MLDs in the Canada Basin were the shallowest(13.55 m in summer,26.76 m in winter)than those in the Makarov(29.51 m in summer,49.08 m in winter)and Eurasian(20.36 m in summer,46.81 m in winter)basins due to the stable stratification in the upper ocean and the subsequent small effects of dynamic and thermodynamic processes(wind-driven stirring and brine rejection)in the Canada Basin.Seasonally,in the three Arctic basins,the average MLD was shallowest(22.77 m)in summer;it deepened through autumn and reached a winter maximum(41.12 m).

THE GENERALIZED MAXIMUM ANGLE CONDITION FOR THE Q1 ISOPARAMETRIC ELEMENT

We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allows the quadrilateral to become a regular triangle in the sense of maximum angle condition [5, 11].

The largest negative refractive angles in uniaxial bicrystals

Using the Maxwell＇s equations, we carry out theoretical analysis on the maximum incident and refractive angles at which negative refraction can be realized at the interfaces associated with conventional uniaxial media. In the numerical analysis, the largest incident and refractive angles at which refraction arises are obtained by optimizing directions of the optical axis of the uniaxial bicrystal. Meanwhile, the optical parameters of the ordinary uniaxial bicrystals （including homogeneity- junction and heterogeneity-junction） are given, and some representative laser wavelengths, the largest incident and refractive angles are obtained. The relation between the largest incident angles （or refractive angles） and refractive index is also discussed.

Stabilization of an abutment under a rigidly fixed bridge by holographical-speckle interferometry

Objective: There are no detailed reports of three-dimensional measurement of abutment teeth in mastication, because it is knotty to observe the rotation in chewing directly, and inexact to estimate indirectly. This work studies the three-dimensional stability of rigidly fixed bridge under the stresses of distributed loads and concentrated loads by optical method that gives the tip angle and rotation angle calculated directly based on measurement data. Methods: The specimen, taken from a 25-year-old male, was a left mandible without the second premolars and the first molars. As abutments, first premolar and second molar have complete periodontium. The specimen was soaked in formaldehyde solution. The bridge was fixed between two abutment teeth (first premolars and second molars), and the mandible was cemented in a steel box. The load was increased from 0 kg to 23 kg. Laser holographic technique was used to measure the three-dimensional bit shift of the dens, both buccolingual bit shift and mesiodistal bit shift, and determine tip angle and rotation angle. Results: The effects of stress distribution on the rigidly fixed bridge were evaluated, and stabilization of the bridge under the stresses of distributed loads and concentrated loads, respectively, were analyzed. The results showed that the tips of two abutments were very similar, and no distinct difference was observed between the distributed load and the concentrated load. However, the maximum rotation angle for the distributed load was two to four times as large as that for the concentrated load. In the experiment, the tip angle of the abutment teeth was no more than 0.65 degree, and the rotation angle was no more than 0.60 degree. All maximum angles occurred in the second molar. Conclusion: The fixed bridge is considered to be safe. In addition, a method for measuring the rotation angle was provided effectively.

Factor analysis of interceptor capture probability

The capture probability of interceptors has been deeply studied.Firstly,the definition of capture probability is analyzed.It is transformed into calculating the probability that the relative position vector between the target and the interceptor locates in a certain cone.The relative position vector and associated covariance matrix are projected in line-of-sight coordinates,and the 3-dimensional integral of a probability function in a cone is calculated to obtain the capture probability.The integral equation is a complicated expression of probability,and it is simplified to an explicit approximate expression according to some assumptions based on the characteristics of the engineering problems.The approximation precision is analyzed by comparative simulation difference,which indicates that approximate assumptions are reasonable.Utilizing the explicit expression,the characteristics of capture probability are analyzed respectively with the factors,such as the distance between the interceptor and the target,the precision of relative position vector,the maximum capture distance and the maximum field angle of interceptor seeker.

Analytical evaluation and experimental validation on dynamic rocking behavior for shallow foundation considering structural response

The challenge in the practical application of rocking foundations is the estimation of its performance,particularly the rotation angle,during a strong earthquake.In this study,the dynamic rocking behavior for a shallow foundation considering structural response was evaluated through two analytical approaches:the conventional soil-foundation-structure interaction(SFSI)governing equation of a single-degree-of-freedom(SDOF)structure on a rocking shallow foundation,and the Housner rocking model(i.e.,a rocking rigid block on a rigid base).Both approaches were validated with dynamic centrifuge tests.The test models consisted of a soft soil deposit,a shallow rectangular foundation,and an SDOF structure dominated by a bending behavior.A total of 11 foundation-structure systems and six seismic waves,including recorded earthquake signals and sinusoidal waves,were utilized.The results showed that the conventional SFSI equation well predicted the maximum rotation during strong earthquakes.However,this method was less accurate regarding the rotational phase information and maximum rotation of the foundation during weak earthquakes.On the other hand,although the modified Housner′s rocking model required five parameters relevant to a soil-foundation-structure system,it overestimated the maximum rotation of the foundation when compared with the results from dynamic centrifuge tests.

Equilibrium state of axially symmetric electric solar wind sail at arbitrary sail angles

This paper studies the equilibrium state and trajectory dynamics of an axially symmetric Electric solar wind sail(E-sail)at arbitrary sail angles.The E-sail is assumed operating in a heliocentric-ecliptic orbit at approximately one astronomic unit(au)from the Sun,and experiencing various dynamic disturbances like solar wind pressure,tether tension oscillations,and centrifugal forces.The study derives analytical expressions for the E-sail's equilibrium state and its maximal coning angle under small coning angle assumption.Subsequently,an improved propulsion model is developed for the E-sail in this equilibrium state.To assess the precision of these formulations,a high-fidelity E-sail dynamic model is constructed using the nodal position finite element method,where the tethers are modeled as two-noded tensile elements and the central spacecraft and remote units are simplified as lumped masses.Through thorough parametric analyses,this paper conclusively demonstrates that the operation of the E-sail at the equilibrium state can be achieved in accordance with the derived analytical prediction of the equilibrium state.Furthermore,the improved propulsion model is employed in trajectory analyses for a mission to reach the solar system's boundary.The study provides valuable insights and findings and foundation for the practical application and further advancement of the E-sail technology.

A New Delaunay Triangulation Algorithm Based on Constrained Maximum Circumscribed Circle

Delaunay triangulation is gradually playing an important role in the field of finite element analysis, image recognition, and medical visualization.Considering the quality and partition efficiency, a new Delaunay triangulation method based on constrained maximum circumscribed circle is proposed. First, according to two important criteria, the empty circle features and the maximized minimum angle characteristics, we established constrained conditions. Then, we iterated the container vertices, structure triangular face linked lists, and finally got the Delaunay data. The experimental results showed that the efficiency of the improved triangulation dissection method increased by 9.47% compared with traditional triangulation algorithms in irregular triangle vertex data.