ABSTRACT
Bicondylar tibial plateau fractures pose many challenges in surgical treatment. The aim of the present study was to analyze three methods of reduction, single medial, single lateral, and dual plating, for the treatment of a bicondylar tibial plateau fracture, through finite element analysis (FEA). A simple metaphyseal fracture, type C1.1 (AO-41) was modeled on a CT-derived 3D model of the knee. Lateral and medial proximal tibial polyaxial plates with screws were modeled and placed accordingly for the three methods of reduction. Simulation of physiological type loading corresponding to the maximal weight acceptance phase during a slow walking gait cycle was performed using FEA. Values of stress and strain were recorded near the fracture lines. Dual plating provided a decrease of stress and strain in the tibial plateau area. However, the differences in the values among the three cases were small. The stress concentration areas were located in the vicinity of the fracture, predominantly in the area of the tibial plateau. Considering the limitations of the present study, the results revealed that dual plating leads to smaller stress and strain values near the fracture lines in the tibial plateau area. However, values obtained for single lateral plating are close in range. Considering the complexity of the surgical approach for dual plating, single lateral plating may be a solution for good reduction with fewer surgical risks and complications. Further studies on the C1.1 fracture (AO-41) are needed to analyze the complex issue of reducing and stabilizing such a fracture and to characterize the postoperative state while providing predictable parameters for an optimal result.
ABSTRACT
The subject of this paper is to analyse the Mathematical Principia of Economic 3D Black Holes in Roegenian economics. In detail, we study two main problems: (i) mathematical origin of economic 3D black holes; and (ii) entropy and internal political stability depending on national income and the total investment, for economic Reissner-Nordström (RN) 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach as they are so different), to complete the thermodynamics-economics dictionary with new entities, and to introduce the flow between two macroeconomic systems. The main contribution is about introducing and studying the Schwarzschild-type metric on an economic 4D system, together with Rindler coordinates, Einstein 4D partial differential equations (PDEs), and economic RN 3D black holes. In addition, we introduce some economic Ricci type flows or waves, for further research.
ABSTRACT
Phase-shifting interferometry (PSI) is the preferred non-contact method for profiling sub-nanometer surfaces. Based on monochromatic light interference, the method computes the surface profile from a set of interferograms collected at separate stepping positions. Errors in the estimated profile are introduced when these positions are not located correctly. In order to cope with this problem, various algorithms that minimize the effects of certain types of stepping errors (linear, sinusoidal, etc.) have been developed. Despite the relatively large number of algorithms suggested in the literature, there is no unified way of characterizing their performance when additional unaccounted random errors are present. Here, we suggest a procedure for quantifying the expected behavior of each algorithm in the presence of independent and identically distributed (i.i.d.) random stepping errors, which can occur in addition to the systematic errors for which the algorithm has been designed. The usefulness of this method derives from the fact that it can guide the selection of the best algorithm for specific measurement situations.
ABSTRACT
Lateral scanning white-light interferometry represents an attractive alternative to the standard white-light interferometry. Its main advantage over the latter procedure consists in the ability to scan large samples continuously, without the need of a cumbersome stitching procedure. Presently, the main drawback in the path of large-scale industrial acceptance of this method is the need for careful calibration of the tilt angle prior to each measurement. A novel self-calibration approach is presented. Using the data acquired during the normal scanning process, the need of an initial tilt angle calibration is eliminated and on-the-fly system adjustments for the best signal-to-noise ratio can be performed without an increase in the measurement time dictated by recalibration.
ABSTRACT
Iterative least square phase-measuring techniques address the phase-shifting interferometry issue of sensitivity to vibrations and scanner nonlinearity. In these techniques the wavefront phase and phase steps are determined simultaneously from a single set of phase-shifted fringe frames where the phase shift does not need to have a nominal value or be a priori precisely known. This method is commonly used in laser interferometers in which the contrast of fringes is constant between frames and across the field. We present step-by-step modifications to the basic iterative least square method. These modifications allow for vibration insensitive measurements in an interferometric system in which fringe contrast varies across a single frame, as well as from frame to frame, due to the limited bandwidth light source and the nonzero numerical aperture of the objective. We demonstrate the efficiency of the new algorithm with experimental data, and we analyze theoretically the degree of contrast variation that this new algorithm can tolerate.
