Towards Further Understanding the Secondary Fracture during Spaghetti Bent Break

When a brittle thin rod, such as a dry spaghetti stick, is bent beyond its flexural limit, it often breaks into more than two pieces, typically three or more. This phenomenon and puzzle has aroused widespread interest and discussion since its first proposal by Feynman. Previous work has partly explained the inevitability of the secondary fracture, but without any adjustable time parameter. In order to further understand this problem, especially the secondary fracture, in this paper we propose and study the dynamics of a half-infinite model to mimic the physics that a spaghetti stick is half-infinite under uniform bending. When the breaking process starts, a gradual release of initial moment of a linearly declining time at the free end, instead of a sudden release, is adopted, resulting in the introduction of a characteristic time parameter to the model and agrees better with the real situation. A specific analytical solution in terms of the excited bending moment using Euler–Bernoulli beam theory is derived, and that the gradual release of initial moment induces a burst of flexural waves, and these flexural waves locally increase the moment in the stick and progressively get to the maximum value, and then lead to the secondary fracture are concluded. The excited moment increases with time and distance, and has an asymptotic extremum value of 1.43 times initial moment. The gradual release in our model requires and gives certain distance and time when the excited bending moment reaches its extremum value, which provides a possibility to predict the detailed fracture parameters such as fragmentation length and time and thus to further understand the secondary fracture during spaghetti bent break.

Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty

The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues. The current work addresses a version of the extremum value theorem for function spaces under explicit consideration of numerical uncertainties. It is shown that certain function spaces are bounded in a suitable sense, i.e., they admit finite approximations up to an arbitrary precision. The proof of this fact is constructive in the sense that it explicitly builds the approximating functions. Consequently, existence of approximate extremal functions is shown. Applicability of the theorem is investigated for finite-horizon optimal control, dynamic programming and adaptive dynamic programming. Some possible computability issues of the extremum value theorem in optimal control are shown on counterexamples.

Statistic thermodynamic analysis of fructans – Part 3: Relationship between polymer structure and mixing entropy at equilibrium conditions

The reduced mixing entropy, which is a concentration and unimer independent equivalent to the polymer mixing entropy defined by Flory, for various probabilistic distributed polymer distributions is calculated. The unbranched most probable distribution proves to reach an extremum value at any given number average degree of polymerization, clearly differentiating it from both broader and narrower polymer distributions with branching structures. Entropy driven polymerization reactions thus inevitably produce unbranched polymer structures as discussed for the case of inulin biosynthesis.

Research in Destruction of Concrete Bridge Expanded Joint Influenced by Temperature Difference

Destruction of bridge expanded joint is a serious problem for concrete bridge. Based on 5 years measured data, the temperature in the different positions of the concrete box girder was systemically analyzed to illuminate the cause of the bridge expanded joint damage. A method for predicting the extremum value of the temperature difference of concrete girder was proposed by use of the extrema analysis and curve fitting based on the temperature in the different positions of the concrete box girder. The relationship is quite useful in estimating the destruction of bridge expanded joint by effective temperature difference in concrete box-girder.

Simulation Research on Optical Performance of Multicrystalline Silicon Texture Structure

The finite element model of double etching pits was established, optical performance of multicrystalline silicon wafer before and after etching was simulated by RF MODULE of COMSOL Multiphysics version 3.5a. Optical characteristic of unetching wafer and acidic textured were compared. It is indicates that acidic textured (double etching pits) has low reflectivity, high power flow Y component , the better light trapping. When the wavelength is 600nm, the maximum and minimum value of surface electric field Z component of acidic textured are 1.9 times and 1.4 times respectively than that of unetching wafer, and two extremum value of surface magnetic field Z component are 2.1 times and 1.9 times respectively than that of unetching wafer. Numerical simulation results of Multi hole model are closely with experimental values, which can guide the practical production.

Pre-Estimating Dynamically the Optimum of Extremum Value Control System with Large Time Delay Element Based on Correlation Identification

As to the optimum of extremum value controlled plant, if the transfer function of its linear part is only with the high order dynamic elements, the optimum of extremum value control system could be dynamically pre-estimated by using the method based on correlation identification we presented, the pre-estimating method has the estimate speed quickly, anti-jamming ability strong, accurate, highly effective and so on the merits. However, if the controlled plant is simultaneously with high order dynamic elements and a large time delay element, the method could not be used directly to pre-estimate dynamically the optimum of the extremum value control system. A new improved pre-estimating method is presented so as to resolve the problem above. After we have in detail analyzed the derivation process of the pre-estimating method we presented, Fully taking into account the effects of large time-delay element, a number of conditions have been improved, the algorithm based on correlation identification has been extended, the optimum of extremum value control system with a large time delay element is well resolved by the extended algorithm.

Method for Pre-Estimating Dynamically the Optimum of Extremum Value Control System Based on Least Squares

As the optimum of extremum value control system drifts faster it may make bigger error for pre-estimating statically the optimum, it is particularly remarkable if the transfer function of the linear part is with a high order dynamic element. In this paper, a method based on LS(least squares) is presented to pre-estimate dynamically the optimum of extremum value control system. The linear part of controlled plant could be approximated by a cascade of 1st order dynamic element and a pure time delay element as the controlled model is simplified it is successfully resolved for pre-estimating dynamically the optimum of extremum value control system with a high order element by LS.

Stresses in thin-walled beams subjected to a traversing mass under a pulsating force

An analytical—numerical method to determine the dynamic response of beams with various boundary conditions subjected to a moving mass under a pulsating force is explained. Governing partial differential equations of the system are changed to a convenience type of ordinary differential equations to be solved through a Runge—Kutta scheme. Pulsating force specifications influenced the dynamic response of the beam depending on the moving mass properties. Results showed the significant effect of the boundary conditions on the dynamic response of the beam, which was considered rarely in the past. Stiffening the constraints reduces the maximum stresses in the beams. Results for identical unsymmetrical beams indicated that stresses in beams would be less when the moving object experiences a stiffer constraint in its start point on the beam. A new extremum value was obtained for the dynamic response of the beam, as the pulsating force on the moving mass oscillates with a special frequency regarded as the main natural frequency of the beam under the moving mass.