Educational Press for Remote Experimentation Applied in the Spring to Study Hooke＇s Law

The aim of this study is to report the use of RE （remote experimentation） in an educational press. The authors developed this remote experiment with the objective to study the Hooke＇s law through the analysis of the coil spring. The remote experiment is available in a website, where the students can manipulate and observe the educational press and confirm Hooke＇s statements with the output information. In addition, the students will have the opportunity to read in the website about the educational press, the physical law, and the use of the press in industrial processes. This remote experimentation exerts a force in the mechanical spring creating a deformation. In the defined point, the microcomputer will collect the data from the sensors, and it will save this data in the database. After the process execution, a graph with the data will be plotted in the website. The tests confirm that the educational press has informational potential because it returned values consistent with Hooke＇s law and the experiment presented repetition in all tests realized.

Hooke's Atom in an Arbitrary External Electric Field: Analytical Solutions of Two-Electron Problem by Path Integral Approach

By using the path integral approach, we investigate the problem of Hooke＇s atom （two electrons interacting with Coulomb potential in an external harmonic-oscillator potential） in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.

Optimizing the Pulsed Current Gas Tungsten Arc Welding Parameters

The selection of process parameter in the gas tungsten arc （GTA） welding of titanium alloy was presented for obtaining optimum grain size and hardness. Titanium alloy （Ti-6Al-4V） is one of the most important non-ferrous metals which offers great potential application in aerospace, biomedical and chemical industries, because of its low density （4.5 g/cm^3）, excellent corrosion resistance, high strength, attractive fracture behaviour and high melting point （1678℃）. The preferred welding process for titanium alloy is frequent GTA welding due to its comparatively easier applicability and better economy. In the case of single pass （GTA） welding of thinner section of this alloy, the pulsed current has been found beneficial due to its advantages over the conventional continuous current process. Many considerations come into the picture and one needs to carefully balance various pulse current parameters to reach an optimum combination. Four factors, five level, central composite, rotatable design matrix were used to optimize the required number of experimental conditions. Mathematical models were developed to predict the fusion zone grain size using analysis of variance （ANOVA） and regression analysis. The developed models were optimized using the traditional Hooke and Jeeve＇s algorithm. Experimental results were provided to illustrate the proposed approach.

Basic Characteristics of a New Flexible Pneumatic Bending Joint

Several typical flexible pneumatic actuators （FPA） and different mechanical models describing their behaviors have been proposed, however, it is difficult to balance compliance and load capacity in conventional designs, and these models still have limitations in predicting behavior of FPAs. A new flexible pneumatic bending joint （FPBJ） with special anisotropic rigidity structure is proposed. The FPBJ is developed as an improvement with regard to existing types of FPA, and its principal characteristic is derived from the special anisotropic rigidity structure. With this structure, the load capacity in the direction perpendicular to bending plane is strengthened. The structure of the new FPBJ is explained and a mathematical model is derived based on Euler-Bernoulli beam model and Hook’s law. To obtain optimum design and usage, some key structure parameters and input-output characteristics are simulated. The simulation results reveal that the relationship between the structure parameters and FPBJ’s bending angle is nonlinear. At last, according to the simulation results, the FPBJ is manufactured with optional parameters and tested. The experimental results show that the joint’s statics characteristics are reflected by the mathematical model accurately when the FPBJ is deflated. The maximum relative error between simulation and experimental results is less than 6%. However, the model still has limitations. When the joint is inflated, the maximum relative error reaches 20%. This paper proposes a new flexible pneumatic bending joint which has sufficient load capacity and compliance, and the mathematical model provides theoretical guidance for the FPBJ’s structure design.

Density-functional-theory formulation of classical and quantum Hooke's law

A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress （σ^M） originates from lat- tice strain （e）, following Hooke＇s law： σ^M=Cε, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress （o-QE） is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke＇s law： ~QE=E（An）, where E is the deformation potential of electronic states and An is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke＇s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain （g=0）, and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.