Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Analysis of the initial stages of the logical process followed by Louis de Broglie in establishing the electron phase wave equation in his 1924 thesis, which triggered the development of Wave Mechanics when Erwin Schrödinger formalized this concept with his vectorial wave equation. This development was soon followed by Quantum Mechanics, when Schrödinger proved that the Matrix Mechanics independently developed by Werner Heisenberg was equivalent to Wave Mechanics, with both theories leaving room for some degree of uncertainty as to the physical localization of the moving electron. This is what led Heisenberg to also formalize the Uncertainty Principle to take this situation into account. This principle was soon regarded as a fundamental axiomatic principle that seemed to make further exploration of the subatomic level of magnitude appear impossible to most researchers. We will analyze in this article the reason why the phase-wave velocity established by de Broglie generated this uncertainty in the localization of the moving electron in light of the current state of knowledge on the behavior of the electron in motion, in view of establishing the relevance of maintaining the Uncertainty Principle in the study of the subatomic level of magnitude.

Aluminum matrix composites reinforced by molybdenum-coated carbon nanotubes

To extend the application of carbon nanotubes （CNTs） and explore novel aluminum matrix composites,CNTs were coated by molybdenum layers using metal organic chemical vapor deposition,and then Mo-coated CNT （Mo-CNT）/Al composites were prepared by the combination processes of powder mixing and spark plasma sintering.The influences of powder mixing and Mo-CNT content on the mechanical properties and electrical conductivity of the composites were investigated.The results show that magnetic stirring is better than mechanical milling for mixing the Mo-CNTs and Al powders.The electrical conductivity of the composites decreases with increasing Mo-CNT content.When the Mo-CNT content is 0.5wt%,the tensile strength and hardness of Mo-CNT/Al reach their maximum values.The tensile strength of 0.5wt% Mo-CNT/Al increases by 29.9%,while the electrical conductivity only decreases by 7.1%,relative to sintered pure Al.The phase analysis of Mo-CNT/Al composites reveals that there is no formation of Al carbide in the composites.

Graphene-reinforced aluminum matrix composites prepared by spark plasma sintering

Graphene-reinforced 7055 aluminum alloy composites with different contents of graphene were prepared by spark plasma sintering（SPS）. The structure and mechanical properties of the composites were investigated. Testing results show that the hardness, compressive strength, and yield strength of the composites are improved with the addition of 1wt% graphene. A clean, strong interface is formed between the metal matrix and graphene via metallurgical bonding on atomic scale. Harmful aluminum carbide（Al_4C_3） is not formed during SPS processing. Further addition of graphene（above 1wt%） results in the deterioration in mechanical properties of the composites. The agglomeration of graphene plates is exacerbated with increasing graphene content, which is the main reason for this deterioration.

Effects of Processing Technologies on Mechanical Properties of SiC Particulate Reinforced Magnesium Matrix Composites

Mg matrix composites with SiC particles ranging from 5vol%-25vol% were prepared using stirring casting method. Die casting, squeezing casting, and extrusion were applied for inhibiting or eliminating the defects such as gas porosity and shrinkage void. Through die casting and squeezing casting, most of the defects in Mg matrix composites could be eliminated, but the mechanical properties were improved limitedly. On the other hand, after hot extrusion, not only most of the defects of as-cast composites ingots were eliminated, but also the mechanical properties were improved markedly. With the addition of SiC, the tensile strength, yield strength and elastic modulus of as extrusion SiCp/AZ61 composites increased remarkably, and the elongation decreased obviously.

Effect of Heat Treatment on Microstructure and Mechanical Properties of Si Cp/2024 Aluminum Matrix Composite

SiCp/2024 aluminum alloy matrix composite was prepared by powder metallurgy method. Effects of heat treatment on the microstructure and mechanical properties of composite were investigated by SEM, EDS, XRD, HREM, tensile and hardness tests. The experimental results showed that SiC particles distributed uniformly in the matrix and were in good combination with matrix. The tensile strength and hardness were improved significantly after heat treatment. With the increase of solid solution temperature, the alloy phases dissolved in the matrix gradually. When the solid solution temperature arrived at 505 ℃, the alloy phases dissolved thoroughly, and the composite exhibited the highest tensile strength and hardness（σb=360 MPa, HBS=104）. The main strengthening phase was Al2Cu, which was granular and distributed dispersively in the matrix. Effect of T6 was better than that of T4 at the same solid solution temperature.

Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations

The adjacency matrix operations,which connect with configuration transformation correspondingly,can be used for analysis of configuration transformation of metamorphic mechanisms and the corresponding algorithm can easily be simulated by computer.But the adjacency matrix based on monochrome topological graph is not suitable for the topological representation of mechanisms with multiple joints.The method of adjacency matrix operations has its own limitations for analysis of configuration transformation of metamorphic mechanisms because it can only be used in the topological representation of mechanisms with single joints.In order to overcome the drawback of the adjacency matrix,a kind of new matrix named as extended adjacency matrix is proposed to express topological structures of all mechanisms.The extended adjacency matrix is not only suitable for the topological representation of mechanisms with single joints,but also can be used in that of mechanisms with multiple joints.On this basis,a method of matrix operations based on the extended adjacency matrix is proposed to analyze the configuration transformation of metamorphic mechanisms.The method is not only suitable for configuration analysis of metamorphic mechanisms with single joints as well as metamorphic mechanisms with multiple joints.The method is evaluated by calculating two examples representing metamorphic mechanisms with single joint and multiple joints respectively.It can be concluded that the method is effective and correct for analysis of configuration transformation of all metamorphic mechanisms.The proposed method is simple and easy to be achieved by computer programming.It provides a basis for structural synthesis of all metamorphic mechanisms.

THE EQUATIONS OF MOTION OF A MECHANICAL SYSTEM IN MATRIX FORM

This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.

Mechanical, electrical, and thermal expansion properties of carbon nanotube-based silver and silver–palladium alloy composites

The mechanical, electrical, and thermal expansion properties of carbon nanotube（CNT）-based silver and silver–palladium（10：1, w/w） alloy nanocomposites are reported. To tailor the properties of silver, CNTs were incorporated into a silver matrix by a modified molecular level-mixing process. CNTs interact weakly with silver because of their non-reactive nature and lack of mutual solubility. Therefore, palladium was utilized as an alloying element to improve interfacial adhesion. Comparative microstructural characterizations and property evaluations of the nanocomposites were performed. The structural characterizations revealed that decorated type-CNTs were dispersed, embedded, and anchored into the silver matrix. The experimental results indicated that the modification of the silver and silver–palladium nanocomposite with CNT resulted in increases in the hardness and Young＇s modulus along with concomitant decreases in the electrical conductivity and the coefficient of thermal expansion（CTE）. The hardness and Young＇s modulus of the nanocomposites were increased by 30%？40% whereas the CTE was decreased to 50%-60% of the CTE of silver. The significantly improved CTE and the mechanical properties of the CNT-reinforced silver and silver–palladium nanocomposites are correlated with the intriguing properties of CNTs and with good interfacial adhesion between the CNTs and silver as a result of the fabrication process and the contact action of palladium as an alloying element.

Microstructure and Mechanical Performance of Cu-SnO_2-rGO based Composites Prepared by Plasma Activated Sintering

A novel chemical technique combined with unique plasma activated sintering（PAS） was utilized to prepare consolidated copper matrix composites（CMCs） by adding Cu-SnO2-rGO layered micro powders as reinforced fillers into Cu matrix. The repeating Cu-SnO2-rGO structure was composed of inner dispersed reduced graphene oxide（r GO）, SnO2 as intermedia and outer Cu coating. SnO2 was introduced to the surface of rGO sheets in order to prevent the graphene aggregation with SnO2 serving as spacer and to provide enough active sites for subsequent Cu deposition. This process can guarantee rGO sheets to suffi ciently disperse and Cu nanoparticles to tightly and uniformly anchor on each layer of rGO by means of the SnO2 active sites as well as strictly control the reduction speed of Cu^2＋. The complete cover of Cu nanoparticles on rGO sheets thoroughly avoids direct contact among rGO layers. Hence, the repeating structure can simultaneously solve the wettability problem between rGO and Cu matrix as well as improve the bonding strength between rGO and Cu matrix at the well-bonded Cu-SnO2-rGO interface. The isolated rGO can effectively hinder the glide of dislocation at Cu-rGO interface and support the applied loads. Finally, the compressive strength of CMCs was enhanced when the strengthening effi ciency reached up to 41.

Chemical, mechanical, and thermal expansion properties of a carbon nanotube-reinforced aluminum nanocomposite

In the present study,the chemical and mechanical properties and the thermal expansion of a carbon nanotube（CNT）-based crystalline nano-aluminum（nano Al） composite were reported.The properties of nanocomposites were tailored by incorporating CNTs into the nano Al matrix using a physical mixing method.The elastic moduli and the coefficient of thermal expansion（CTE） of the nanocomposites were also estimated to understand the effects of CNT reinforcement in the Al matrix.Microstructural characterization of the nanocomposite reveals that the CNTs are dispersed and embedded in the Al matrix.The experimental results indicate that the incorporation of CNTs into the nano Al matrix results in the increase in hardness and elastic modulus along with a concomitant decrease in the coefficient of thermal expansion The hardness and elastic modulus of the nanocomposite increase by 21%and 20%,respectively,upon CNT addition.The CTE of CNT/A1 nanocomposite decreases to 70%compared with that of nano Al.

Effects of metal binder on the microstructure and mechanical properties of Al2O3-based micro-nanocomposite ceramic tool material

The Al_2O_3-（W,Ti）C composites with Ni and Mo additions varying from 0vol% to 12vol% were prepared via hot pressing sintering under 30 MPa. The microstructure was investigated via X-ray diffraction（XRD） and scanning electron microscopy（SEM） equipped with energy dispersive spectrometry（EDS）. Mechanical properties such as flexural strength, fracture toughness, and Vickers hardness were also measured. Results show that the main phases A12O3 and（W,Ti）C were detected by XRD. Compound Mo Ni also existed in sintered nanocomposites. The fracture modes of the nanocomposites were both intergranular and transgranular fractures. The plastic deformation of metal particles and crack bridging were the main toughening mechanisms. The maximum flexural strength and fracture toughness were obtained for 9vol% and 12vol% additions of Ni and Mo, respectively. The hardness of the composites reduced gradually with increasing content of metals Ni and Mo.

Material microstructures analyzed by using gray level Co-occurrence matrices

The mechanical properties of materials greatly depend on the microstructure morphology. The quantitative characterization of material microstructures is essential for the performance prediction and hence the material design. At present,the quantitative characterization methods mainly rely on the microstructure characterization of shape, size, distribution,and volume fraction, which related to the mechanical properties. These traditional methods have been applied for several decades and the subjectivity of human factors induces unavoidable errors. In this paper, we try to bypass the traditional operations and identify the relationship between the microstructures and the material properties by the texture of image itself directly. The statistical approach is based on gray level Co-occurrence matrix（GLCM）, allowing an objective and repeatable study on material microstructures. We first present how to identify GLCM with the optimal parameters, and then apply the method on three systems with different microstructures. The results show that GLCM can reveal the interface information and microstructures complexity with less human impact. Naturally, there is a good correlation between GLCM and the mechanical properties.

Damage characteristics and constitutive modeling of the 2D C/Si C composite: Part I – Experiment and analysis

This paper reports an experimental investigation on the macroscopic mechanical behaviors and damage mechanisms of the plain-woven（2D） C/Si C composite under in-plane on- and offaxis loading conditions. Specimens with 15, 30, and 45 off-axis angles were prepared and tested under monotonic and incremental cyclic tension and compression loads. The obtained results were compared with those of uniaxial tension, compression, and shear specimens. The relationships between the damage modes and the stress state were analyzed based on scanning electronic microscopy（SEM） observations and acoustic emission（AE） data. The test results reveal the remarkable axial anisotropy and unilateral behavior of the material. The off-axis tension test results show that the material is fiber-dominant and the evolution rate of damage and inelastic strain is accelerated under the corresponding combined biaxial tension and shear loads. Due to the damage impediment effect of compression stress, compression specimens show higher mechanical properties and lower damage evolution rates than tension specimens with the same off-axis angle. Under cyclic tension–compression loadings, both on-axis and off-axis specimens exhibit progressive damage deactivation behaviors in the compression range, but with different deactivation rates.

Ultra-wide tuning single channel filter based on one-dimensional photonic crystal with an air cavity

By inserting an air cavity into a one-dimensional photonic crystal of LiF/GaSb, a tunable filter covering the whole visible range is proposed. Following consideration of the dispersion of the materials, through modulating the thickness of the air cavity, we demonstrate that a single resonant peak can shift from 416.1 to 667.3 nm in the band gap at normal incidence by means of the transfer matrix method. The research also shows that the transmittance of the channel can be maximized when the number of periodic Li F/Ga Sb layers on one side of the air defect layer is equal to that of the other side. When adding a period to both sides respectively, the full width at half maximum of the defect mode is reduced by one order of magnitude. This structure will provide a promising approach to fabricate practical tunable filters in the visible region with ultra-wide tuning range.

Microstructural Characterization and Mechanical Properties of VB_2/A390 Composite Alloy

In this work, we make the best use of the vanadium element; a series of A1-V-B alloys and VB2/A390 composite alloys were fabricated. For Ak-10V-6B alloy, the grain size of VB2 can be controlled within about 1 μm and is distributed uniformly in the AI matrix. Further, it can be found that VB2 promises to be a useful reinforcement particle for piston alloy. The addition of VB2 can improve the mechanical properties of the A390 composite alloys significantly. The results show that with 1 % VB2 addition, A390 composite alloy exhibits the best performance. Compared with the A390 alloy, the coefficient of thermal expansion is 13.2 × 10^-6 K-1, which decreased by 12.6%; the average Brinell hardness can reach 156.5 HB, wear weight loss decreased by 28.9% and ultimate tensile strength at 25℃ （UTS25 ℃） can reach 355 MPa, which increased by 36.5%.