Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

The Minimum Energy Principle in Description of Nonlinear Properties of Orthotropic Material

In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.

Electrothermal energy conversion mechanism of micro-scale semiconductor bridge

The response characteristics of resistance is observed by the analysis of experimental data of micro scale semiconductor bridge （MSCB） under different voltage inputs. Two critical voltages are found. One is called exploding voltage, above which the MSCB can be melted and vaporized without generating a plasma, and the other is called producing a plasma voltage, above which the MSCB is entirely vaporized, and then the current flows through the vapor producing the plasma. Based on the non Fourier heat conduction theory, the electrothermal energy conversion model is es tablished for the stage from heating to exploding, and then the correlation of MSCB and time is ob tained by graphic calculation. Importantly, the critical exploding voltage and exploding time are also derivate. With the comparison between the analytical result from the theoretical model and that from experimental data, it has been demonstrated that the theoretical model is reasonable and feasible for designing the exploding voltage and exploding time.

Some Ideas of James Watt in Contemporary Energy Conversion Thermodynamics

James Watt contributed significantly to the development of the thermodynamics of energy conversion as a science. Several of his ideas are now integral part of thermodynamics, but Watt as their creator is not mentioned. This paper presents some of Watt’s concepts of energy conversion, including his thermodynamic analysis of the Newcomen steam engine that marks the beginning of thermal engineering. The analysis illuminated the causes of the enormously high heat losses in the installation and showed the ways for their reduction. This led him to a new conception of the steam engine with a separate condenser. Not less important was Watt’s determination of some physical properties of water and steam used as the working substance. In the experiments he observed the decrease of the latent heat of steam with increasing temperature and its disappearance at very high temperature led him to postulate the existence of a thermodynamic critical state of water. He introduced the work associated with volume change into thermodynamics and illustrated it graphically. Several of Watt’s numerous ideas deserve to be included into the history of the thermodynamics of energy conversion but they are rarely mentioned in the scientific literature. Arguably the most important is the First Law of Thermodynamics, which he introduced in his 1769 patent and related works in 1774 and 1778.

Mass-to-Energy Conversion, the Astrophysical Mechanism

A new interpretation of the relativistic equation relating total-, momentum-, and mass-energies is presented. With the aid of the familiar energy-relationship triangle, old and new interpretations are compared. And the key difference is emphasized—apparent relativity versus intrinsic relativity. Mass-to-energy conversion is then brought about by adopting a three-part strategy: 1) Make the motion relative to the universal space medium. This allows the introduction of the concept of intrinsic energy (total, kinetic, and mass energies) as counterpart to the apparent version. 2) Recognize that a particle’s mass property diminishes with increase in speed. This means introducing the concept of intrinsic mass (which varies with intrinsic speed). 3) Impose a change in the particle’s gravitational environment. Instead of applying an electromagnetic accelerating force or energy in order to alter the particle’s total energy, there will simply be an environmental change. Thus, it is shown how to use relativity equations and relativistic motion—in a way that exploits the distinction between apparent and innate levels of reality—to explain the mass-to-energy-conversion mechanism. Moreover, the mechanism explains the 100-percent conversion of mass to energy;which, in turn, leads to an explanation of the mechanism driving astrophysical jets.

Influence of iron powder content on the electromagnetic and mechanical performance of soft magnetic geopolymer composite

In the induction heating of airport pavement to remove snow and ice,soft magnetic geopolymer composite(SMGC)can be used to gather the dissipated electromagnetic energy,thus enhancing the energy utilization efficiency.The aim of this work is to analyze the influence mechanism of iron powder content on the electromagnetic and mechanical performance of SMGC,so as to provide theoretical guidance for the design of soft magnetic layer within airport pavement structure.The results show that the increase of iron powder content reduces the resistance and magnetoresistance of SMGC by decreasing the content of non-magnetic phases between iron powder.However,the reduction of iron powder spacing also provides a shorter transmission path for the inter-particle eddy currents in the SMGC specimen,which enhances the exchange coupling between iron powder,thus increasing the electromagnetic loss.Therefore,the compatibility between magnetic permeability and electromagnetic loss should be considered comprehensively in the mix design of SMGC.In addition,although iron powder can enhance the mechanical properties of SMGC by improving the density of geopolymer matrix,the excessive amount of iron powder can lead to a weak interfacial transition zone between geopolymer matrix and iron powder.According to the induction heating results,optimized SMGC can improve the energy transfer efficiency of induction heating by 24.03%.

Mechanical model for failure modes of rock and soil under compression

The failure modes of rock and soil under compression are complex phenomena that have not been explained in a mechanical perspective. However, large amounts of studies indicate that the failure modes of rock and soil samples can be categorized into eight types. In this work, the inner tensile stress and the dissipation and conversion of energy of rock and soil under compression are analyzed, then the effective conversion coefficient of energy is deduced, thus the tensile failure criterion of rock and soil under compression is established. Combined with the shear strength criterion of Mohr–Coulomb, a tensile joint shear strength criterion for rock and soil under compression is built. Therefore, a mechanical criterion model concerning the failure modes of rock and soil under compression is established and verified by tests. This model easily explains the test results in the existing literature and many natural phenomena, such as collapse.

CFD Simulation and Experimental Study of a New Elastic Blade Wave Energy Converter

Small moving vehicles represent an important category of marine engineering tools and devices(equipment)typically used for ocean resource detection and maintenance of marine rights and interests.The lack of efficient power supply modes is one of the technical bottlenecks restricting the effective utilisation of this type of equipment.In this work,the performance characteristics of a new type of elastic-blade/wave-energy converter(EBWEC)and its core energy conversion component(named wave energy absorber)are comprehensively studied.In particular,computational fluid dynamics(CFD)simulations and experiments have been used to analyze the hydrodynamics and performance characteristics of the EBWEC.The pressure cloud diagrams relating to the surface of the elastic blade were obtained through two-way fluid-solid coupling simulations.The influence of blade thickness and relative speed on the performance characteristics of EBWEC was analyzed accordingly.A prototype of the EBWEC and its bucket test platform were also developed.The power characteristics of the EBWEC were analyzed and studied by using the blade thickness and motion cycle as control variables.The present research shows that the EBWEC can effectively overcome the performance disadvantages related to the transmission shaft torque load and power curve fluctuations of rigid blade wave energy converters(RBWEC).

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

Study on Sinking-Sliding Failure Mechanism of Perilous Rock at Wangxia in Three Gorges of the Yangtze River, China

The giant perilous rock at Wangxia (named Wangxia perilous rock) is representative in Three Gorges of the Yangtze River, China, has threatened badly the navigation of the Yangtze River channel for a long period. The giant perilous rock is composed of siliceous limestone and argillaceous limestone, and includes two elements marking by W1 and W2, respectively. The W1 is an isolated pillar while the W2 is in clintheriform. The linking segment of dominant fissure in the W2 is composed by moniliform solution funnels at its back, and the locked segment of the dominant fissure at the base of the W2 is composed by two parts. For the locked part of the dominant fissure of the W2, the upper segment shows the same lithology with the perilous rock and it can be simplified as an elastic medium, for the lower segment composed by argillaceous shale and mudstone can be simplified as a strain-softening medium. Introducing the water-softened function, the constitutive curves with two kinds of medium materials for the locked segment in the dominant fissure of the W2 have been proposed. Based on energy principle, the cusp catastrophe model for perilous rock rupture is built and formulas for the transient elastic and impulsive acceleration and the elastic-impulsive velocity of perilous rock catastrophe rupture have been established. By the calculation, the elastic-impulsive acceleration for the catastrophe rupture of the W2 is 531.4 m/s2, while the average elastic-impulsive velocity is 2.608 m/s. Further, it is deduced that the elastic-impulsive velocity at the base of the W2 is about 5.2 m/s. For the transient ruture of the W2, there is a greater speed difference between the top and the base of the W2, which impels the giant perilous rock to be retroverted sliding rupture, coinciding with the fact. Undoubtedly, studies in this paper must play an important role to analyze the catastrophe rupture mechanism of giant perilous rocks at both banks in Three Gorges of the Yangtze River, China.

Application and Popularization of Energy Formula

In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.

Event-triggered mechanism based robust fault-tolerant control for networked wind energy conversion system

In this paper,a novel robust fault-tolerant control scheme based on event-triggered communication mechanism for a variable-speed wind energy conversion system(WECS)with sensor and actuator failures is proposed.The nonlinear WECS with event-triggered mechanism is modeled based on the Takagi-Sugeno(T-S)fuzzy model.By Lyapunov stability theory,the parameter expression of the proposed robust fault-tolerant controller with event-triggered mechanisms is proposed based on a feasible solution of linear matrix inequalities.Compared with the existing WECS fault-tolerant control methods,the proposed scheme significantly reduces the pressure of network packet transmission and improves the robustness and reliability of the WECS.Considering a doubly-fed variable speed constant frequency wind turbine,the eventtriggered mechanism based fault-tolerant control for WECS is analyzed considering system model uncertainty.Numerical simulation results demonstrate that the proposed scheme is feasible and effective.

A retrospective view on the history of natural sciences in XX-XXI

The presented paper is dedicated to a new ret-rospective view on the history of natural sci-ences in XX-XXI cc, partially including the sci-ence philosophy (mainly, the problems of the scientific realism, i.e. the correspondence of science to reality) and also a novel scheme for different classes of sciences with different ob-jects and paradigms. There are analyzed the chosen “great” and “grand” problems of phys-ics (including the comprehension of quantum mechanics, with a recently elaborated new chapter, connected with time as a quantum obs- ervable and time analysis of quantum processes) and also of natural sciences as a whole. The particular attention is paid to the interpretation questions and slightly to the aspects, inevitably connected with the world- views of the res- earchers (which do often constitute a part of the interpretation questions).

A Study of the Pit-Aided Construction of Egyptian Pyramids

Pyramids,symbols of the Ancient Egyptian civilization,are visited by tourists and studied by researchers from all around the world.However,the techniques used by Ancient Egyptians to construct the pyramid,specifically,how such a tall structure could have been constructed from huge blocks of stone with the limited productive forces at the time,remains a mystery to the world.Though numerous theories,such as the use of ramps,levers,pulleys,fluid buoyancy,and cast-in-place concrete,have been proposed in academia,no consensus has been reached to date.Based on mechanical principles and the productive forces available at the time,the famous Pyramid of Khufu is used as a case study in this paper to propose a theory of pit-aided construction.The main steps include the digging of the pit,the transportation of stone blocks into the pit,the layer-by-layer construction,and the layer-by-layer filling of soil until the top of the pyramid is completed.The main idea of the pit-aided construction was to use the self-weight of the stone material to achieve the transportation of stone blocks by converting potential energy to kinetic energy,thereby avoiding the large amounts of work that must be done to elevate the huge blocks of stone.The proposed theory of pit-aided construction is consistent with the cultural custom of burial that is associated with tomb construction,namely laying the deceased to rest through burial,and is also consistent with the productive forces available in Ancient Egypt at the time.

Broadband energy harvesting via magnetic coupling between two movable magnets

Harvesting energy from ambient mechanical vibrations by the piezoelectric effect has been proposed for powering microelectromechanical systems and replacing batteries that have a finite life span. A conventional piezoelectric energy harvester （PEH） is usually designed as a linear resonator, and suffers from a narrow operating bandwidth. To achieve broadband energy harvesting, in this paper we introduce a concept and describe the realization of a novel nonlinear PEH. The proposed PEH consists of a primary piezoelectric cantilever beam coupled to an auxiliary piezoelectric cantilever beam through two movable magnets. For predicting the nonlinear response from the proposed PEH, lumped parameter models are established for the two beams. Both simulation and experiment reveal that for the primary beam, the introduction of magnetic coupling can expand the operating bandwidth as well as improve the output voltage. For the auxiliary beam, the magnitude of the output voltage is slightly reduced, but additional output is observed at off-resonance frequencies. Therefore, broadband energy harvesting can be obtained from both the primary beam and the auxiliary beam.

Fracture behavior and acoustic emission characteristics of sandstone samples with inclined precracks

Sandstone samples with precracks of different dip angles were collected from a coal mine roof and subjected to uniaxial compression tests,and acoustic emission(AE)and scanning electron microscopy(SEM)were used to study how the crack dip angle affected the fracture mechanism.In the precracked sandstone samples,as the dip angle between the crack line and loading direction decreased,so did the peak stress and its completion time.The SEM observations revealed a fracture transition from tensile cleavage to shear slip,which was manifested by a microstructure change from aggregate to staggered.According to energy conversion,a decreased crack dip angle results in gradually decreasing total and dissipative peak energies,whose variation amplitudes at different stages are consistent with those of the peak stress of the samples.The decreased crack dip angle lowered the stress required to trigger the first appearance of AE energy peaks and ring-down counts,as well as shortening the period before the occurrence of the first AE peak signal.However,the AE energy and ring-down count during the failure stage after the stress peak increased gradually.A stepped increase was observed in the AE ring-down count curves,with each step corresponding to a jump in the stress-strain curve.From the characteristics of the AE signal of the fracture of a precracked rock sample,the occurrence of joints or faults in the rock mass can be reasonably inferred.This is expected to provide a new method and approach for predicting coal and rock dynamic disasters.

Joint Bearing Mechanism of Coal Pillar and Backfilling Body in Roadway Backfilling Mining Technology

In the traditional mining technology,the coal resources trapped beneath surface buildings,railways,and water bodies cannot be mined massively,thereby causing the lower coal recovery and dynamic disasters.In order to solve the aforementioned problems,the roadway backfilling mining technology is developed and the joint bearing mechanism of coal pillar and backfilling body is presented in this paper.The mechanical model of bearing system of coal pillar and backfilling body is established,by analyzing the basic characteristics of overlying strata deformation in roadway backfilling mining technology.According to the Ritz method in energy variation principle,the elastic solution expression of coal pillar deformation is deduced in roadway backfilling mining technology.Based on elastic-viscoelastic correspondence principle,combining with the burgers rheological constitutive model and Laplace transform theory,the viscoelastic solution expression of coal pillar deformation is obtained in roadway backfilling mining technology.By analyzing the compressive mechanical property of backfilling body,the time formula required for coal pillar and backfilling body to play the joint bearing function in roadway backfilling mining technology is obtained.The example analysis indicates that the time is 140 days.The results can be treated as an important basis for theoretical research and process design in roadway backfilling mining technology.

Activation of 2D MoS_(2) electrodes induced by high-rate lithiation processes

MoS_(2) is a highly promising material for application in lithium-ion battery anodes due to its high theoretical capacity and low cost.However,problems with a fast capacity decay over cycling,especially at the first cycles,and poor rate performance have deterred its practical implementation.Herein,electrodes comprised solely of few-layers 2D MoS_(2) nanosheets have been manufactured by scalable liquid-phase exfoliation and spray deposition methods.The long-standing controversy questioning the reversibility of conversion processes of MoS_(2)-based electrodes was addressed.Raman studies revealed that,in 2D MoS_(2) electrodes,conversion processes are indeed reversible,where nanostructure played a key role.Cycling of the electrodes at high current rates revealed an intriguing phenomenon consisting of a continuously increasing capacity after ca.100-200 cycles.This phenomenon was comprehensively addressed by a variety of electrochemical and microscopy methods that revealed underlying physical activation mechanisms that involved a range of profound electrode structural changes.Activation mechanisms delivered a capacitive electrode of a superior rate performance and cycling stability,as compared to the corresponding pristine electrodes,and to MoS_(2) electrodes previously reported.Herein,we have devised a methodology to overcome the problem of cycling stability of 2D MoS_(2) electrodes.Moreover,activation of electrodes constitutes a methodology that could be applied to enhance the energy storage performance of electrodes based on other 2D nanomaterials,or combinations thereof,strategically combining chemistries to engineer electrodes of superior energy storage properties.

From Black Holes to Information Erasure: Uniting Bekenstein’s Bound and Landauer’s Principle

This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 1030 bits/m3), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.

阴离子密堆二次电池正极材料中离子宿住迁移与能量存蓄机制晶体化学新探索

在二次电池电极材料中,有一类性能优良的材料具有阴离子密堆或近密堆方式构筑的晶体结构。宿住阳离子在密堆留下的空隙空间中宿住、迁移,从而实现能量转换与存储。相关过程微观机理的研究由于涉及原子尺度的微观结构辨析和电子层面的分析,实验研究难度较大。因此,更多是通过晶体学理论分析与晶体场理论和量子力学第一性原理计算结合展开。已有的理论从过渡金属配位体晶体场分析展开,但宿住离子宿住迁移中电子相互作用关注相对不足。本文根据已有的实验事实,在精准描述最具代表性的阴离子(氧离子)面心立方紧密堆积(FCC)结构中空隙空间准确形态和微分几何方法准确解析空腔真实体积的基础上,结合空隙空腔独特形态,对经典晶体学中Pauling第一规则的分析方法作了拓展。根据新的理解,提出了宿住阳离子在空隙空腔宿住和徒迁拓扑形变新模式,及其可能拥有的电子形态学新特征,提出了空隙空腔中宿住阳离子体积与密堆阴离子半径间的新关系。为了进一步说明住宿离子电子形态特征,通过第一性原理计算获得了典型FCC结构LiMn_(2)O_(4)尖晶石中电子密度等势图,构造了锂离子宿住四面体空隙空腔的电子密度等势特征分布的三维形态,与晶体学分析中获得的电子形态新特征变化一致。通过夹在两个密排面间的{110}面族电子云密度分布分析,首次清晰地揭示了LiMn_(2)O_(4)中锂离子的“S”形徒迁途径,及其对附近锰离子配位多面体电子云密度分布的影响。依据宿住离子脱/嵌新特征,提出阴离子拓扑多面体晶体场对宿住阳离子电子云压缩发生拓扑变形实现能量转换储蓄的新思路,据此计算了典型紧密堆积构造的电极材料新的理论能量密度,并和传统方法计算的理论值进行了比较,二者十分接近,为从晶体学和量子力学理解二次电池能量储存提供了新视角。