A non-contact method for millimeter-scale inspection of material surface flatness via Laser-Induced Breakdown Spectroscopy(LIBS)is investigated experimentally.The experiment is performed using a planished surface of a...A non-contact method for millimeter-scale inspection of material surface flatness via Laser-Induced Breakdown Spectroscopy(LIBS)is investigated experimentally.The experiment is performed using a planished surface of an alloy steel sample to simulate its various flatness,ranging from 0 to 4.4 mm,by adjusting the laser focal plane to the surface distance with a step length of 0.2 mm.It is found that LIBS measurements are successful in inspecting the flatness differences among these simulated cases,implying that the method investigated here is feasible.It is also found that,for achieving the inspection of surface flatness within such a wide range,when univariate analysis is applied,a piecewise calibration model must be constructed.This is due to the complex dependence of plasma formation conditions on the surface flatness,which inevitably complicates the inspection procedure.To solve the problem,a multivariate analysis with the help of Back-Propagation Neural Network(BPNN)algorithms is applied to further construct the calibration model.By detailed analysis of the model performance,we demonstrate that a unified calibration model can be well established based on BPNN algorithms for unambiguous millimeter-scale range inspection of surface flatness with a resolution of about 0.2 mm.展开更多
Elucidating the flow features around piles in local scouring processes is crucial for studies of local scouring mechanisms and scour depth estimates.This study details the flow turbulence characteristics of two submer...Elucidating the flow features around piles in local scouring processes is crucial for studies of local scouring mechanisms and scour depth estimates.This study details the flow turbulence characteristics of two submerged piles that are determined by solving the Navier-Stokes equations with the improved delayed detached eddy simulation model.This model is verified by comparing experimental and numerical results for hydrodynamic parameters with the literature for both square-crossing piles(SCPs)and circular-crossing piles(CCPs).Original topographies of flat and scoured beds(i.e.,the initial and equilibrium scouring stages)are based on experimental results obtained by the authors in the present paper.SCP and CCP flow features in the scouring process are discussed.The results indicate that during the scouring process,the time-averaged drag coefficient and root mean square(rms)of the lift coefficient increase linearly in the CCP test,while the rms of the lift coefficient in the SCP test decreases linearly.Moreover,the minimum pressure coefficient is always located in the upstream corners in the SCP case but moves from 72.5°to 79.5°when the scour hole is completely developed in the CCP case.Downward flow behind the pile,which is generated by separated boundary layers above the top face of the pile,can reach the sand bed and turn the separated shear layers into patches of small vortices in the near-wake regions.Thus,the high shear stress zones are mainly at the scour edges under scoured-bed conditions.展开更多
Kagome materials are a class of material with a lattice structure composed of corner-sharing triangles that produce various exotic electronic phenomena,such as Dirac fermions,van Hove singularities,and flat bands.Howe...Kagome materials are a class of material with a lattice structure composed of corner-sharing triangles that produce various exotic electronic phenomena,such as Dirac fermions,van Hove singularities,and flat bands.However,most of the known kagome materials have a flat band detached from the Fermi energy,which limits the investigation of the emergent flat band physics.In this work,by combining soft x-ray angle-resolved photoemission spectroscopy(ARPES)and the first-principles calculations,the electronic structure is investigated of a novel kagome metal CeNi_(5) with a clear dispersion along the kz direction and a Fermi level flat band in theΓ–K–M–Γplane.Besides,resonant ARPES experimental results indicate that the valence state of Ce ions is close to 4^(+),which is consistent with the transport measurement result.Our results demonstrate the unique electronic properties of CeNi_(5) as a new kagome metal and provide an ideal platform for exploring the flat band physics and the interactions between different types of flat bands by tuning the valence state of Ce ions.展开更多
We report structural and electronic properties of Na_(2)Ni_(3)S_(4),a quasi-two-dimensional compound composed of alternating layers of[Ni_(3)S_(4)]^(2-)and Na^(+).The compound features a remarkable Ni-based kagome lat...We report structural and electronic properties of Na_(2)Ni_(3)S_(4),a quasi-two-dimensional compound composed of alternating layers of[Ni_(3)S_(4)]^(2-)and Na^(+).The compound features a remarkable Ni-based kagome lattice with a square planar configuration of four surrounding S atoms for each Ni atom.Magnetization and electrical measurements reveal a weak paramagnetic insulator with a gap of about 0.5 eV.Our band structure calculation highlights a set of topological flat bands of the kagome lattice derived from the rotated dxz-orbital with C_(3)+T symmetry in the presence of crystal-field splitting.展开更多
We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple twoand four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on th...We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple twoand four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.展开更多
This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is n...This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.展开更多
According to our hypothesis, at the very beginning of the Big Bang, a hyperenergetic spherical wave was created. We described its characteristics in our previous work, and the present work is based on them. Logically,...According to our hypothesis, at the very beginning of the Big Bang, a hyperenergetic spherical wave was created. We described its characteristics in our previous work, and the present work is based on them. Logically, we saw that in cosmic inflation the frequency of such a wave would decrease sharply. Based on the temperature that prevailed immediately after inflation according to the hot Big Bang model, we determined a measure of the size of the inflation in this model, in accordance with our hypothesis.展开更多
To research solar energy's efficiency and environmental benefits,the thermal efficiency,exergy,and entropy of solar collectors were calculated.The experiment involved two glass-topped collectors,fluid transfer tub...To research solar energy's efficiency and environmental benefits,the thermal efficiency,exergy,and entropy of solar collectors were calculated.The experiment involved two glass-topped collectors,fluid transfer tubes,and aluminum heat-absorbing plates.Glass wool insulation minimized heat loss.A 0.5% TiO_(2)/Water nanofluid was created using a mechanical and ultrasonic stirrer.Results showed that solar radiation increased thermal efficiency until midday,reaching 48.48% for water and 51.23% for the nanofluid.With increasing mass flow rates from 0.0045 kg/s to 0.02 kg/s,thermal efficiency improved from 16.26% to 47.37% for water and from 20.65% to 48.76% for the nanofluid.Filtered water provided 380 W and 395 W of energy in March and April,while the nanofluid increased it to 395 W and 415 W during these months.Mass flow generated energy,and the Reynolds number raised entropy.The noon exergy efficiency for nanofluids was 50%-55%,compared to 30% for water.At noon,the broken exergy measured 877.53 W for the nanofluid and 880.12 W for water.In Kirkuk,Iraq,the 0.5% TiO_(2)/Water nanofluid outperformed water in solar collectors.展开更多
This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the co...This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.展开更多
The change processes and trends of shoreline and tidal flat forced by human activities are essential issues for the sustainability of coastal area,which is also of great significance for understanding coastal ecologic...The change processes and trends of shoreline and tidal flat forced by human activities are essential issues for the sustainability of coastal area,which is also of great significance for understanding coastal ecological environment changes and even global changes.Based on field measurements,combined with Linear Regression(LR)model and Inverse Distance Weighing(IDW)method,this paper presents detailed analysis on the change history and trend of the shoreline and tidal flat in Bohai Bay.The shoreline faces a high erosion chance under the action of natural factors,while the tidal flat faces a different erosion and deposition patterns in Bohai Bay due to the impact of human activities.The implication of change rule for ecological protection and recovery is also discussed.Measures should be taken to protect the coastal ecological environment.The models used in this paper show a high correlation coefficient between observed and modeling data,which means that this method can be used to predict the changing trend of shoreline and tidal flat.The research results of present study can provide scientific supports for future coastal protection and management.展开更多
This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the...This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.展开更多
With the continuous development of mechanical industry,higher requirements are put forward for the comprehensive properties of spring steel.The chemical composition and production process of spring flat steel are desi...With the continuous development of mechanical industry,higher requirements are put forward for the comprehensive properties of spring steel.The chemical composition and production process of spring flat steel are designed to meet the requirements of high strength and high toughness of spring flat steel,through the test,the product surface quality and internal quality all meet the national standards,the performance indicators to meet user requirements.展开更多
This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmo...This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.展开更多
Nanogrinding of SiC wafers with high flatness and low subsurface damage was proposed and nanogrinding experiments were carried out on an ultra precision grinding machine with fine diamond wheels. Experimental results ...Nanogrinding of SiC wafers with high flatness and low subsurface damage was proposed and nanogrinding experiments were carried out on an ultra precision grinding machine with fine diamond wheels. Experimental results show that nanogrinding can produce flatness less than 1.0μm and a surface roughness Ra of 0.42nm. It is found that nanogrinding is capable of producing much flatter SiC wafers with a lower damage than double side lapping and mechanical polishing in much less time and it can replace double side lapping and mechanical polishing and reduce the removal amount of chemical mechanical polishing.展开更多
基金supported in part by the National Key Research and Development Program of China(No.2022YFA1602500)National Natural Science Foundation of China program(No.U2241288).
文摘A non-contact method for millimeter-scale inspection of material surface flatness via Laser-Induced Breakdown Spectroscopy(LIBS)is investigated experimentally.The experiment is performed using a planished surface of an alloy steel sample to simulate its various flatness,ranging from 0 to 4.4 mm,by adjusting the laser focal plane to the surface distance with a step length of 0.2 mm.It is found that LIBS measurements are successful in inspecting the flatness differences among these simulated cases,implying that the method investigated here is feasible.It is also found that,for achieving the inspection of surface flatness within such a wide range,when univariate analysis is applied,a piecewise calibration model must be constructed.This is due to the complex dependence of plasma formation conditions on the surface flatness,which inevitably complicates the inspection procedure.To solve the problem,a multivariate analysis with the help of Back-Propagation Neural Network(BPNN)algorithms is applied to further construct the calibration model.By detailed analysis of the model performance,we demonstrate that a unified calibration model can be well established based on BPNN algorithms for unambiguous millimeter-scale range inspection of surface flatness with a resolution of about 0.2 mm.
基金support from the National Natural Science Foundation of China (Nos.52301324 and 52001276)the Natural Science Foundation of Zhejiang Province (No.LQ24E090001)+2 种基金the Open Fund of Key Laboratory of Estuary and Coast of Zhejiang Province (No.ZIHE21005)the Natural Science Foundation of Ningbo (No.2021J096)the Zhejiang Transportation Science and Technology (No.2021064)。
文摘Elucidating the flow features around piles in local scouring processes is crucial for studies of local scouring mechanisms and scour depth estimates.This study details the flow turbulence characteristics of two submerged piles that are determined by solving the Navier-Stokes equations with the improved delayed detached eddy simulation model.This model is verified by comparing experimental and numerical results for hydrodynamic parameters with the literature for both square-crossing piles(SCPs)and circular-crossing piles(CCPs).Original topographies of flat and scoured beds(i.e.,the initial and equilibrium scouring stages)are based on experimental results obtained by the authors in the present paper.SCP and CCP flow features in the scouring process are discussed.The results indicate that during the scouring process,the time-averaged drag coefficient and root mean square(rms)of the lift coefficient increase linearly in the CCP test,while the rms of the lift coefficient in the SCP test decreases linearly.Moreover,the minimum pressure coefficient is always located in the upstream corners in the SCP case but moves from 72.5°to 79.5°when the scour hole is completely developed in the CCP case.Downward flow behind the pile,which is generated by separated boundary layers above the top face of the pile,can reach the sand bed and turn the separated shear layers into patches of small vortices in the near-wake regions.Thus,the high shear stress zones are mainly at the scour edges under scoured-bed conditions.
基金Project support by the Science Fund from Shanghai Committee of Science and Technology,China (Grant No.23JC1403300)the Shanghai Municipal Science and Technology Major Project,China+3 种基金the TDLI Starting up Grant,the National Natural Science Foundation of China (Grant Nos.12374063,12204223,and 23Z990202580)the Fund from the Ministry of Science and Technology of China (Grant No.2023YFA1407400)the Shanghai Natural Science Fund for Original Exploration Program,China (Grant No.23ZR1479900)Shanghai Talent Program,China。
文摘Kagome materials are a class of material with a lattice structure composed of corner-sharing triangles that produce various exotic electronic phenomena,such as Dirac fermions,van Hove singularities,and flat bands.However,most of the known kagome materials have a flat band detached from the Fermi energy,which limits the investigation of the emergent flat band physics.In this work,by combining soft x-ray angle-resolved photoemission spectroscopy(ARPES)and the first-principles calculations,the electronic structure is investigated of a novel kagome metal CeNi_(5) with a clear dispersion along the kz direction and a Fermi level flat band in theΓ–K–M–Γplane.Besides,resonant ARPES experimental results indicate that the valence state of Ce ions is close to 4^(+),which is consistent with the transport measurement result.Our results demonstrate the unique electronic properties of CeNi_(5) as a new kagome metal and provide an ideal platform for exploring the flat band physics and the interactions between different types of flat bands by tuning the valence state of Ce ions.
基金supported by the National Natural Science Foundation of China(Grant Nos.12141002 and 12225401)the National Key Research and Development Program of China(Grant No.2021YFA1401902)+1 种基金the CAS Interdisciplinary Innovation Teamthe Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)。
文摘We report structural and electronic properties of Na_(2)Ni_(3)S_(4),a quasi-two-dimensional compound composed of alternating layers of[Ni_(3)S_(4)]^(2-)and Na^(+).The compound features a remarkable Ni-based kagome lattice with a square planar configuration of four surrounding S atoms for each Ni atom.Magnetization and electrical measurements reveal a weak paramagnetic insulator with a gap of about 0.5 eV.Our band structure calculation highlights a set of topological flat bands of the kagome lattice derived from the rotated dxz-orbital with C_(3)+T symmetry in the presence of crystal-field splitting.
基金Project supported by the National Natural Science Foundation of China (Grant No.12074367)Anhui Initiative in Quantum Information Technologies,the National Key Research and Development Program of China (Grant No.2020YFA0309804)+3 种基金Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01)the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No.XDB35020200)Innovation Program for Quantum Science and Technology (Grant No.2021ZD0302002)New Cornerstone Science Foundation。
文摘We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple twoand four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.
文摘This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.
文摘According to our hypothesis, at the very beginning of the Big Bang, a hyperenergetic spherical wave was created. We described its characteristics in our previous work, and the present work is based on them. Logically, we saw that in cosmic inflation the frequency of such a wave would decrease sharply. Based on the temperature that prevailed immediately after inflation according to the hot Big Bang model, we determined a measure of the size of the inflation in this model, in accordance with our hypothesis.
文摘To research solar energy's efficiency and environmental benefits,the thermal efficiency,exergy,and entropy of solar collectors were calculated.The experiment involved two glass-topped collectors,fluid transfer tubes,and aluminum heat-absorbing plates.Glass wool insulation minimized heat loss.A 0.5% TiO_(2)/Water nanofluid was created using a mechanical and ultrasonic stirrer.Results showed that solar radiation increased thermal efficiency until midday,reaching 48.48% for water and 51.23% for the nanofluid.With increasing mass flow rates from 0.0045 kg/s to 0.02 kg/s,thermal efficiency improved from 16.26% to 47.37% for water and from 20.65% to 48.76% for the nanofluid.Filtered water provided 380 W and 395 W of energy in March and April,while the nanofluid increased it to 395 W and 415 W during these months.Mass flow generated energy,and the Reynolds number raised entropy.The noon exergy efficiency for nanofluids was 50%-55%,compared to 30% for water.At noon,the broken exergy measured 877.53 W for the nanofluid and 880.12 W for water.In Kirkuk,Iraq,the 0.5% TiO_(2)/Water nanofluid outperformed water in solar collectors.
基金Project supported by the National Natural Science Foundation of China (Nos. 62373025, 12332004,62003013, and 11932003)。
文摘This paper proposes a distributed control method based on the differential flatness(DF) property of robot swarms. The swarm DF mapping is established for underactuated differentially flat dynamics, according to the control objective. The DF mapping refers to the fact that the system state and input of each robot can be derived algebraically from the flat outputs of the leaders and the cooperative errors and their finite order derivatives. Based on the proposed swarm DF mapping, a distributed controller is designed. The distributed implementation of swarm DF mapping is achieved through observer design. The effectiveness of the proposed method is validated through a numerical simulation of quadrotor swarm synchronization.
基金supported by the National Natural Science Foundation of China (41602205, 42293261)the China Geological Survey Program (DD20189506, DD20211301)+2 种基金the Special Investigation Project on Science and Technology Basic Resources of the Ministry of Science and Technology (2021FY101003)the Central Guidance for Local Scientific and Technological Development Fund of 2023the Project of Hebei University of Environmental Engineering (GCY202301)
文摘The change processes and trends of shoreline and tidal flat forced by human activities are essential issues for the sustainability of coastal area,which is also of great significance for understanding coastal ecological environment changes and even global changes.Based on field measurements,combined with Linear Regression(LR)model and Inverse Distance Weighing(IDW)method,this paper presents detailed analysis on the change history and trend of the shoreline and tidal flat in Bohai Bay.The shoreline faces a high erosion chance under the action of natural factors,while the tidal flat faces a different erosion and deposition patterns in Bohai Bay due to the impact of human activities.The implication of change rule for ecological protection and recovery is also discussed.Measures should be taken to protect the coastal ecological environment.The models used in this paper show a high correlation coefficient between observed and modeling data,which means that this method can be used to predict the changing trend of shoreline and tidal flat.The research results of present study can provide scientific supports for future coastal protection and management.
文摘This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.
文摘With the continuous development of mechanical industry,higher requirements are put forward for the comprehensive properties of spring steel.The chemical composition and production process of spring flat steel are designed to meet the requirements of high strength and high toughness of spring flat steel,through the test,the product surface quality and internal quality all meet the national standards,the performance indicators to meet user requirements.
文摘This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.
基金Project (50975040) supported by the National Natural Science Foundation of China
文摘Nanogrinding of SiC wafers with high flatness and low subsurface damage was proposed and nanogrinding experiments were carried out on an ultra precision grinding machine with fine diamond wheels. Experimental results show that nanogrinding can produce flatness less than 1.0μm and a surface roughness Ra of 0.42nm. It is found that nanogrinding is capable of producing much flatter SiC wafers with a lower damage than double side lapping and mechanical polishing in much less time and it can replace double side lapping and mechanical polishing and reduce the removal amount of chemical mechanical polishing.