Equistrong heavy beam: Solving the problem of Galileo Galilei

In his main book “Discorsie Dimostrazioni Matematiche, Intorno a Due Nuove Scienze” published in 1638 by Elsevier in Leiden, Galileo Galilei, “the Father” of modern science, put the material science and strength of materials on the first place. He introduced the notions of stress and strength that have been fundamental since then. Moreover, in unison with Plato’s theory of forms he found out the perfect shape of a force-bent beam we call today equistrong. This discovery laid the foundation for search of other perfect elastic bodies as a continuation of Galilei’s work. There are no theorems of existence for equistrong bodies so that the quest for them is like a gold-digging. In what follows, the shapes of the following heavy, equistrong beams were found out: a) beam of constant thickness and of variable width, simply supported at both ends, b) beam clamped at one end and loaded at the other end while having either constant thickness and variable width, or constant width and variable thickness, and c) equistrong shape of the profile of aircraft wings accounting for gravity and lift loads. The shape of equistrong rod at buckling under a compressive force is found in the Euler’s problem. Equistrong structures possess minimum weight for given safety factor or maximum safety factor for given weight.     

How old is surface science?

Philosophical and literary testimonies from the Classical World (5th century b.c. to 3rd century a.d.) involving solid surfaces are reviewed. Plato thought the surface to be a real entity, whereas Aristotle considered it to possess an unqualified existence, i.e. not to be a substance, but just an accidental entity. The Old Stoics asserted that surfaces do not possess any physical existence, although the Stoic philosopher Posidonius—apparently the only exception in his school—held them to exist both in thought and reality. While both the Atomists and the Epicureans were very little interested in them, the Sceptic philosopher Sextus Empiricus considered surfaces to be the limits of a body, although he maintained that both the view that they are corporeal or the view that they are incorporeal present unsurmountable difficulties.Among Roman authors, the testimony from Pliny the Elder is mostly concerned with metallic surfaces, chemical change occurring there, and surface treatments used in antiquity.Besides the philosophical motivations, the implications of the testimonies are discussed in the light of surface science. The purely geometrical surface of Plato is found to compare favorably to single-crystal surface, Posidonius’ “corporeal” surface is best likened to an air-oxidized, or otherwise ambient-modified surface, and ancient accounts on mixture are compared to XPS results obtained in adhesion studies of enameled steels. I argue that the long-standing dominance of Aristotle’s view from antiquity onwards may have had a part in delaying theoretical speculation into solid surfaces.     

Process designing for laser forming of circular sheet metal

Laser forming is a new type of flexible manufacturing process that has become viable for the shaping of metallic components. Process designing of laser forming involves finding a set of process parameters, including laser power, laser scanning paths, and scanning speed, given a prescribed shape. To date, research has focused on process designing for rectangular plates, and only a few studies are presented for axis-symmetric geometries like circular plates. In the present study, process designing for axis-symmetric geometries-with focus on class of shapes-is handled using a formerly proposed distance-based approach. A prescribed shape is achieved for geometries such as quarter-circular and half-circular ring plates. Experimental results verify the applicability of the proposed method for a class of shapes.     

Newton’s Metaphysics of Space as God’s Emanative Effect

In several of his writings, Isaac Newton proposed that physical space is God’s “emanative effect” or “sensorium,” revealing something interesting about the metaphysics underlying his mathematical physics. Newton’s conjectures depart from Plato and Aristotle’s metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton’s ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.     

The effects of large vibration amplitudes on the axisymmetric mode shapes and natural frequencies of clamped thin isotropic circular plates. Part I: iterative and explicit analytical solution for non-linear transverse vibrations

The effects of large vibration amplitudes on the first two axisymmetric mode shapes of clamped thin isotropic circular plates are examined. The theoretical model based on Hamilton's principle and spectral analysis developed previously by Benamar et al. for clamped-clamped beams and fully clamped rectangular plates is adapted to the case of circular plates using a basis of Bessel's functions. The model effectively reduces the large-amplitude free vibration problem to the solution of a set of non-linear algebraic equations. Numerical results are given for the first and second axisymmetric non-linear mode shapes for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency are given. The non-linear frequencies associated to the fundamental non-linear mode shape predicted by the present model were compared with numerical results from the available published literature and a good agreement was found. The non-linear mode shapes exhibit higher bending stresses near to the clamped edge at large deflections, compared with those predicted by linear theory. In order to obtain explicit analytical solutions for the first two non-linear axisymmetric mode shapes of clamped circular plates, which are expected to be very useful in engineering applications and in further analytical developments, the improved version of the semi-analytical model developed by El Kadiri et al. for beams and rectangular plates, has been adapted to the case of clamped circular plates, leading to explicit expressions for the higher basic function contributions, which are shown to be in a good agreement with the iterative solutions, for maximum non-dimensional vibration amplitude values of 0.5 and 0.44 for the first and second axisymmetric non-linear mode shapes, respectively.     

BC5力学性质的第一性原理计算

采用平面波赝势密度泛函理论方法对0—60 GPa静水压下BC₅ 六角晶系P3m1和四方晶系I4m2结构的平衡态晶格常数、弹性常数、各向异性以及泊松比与Cauchy扰动进行了研究. 研究结果表明, BC₅的两种结构在高压下是稳定的, 且不可压缩性随着压强的增加而增大. 另外, 对其电子结构也进行了计算, 计算结果表明, BC₅存在一个较宽的带隙, 两种原子间有较强的共价杂化, 材料的性质主要由B的2p¹和C的2p²态电子共同决定. 压强对材料带隙和费米能级附近的态密度几乎没有影响, 只引起微小的漂移, 可推断其很好的高压稳定性.     

Generalized Locking Profile for Angular Particles - Locked Particle Theory

Locked particles are defined as those comminuted or particles which contain both gangue and target material. By considering the shape of the comminuted particles and assuming their random distribution in the ore body prior to comminution, it is possible to derive locking profiles which give the frequency of occurrence of particles which have a given fraction of their volume occupied by target material. For most particle shapes (spheres, angular particles, angular plates and rods) the locking profile is a deep U-shaped curve. This suggests that few particles by number contain about 50% target material while a far greater number contain either very little or very much target material. Such a conclusion is important in planning separation processes for locked particles in the mineral industry.     

Vibrations of completely free shallow shells of rectangular planform

Although much has been written about the free vibrations of rectangular plates having completely free boundaries, very little has appeared for the case when the plates have curvature: i.e., shallow shells. A solution of the problem is presented here for shells having arbitrary (but constant) curvature. The Ritz method is used, with displacement functions assumed in the form of polynomials. Convergence studies were made to determine the number of terms required for reasonable solution accuracy. Numerical results were obtained for the frequencies and mode shapes of three types of shells—circular cylindrical, spherical and hyperbolic paraboidal—and these are compared with those of a flat plate.     

Experimental and theoretical study of the far-infrared spectra of HCl dissolved in liquid Ar,Kr, and Xe

New experimental results are reported on the relative absorption intensity distribution in the FIR spectra of HCl dissolved in liquefied Ar, Kr, and Xe at several temperatures along the liquid—vapour coexistence curve. These are treated further by applying a previously developed quantum-statistical spectral theory, which accounts for the line mixing and memory effects. Theoretical spectra are given in terms of the anisotropic potential time autocorrelation functions obtained from classical MD simulations using several empirical analytical potentials with density-adjusted well depths. Globally fair agreement between the theoretical and experimental spectra is demonstrated, except in the high frequency wings, where the theory underestimates the observed intensities. The choice of a particular radial form for the anisotropic HCl/RG potentials is found to be not critical for reproducing the experimental absorption profiles.     

Free vibrations of a simply supported,rectangular plate: An exact elasticity solution

An exact, three-dimensional solution for the free vibrations of simply supported, rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper. The solution, obtained in a semi-inverse fashion as was the solution of the elastostatic problem for such plates, satisfies all of the boundary conditions of the problem in a pointwise manner. It is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi-inverse solution. Other modes of oscillation may exist in the three-dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes. The two types of modes found are analogous to the flexural modes of classical plate theory and the thickness-twist modes, here called breathing modes, of Mindlin plate theory. Some numerical results are given which indicate that the predictions of Mindlin plates are uncannily good approximations to the flexural frequencies given by the present, three-dimensional analysis even for very thick plates. However, the predictions of Mindlin plate theory for the thickness-twist, or breathing, frequencies are not nearly so good. These discrepancies are discussed briefly in an appendix.     

Vibrations of nearly annular and circular plates

A general procedure is presented to determine the natural frequencies and mode shapes of nearly annular and circular plates. A straightforward perturbation procedure is used with a transfer of the boundary conditions to obtain solutions given by simple expressions. As well as yielding good accuracy quantitatively, the method accurately predicts qualitative behavior. Numerical results are presented for clamped elliptical and square plates.     

Vibration of moderately thick square orthotropic stepped thickness plates

Numerous studies that address the vibration of stepped thickness plates are reported in the literature. Predominately, classical plate theory has been used to formulate studies for both isotropic and anisotropic stepped plates. Mindlin plate theory has been employed to obtain results for thick isotropic stepped thickness plates. Exact solutions, Rayleigh-Ritz, differential quadrature and finite element methods have been employed to compute results for frequency of vibration. Results for frequency of vibration for thick orthotropic stepped thickness plates are presented here using orthorhombic material properties of aragonite. The finite element method has been used to compute frequencies and determine mode shapes for simply supported and clamped square Mindlin plates.     

Microscopic theory of the liquid-wall boundary conditions; Thermophoresis

A microscopic theory of the boundary conditions (BC) obeyed by the hydrodynamic equations at a smooth wall is presented. The BC thus obtained contain several new features. Special attention is given to the role of surface tension. A purely hydrodynamic theory of thermophoresis is worked out based upon the new BC.     

Doppler spectroscopy of hydrogen and deuterium Balmer alpha line in an abnormal glow discharge

The results of hydrogen and deuterium Balmer alpha line shapes and line intensities study in an abnormal glow discharge are reported and analyzed. The Doppler shifts along line wings are used to determine energies of excited hydrogen and deuterium atoms. For 12 different cathodes, intensity and shape of line wings are examined and dependence upon cathode material is determined. Tentative explanation of line wings intensity dependence is related to the sputtering of cathode material and back-scattering coefficients of incident hydrogen or deuterium ions and atoms from cathode surface. The influence of the light reflected on a cathode surface to the line shape measurements along discharge axis is considered. In hydrogen, deuterium, and Ar+3%H/sub 2/ discharges, basic mechanisms of fast hydrogen generation and excitation are studied. The shape and intensities of the H/sub /spl alpha// line profiles in pure hydrogen and in argon-hydrogen mixture may be correlated with hydrogen atom-carrier gas collision excitation cross sections. In order to assess the importance of reflected fast hydrogen atoms back scattered from the cathode surface, for the Balmer line shape formation, a simulation program is used. The results are in a qualitative agreement with Balmer line shapes observations.     

Axisymmetric vibrations of polar orthotropic mindlin annular plates of variable thickness

Analysis and numerical results are presented for the axisymmetric vibrations of polar orthotropic annular plates with linear variation in thickness, according to Mindlin's shear theory of plates. A chebyshev collocation technique has been employed to obtain the frequency equations for the transverse motion of such plates, for three different boundary conditions. Frequencies, mode shapes and moments for the first three modes of vibration have been computed for different plate parameters. A comparison of frequencies with the corresponding values obtained by classical plate theory leads to some interesting conclusions.     

Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions

In this paper, we study the free vibration of multilayered magneto-electro-elastic plates under combined clamped/free lateral boundary conditions using a semi-analytical discrete-layer approach. More specifically, we use piecewise continuous approximations for the field variables in the thickness direction and continuous polynomial approximations for those within the plane of the plate. Group theory is further used to isolate the nature of the vibrational modes to reduce the computational cost. As numerical examples, two cases of the lateral boundary conditions combined with the clamped and free edges are considered. The non-dimensional frequencies and mode shapes of elastic displacements, electric and magnetic potentials are presented. Our numerical results clearly illustrate the effect of the stacking sequences and magneto-electric coupling on the frequencies and mode shapes of the anisotropic magneto-electro-elastic plate, and should be useful in future vibration study and design of multilayered magneto-electro-elastic plates.     

Vortices in superconducting bulk, films and SQUIDs

The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).     

Influence of line interference on the vibration-rotation band shapes

The shapes of the CO, v₃, CO₂, and v₃ N₂O fundamental vibration-rotation bands have been studied at various temperatures and in the presence of several perturbing gases. Also the half-widths of CO vibration-rotation lines have been measured at 78 K. In the region of line wings, the measured absorption coefficients deviate from those given by the superposition of Lorentzian profiles. These deviations are explained by the collision-induced line interference that causes redistribution of absorption inside the band. A theory of line mixing is formulated which is based on Markov approximation and on the strong collision model. Simple analytical expressions are obtained for the band shape. The computed shapes are in satisfactory agreement with the experimental results. The deviations from the Lorentz absorption observed in pure CO and in CO-N₂ at low temperature are partially ascribed to the formation of van der Waals dimers.     

A fluid–structure interaction model of insect flight with flexible wings

We present a fluid–structure interactions (FSI) model of insect flapping flight with flexible wings. This FSI-based model is established by loosely coupling a finite element method (FEM)-based computational structural dynamic (CSD) model and a computational fluid dynamic (CFD)-based insect dynamic flight simulator. The CSD model is developed specifically for insect flapping flight, which is capable to model thin shell structures of insect flexible wings by taking into account the distribution and anisotropy in both wing morphology involving veins, membranes, fibers and density, and in wing material properties of Young’s modulus and Poisson’s ratios. The insect dynamic flight simulator that is based on a multi-block, overset grid, fortified Navier–Stokes solver is capable to integrate modeling of realistic wing-body morphology, realistic flapping-wing and body kinematics, and unsteady aerodynamics in flapping-wing flights. Validation of the FSI-based aerodynamics and structural dynamics in flexible wings is achieved through a set of benchmark tests and comparisons with measurements, which contain a heaving spanwise flexible wing, a heaving chordwise-flexible wing with a rigid teardrop element, and a realistic hawkmoth wing rotating in air. A FSI analysis of hawkmoth hovering with flapping flexible wings is then carried out and discussed with a specific focus on the in-flight deformation of the hawkmoth wings and hovering aerodynamic performances with the flexible and rigid wings. Our results demonstrate the feasibility of the present FSI model in accurately modeling and quantitatively evaluating flexible-wing aerodynamics of insect flapping flight in terms of the aerodynamic forces, the power consumption and the efficiency.     

Density field theory for a fluid interacting with the Yukawa potential. Role of the ideal entropy

We present a field theory to describe liquids where the field represents the density. In terms of this field, the Hamiltonian contains the ideal entropy and the interaction between the density fields. The approach is illustrated with the Yukawa interaction and presented in the grand canonical ensemble formalism. In this framework, first, we derive a relation specific to the field theory. This relation is equivalent to the ‘equation of motion’ in field theory for interacting quantum particles. Then, focusing on the effect of the fluctuations, we calculate thermodynamic quantities beyond the mean field. The pressure, the density and the compressibility at a given chemical potential in the quadratic approximation and beyond are given. The aim of this paper is to illustrate the importance and the role of the ideal entropy in this type of approach. The density and the compressibility at a given chemical potential are calculated perturbatively in various ways. Whether from their field theoretical definition, or deriving them from one another using the thermodynamical relations or also using the ‘equation of motion’, the results are in all ways of calculation consistent. However, the different calculations require different levels of expansion of the ideal entropy term involving in our case three and four body coupling constants. The consistency is then closely related to the form of the functional of the ideal entropy.