Quadratic Cross Section Research Articles

Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields.

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic LxLxL(y) Ising lattices with nearest neighbor ferromagnetic exchange and four free LxL(y) surfaces, at which antisymmetric surface fields +/-H(s) act, are studied for a wide range of linear dimensions (4</=L</=320, 30</=L(y)</=1000), in an attempt to clarify finite size effects on the wedge filling transition in this "double-wedge" geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature T(c) this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,L(y)--> infinity and T larger than the filling transition temperature T(f)(H(s)), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T<T(f)(H(s)), however, this interface is bound either to the wedge where the two surfaces with field -H(s) meet (then the total magnetization m of the system is positive) or to the opposite wedge (then m<0). The distance l(0) of the interface midpoint from the wedges is studied as T-->T(f)(H(s)) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l(0) for T>T(f)(H(s)) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length xi(y) in the y direction along the wedges is also studied, and we find no transition for finite L and L(y)--> infinity. For L--> infinity the prediction l(0) proportional, variant (H(sc)-H(s))(-1/4) is verified, where H(sc)(T) is the inverse function of T(f)(H(s)) and xi(y) proportional, variant (H(sc)-H(s))(-3/4), respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.

Interface Localization-Delocalization in a Double Wedge: A New Universality Class with Strong Fluctuations and Anisotropic Scaling

Using Monte Carlo simulations and finite-size scaling methods we study "wetting" in Ising systems in a LxLxL(y) pore with quadratic cross section. Antisymmetric surface fields H(s) act on the free LxL(y) surfaces of the opposing wedges, and periodic boundary conditions are applied along the y direction. In the limit L--> infinity, L(y)/L(3)=const, the system exhibits a new type of phase transition, which is the analog of the "filling transition" that occurs in a single wedge. It is characterized by critical exponents alpha=3/4, beta=0, and gamma=5/4 for the specific heat, order parameter, and susceptibility, respectively.

Three-dimensional analysis of compaction of metal powder

Three-dimensional compaction simulations of geometries with circular and quadratic cross-sections are reported using dilatant viscoplastic material models representing a ductile steel powder. The simulations are compared with experiments using in situ measurements of the wall-tractions within the die. Two different porous viscoplastic material models have been used: the combined Fleck–Kuhn–McMeeking (FKM) and Gurson model and the Shima–Oyane model. The contact between the die and the powder was modelled with Coulomb-type friction. Effects such as the applied traction – density response and average relations for the upper, lower and the normal tractions against the die wall are compared. Comparisons between the numerical results and experimental results show that both material models can well be used to capture the overall density distributions for the geometries studied and that many of the coarse three-dimensional features of the powder-pressing process are well described by the simulations.

Problems with Computer Simulation of the Diffusional Transport in Reconstructed Porous Media

In order to determine the yield of a given gas reaction catalyzed by a so-called reconstructed porous catalyst as a function of the operation conditions, two processes have to be simulated: the reaction on the catalytically active walls and the diffusional material transport within the pore space of the catalyst. In this contribution, the diffusional material transport of a pure gas through a capillary of constant quadratic cross section under steady-state conditions without the influence of a chemical reaction is discussed and the procedure tested for use in computer-aided catalyst design.

Problems with Computer Simulation of the Diffusional Transport in Reconstructed Porous Media

In this contribution, the diffusional material transport of a pure gas through a capillary of constant quadratic cross section under steady-state conditions without the influence of a chemical reaction is discussed and the procedure tested for use in computer-aided catalyst design.

Application of a high-power KrF laser for the study of supersonic gas flows and the development of hydrodynamic instabilities in layered media

The design of a miniature laser shock tube for the study of a wide range of hydrodynamic phenomena in liquids at pressures greater than 10 kbar and in supersonic flows with large Mach numbers (greater than 10) is discussed. A substance filling a chamber of quadratic cross section, with a characteristic size of several centimetres, is compressed and accelerated due to local absorption of 100 ns, 100 J KrF laser pulses near the entrance window. It is proposed to focus a laser beam by a prism raster, which provides a uniform intensity distribution over the tube cross section. The system can be used to study the hypersonic flow past objects of complex shape and the development of hydrodynamic instabilities in the case of a passage of a shock wave or a compression wave through the interfaces between different media.

Shape factors for conductive heat flow in circular and quadratic cross-sections

The two-dimensional steady heat flow in bodies with different cross-sections and isothermal boundaries is a problem that has been investigated intensively in the literature. For the cross-section of two concentric circles the analytical solution of the shape factor as a function of the ratio of the outer diameter to the inner diameter is well known and can be found in most textbooks on heat transfer. For some simple well defined geometries it is possible to calculate the shape factor by the method of conformal mapping. But for arbitrarily shaped cross-sections numerical methods or correlations fitted to measured or calculated values have to be used. We applied the Method of Finite Elements and the Method of Finite Differences to calculate shape factors for cross-sections bounded by concentric circles and squares. By developing the shape factor for the investigated cross-sections analytical approximations for the shape factor are obtained. The approximations fulfil limiting cases and are close to the exact solutions when being fitted to the numerical values.

Crash and energy absorption behaviour of interleaved carbon-fibre-reinforced epoxy tubes

It is well known that the energy absorption capacity per unit weight of composite structural parts under axial crush load is much better than those of steel or aluminium [1±4]. For that reason they are increasingly used in crush-loaded structures of any kind of vehicle, especially in automobiles. Beside special composite crush elements, complex composite structures such as longitudinal girder, cross-members, mudguards, underbodies and even complete car bodies are subjects of research. The investigations on the crush behaviour of composites focused mainly on crush elements with simple geometry, e.g., tubes with cylindrical and quadratic cross-sections and cones [1±7]. A useful measure of energy absorption capability is the speci®c sustained crash stress. The speci®c sustained crash stress, oss, is de®ned as follows: o ss ˆ Fav Ar

Scaling laws for integrated optics waveguides

The accurate design of integrated optical S bends, power splitters, and directional couplers is described through a minimum number of normalized parameters. General design curves showing these normalized parameters for waveguides with a step refractive index profile and a quadratic core cross section are given. Thus a wide variety of integrated optical components may be designed accurately without the use of time-consuming numerical methods.

Visualization of Taylor-Couette flow in superfluid helium

The flow of superfluid helium in an annular gap of 5 mm width between two concentric cylinders has been investigated in the temperature range 1.6–2.1 K. While the outer cylinder was fixed, the inner cylinder rotated at rotation rates between 0.2 and 1.0 rev s −1. Hollow glass spheres of an appropriate average density and a diameter 20 μm ⩽ d ⩽ 50 μm were used to visualize the flow field. Taylor vortices with an approximately quadratic cross-section were observed over the whole parameter range investigated.

Fine structure of excitons and polariton dispersion in quantum wires

We obtain the fine structure of excitons caused by the electron-hole exchange interaction in quantum well wires of quadratic cross-section. The exciton-photon interaction is formulated in second quantization. By solving the coupled equations of motion for excitons and photons we find the dispersion relations for localized and resonant polaritons as well as the radiative lifetime for the resonant modes. We compare this with our previous results for quantum well excitons.

Monte Carlo simulation of ion implantation into two- and three-dimensional structures

Until now, rigorous Monte Carlo simulations of ion implantation into 3-D structures have been prohibited by the large amount of computer time required, and 2-D simulations have been restricted to simple structures like linear mask edges or rectangular trenches. Methods are presented which made 2-D simulations with arbitrary geometries as well as 3-D simulations with simple geometries feasible. First, an auxiliary grid is used to reduce the time required to check whether an ion crosses a boundary. Second, each ion trajectory is used several times to determine the history of ions entering the target at different positions. The methods are demonstrated by three examples: implantation into a rectangular trench, implantation into a 2-D trench with nonplanar sidewalls, and implantation into a 3-D trench with quadratic cross section. >

On the fluid dynamics of the aortic valve

An aortic-valve model is developed, having a quadratic cross-section, two rigid cusps and two wedge-shaped aortic sinuses. The flow through this valve is assumed to be one-dimensional, just as the flow behind the cusps should be one-dimensional. The resulting model equations are two nonlinear ordinary differential equations of second order for the valve opening area as a function of time in two different ranges.This model allows the size of the aortic sinus to be varied; it also permits a computation of the pressure at both sides of the cusps (unlike previous models of this kind, which consider the flow behind the cusps as stagnant). The computed valve motion due to this pressure difference is in good agreement with experimental results, although no vortex with circular streamlines is postulated in the aortic sinuses. Obviously such vortices trapped in the sinuses are not important for the valve closure, which is controlled solely by the flow deceleration.

Influence of natural convection on the concentrational limits of ignition of a fuel mixture in a closed vessel

This article attempts to calculate the concentrational limits of the ignition of a fuel mixture in a subcritical initial state when the chemical reaction is initiated by a specified heat source. In order to examine the role of convection, a broad range of Damkohler numbers are used which characterize the ratio between the gas-dynamic and chemical time, and the concentrational limits in the field of an external force (gravity) and when g=O are compared. A methane-air mixture is investigated. The motion of a gaseous fuel mixture in a plane vessel of quadratic cross section is described by nonsteady two-dimensional NavierStokes equations, taking account of the consumption of the reagent present in adequate amounts, in a first-order exothermal chemical reaction. The aim of the calculation of the concentration limits is to establish the dependence of the Damkohler number on a parameter which characterizes the initial mixture composition. Improvements are made in a numerical method allowing the process of combustion-source development in a closed vessel to be modeled on the basis of sufficiently complete nonsteady two-dimensional equations of motion of the reacting gas, and allowing the limits of ignition of the fuel mixture with a subcritical initial state to be calculated. Itmore » is shown that convection leads to different concentrational limits in the ignition of a fuel mixture.« less

A fossil baboon skull from the lower Omo basin, southwest Ethiopia

A well-preserved fossil skull assignable to the genusPapio was discovered in the late Pliocene deposits at the “White Sands locality” of the lower Omo basin, southwest Ethiopia in November 1978. This skull obviously belongs to a male baboon which is morphologically somewhat different from the extant species ofPapio and closely resemblesPapio baringensisR. E. F. Leakey, 1969. Its muzzle is not only long but comparatively wide and robust with a very flat dorsum, an almost quadrate vertical cross section, short and obtuse maxillary ridges and virtually absent maxillary fossae, and its zygomatic portion flares laterally to widen the large temporal process of the zygomatic bone. The post-orbital constriction is very marked, the temporal fossa is squarish in basal view, and the sagittal crest is placed rather posteriorly and meets a large nuchal crest, all of which suggest heavy temporal musculature. The incisors are lacking but were probably not as small as inP. baringensis. As a result of morphological comparisons with extant and fossil species ofPapio, this newly discovered skull was considered to represent a new species,Papio quadratirostris.

Echo width of foam supports used in scattering measurements

Theoretically and experimentally determined echo widths of dielectric cylinders having circular, triangular, and quadratic cross sections have been compared. The cylinders were made of foam material having a relative dielectric constant of about 1.035. The purpose of the investigation was to find a cross section with a small echo width. The result can be used in selecting a proper support for test objects in backscattering measurement studies.

Über die Ursache der Supraleitung. III / On the cause of superconductivity. III.

Abstract By consideration of superconducting compounds, whose chemical bond nature is known or can be derived with some certainty, it is shown that superconductivity only occurs, if valency electrons of a band can move in at least one space direction without intersecting any nodal surfaces. This applies both for metallic substances and for semiconductors. The following examples are discussed: 1. Metallic and semiconducting compounds composed of elements of the main groups and having a lattice similar to that of NaCl. 2. Nb- and Ta-chalcogenides with MoS2-structure. 3. The clathrate-compound [Ag7O8]+X-. 4. LaC2 with CaC2-structure. 5. Metallic and semiconducting perovskites. 6. Spinels and interstitial compounds with NaCl-structure. 7. Pyrites. 8. Some metals and their alloys. In the case of s-electrons, this condition is fulfilled for all space directions, in the case of &lt;5-bonds only along the intersecting line of the two nodal planes. A “δ”-bond is often - especially in an NaCl-type lattice - associated with a translation perpendicular to this intersecting line (in the NaCl-type lattice a translation by a/2) and a rotation by 90°. In such a “δt”-bond system the four segments of a dt2g-electron belong to four adjacent canals of quadratic cross-section (in the NaCl-type lattice the side length is a/2) which are not intersected by nodal surfaces. Only electrons fulfilling the condition indicated above can be considered as “free electrons”.

The slip systems in KC1: Pb: A piezospectroscopic investigation of the Pb ++ centre

The stress-induced polarization of the luminescence of KC1: Pb is determined. It reveals the many possible slip systems in KC1. If the uniaxial stress is applied along 〈100〉 the frequently observed {1 1 0}〈100〉 systems are stressed. In general, at low stresses one or two of the four stressed systems are active (orthogonal slip), at high stresses all four stressed systems are active (oblique slip). If the uniaxial stress is applied along 〈111〉 it is highly probable that one of the three stressed {001}〈110〉 systems is active. A uniaxial stress along 〈110〉 can produce slip in many different ways. If the sample has a nearly quadratic cross section two or four {1 1 0}〈110〉 systems are active, if the sample is uncommonly shaped it is possible to force slip on one, two, three, or even four {001}〈110〉 systems.