Free Planes Research Articles

First-order model theory of free projective planes

We prove that the theory of open projective planes is complete and strictly stable, and infer from this that Marshall Hall's free projective planes (πn:4⩽n⩽ω) are all elementary equivalent and that their common theory is strictly stable and decidable, being in fact the theory of open projective planes. We further characterize the elementary substructure relation in the class of open projective planes, and show in particular that (πn:4⩽n⩽ω) is an elementary chain. We then prove that the theory of open projective planes does not have a prime model, that it has elimination of quantifiers down to Boolean combinations of existential formulas, and that it is not model complete. Finally, we characterize the forking independence relation in models of the theory and prove that the πn's (4⩽n⩽ω) are strongly type-homogeneous.

On the ∀∃-Theories of Free Projective Planes

Studying the elementary properties of free projective planes of finite rank, we prove that for m > n, an arbitrary ∀∃∀-formula Φ(ȳ) and a tuple ū of elements of the free projective plane $$\mathfrak{F}_{n}$$ if Φ(ū) holds on the plane $$\mathfrak{F}_{m}$$ then Φ(ū) holds on the plane $$\mathfrak{F}_{n}$$ too. This implies the coincidence of the ∀∃-theories of free projective planes of different finite ranks.

Примеры точных решений задач изгиба пластины со свободными лицевыми плоскостями

Примеры точных решений задач изгиба пластины со свободными лицевыми плоскостями

Complexity of the Isomorphism Problem for Computable Free Projective Planes of Finite Rank

Studying computable representations of projective planes, we prove that the isomorphism problem in the class of free projective planes of finite rank is an m-complete Δ03-set within the class.

Three-dimensional analysis of an edge crack in a plate of finite thickness with the first-order plate theory

In this paper, plasticity effects at the tip of an edge through-the-thickness crack are investigated by invoking the strip-yield model and the first order plate theory. The latter theory is the simplest extension of the classical plane theories of elasticity, which is capable of accounting for three-dimensional effects and, in particular, the plate thickness effect. By utilising the distributed dislocation technique, new results are obtained on the interaction of the free boundaries (free edge and free plate planes) with the crack tip plasticity region. Numerical results for the crack tip opening displacement and global constraint factor are first presented at various crack length to plate thickness and applied stress to yield stress ratios. The results are validated against past 3D solutions for an embedded crack as well as analytical solutions obtained under the plane stress or plane strain assumption. The new model and results can be utilised in advanced fracture and fatigue analyses of cracks emanating from a free surface.

Locating Critical Circular and Unconstrained Failure Surface in Slope Stability Analysis with Tailored Genetic Algorithm

Abstract This article presents an efficient search method for representative circular and unconstrained slip surfaces with the use of the tailored genetic algorithm. Searches for unconstrained slip planes with rigid equilibrium methods are yet uncommon in engineering practice, and little publications regarding truly free slip planes exist. The proposed method presents an effective procedure being the result of the right combination of initial population type, selection, crossover and mutation method. The procedure needs little computational effort to find the optimum, unconstrained slip plane. The methodology described in this paper is implemented using Mathematica. The implementation, along with further explanations, is fully presented so the results can be reproduced. Sample slope stability calculations are performed for four cases, along with a detailed result interpretation. Two cases are compared with analyses described in earlier publications. The remaining two are practical cases of slope stability analyses of dikes in Netherlands. These four cases show the benefits of analyzing slope stability with a rigid equilibrium method combined with a genetic algorithm. The paper concludes by describing possibilities and limitations of using the genetic algorithm in the context of the slope stability problem.

Centroid sliding pyramid method for removability and stability analysis of fractured hard rock

This paper proposes a new method using centroid sliding pyramid (CSP) to identify the removability and stability of fractured hard rock in tunnel and slope engineering. The new method features two geometrical and topological improvements over the original key block method (KBM). Firstly, all the concave corners are considered as starting points of cutting process when a concave block is divided into a set of convex blocks in the original KBM. Only the concave corners formed by two joint planes are used for partitioning a concave block in the presented method and concave corners with free planes are excluded. Secondly, joint pyramid for removability computation in the original KBM is generated using all of the joint planes, while CSP is calculated only from the joint planes adjoining the free planes. The cone angle θ of CSP is the vectorial angle formed by the two candidate sliding surfaces of this CSP. Removability analysis of a block is transformed into calculating the cone angle of CSP. The geometrical relationship is simplified, and data size for removability computation is reduced compared with the original KBM. The provided method is implemented in a computer program and validated by examples of fractured rock slopes and tunnels.

Large-n approach to thermodynamic Casimir effects in slabs with free surfaces.

The classical n-vector ϕ{4} model with O(n) symmetrical Hamiltonian H is considered in a ∞{2}×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature T_{c}. Their n=∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L{-1}, anomalous ones ∝L{-1}lnL should occur. They can be considerably decreased by taking an appropriate g→∞ (T_{c}→∞) limit of the ϕ{4} interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness L_{eff}=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of {4}He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below T_{c}. The results are in conformity with various analytically known exact properties of the scaling functions.

Interlaminar Stresses in Composite Laminates Subjected to Anticlastic Bending Deformation

Approximate elasticity solutions for prediction of the displacement, stress, and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension and uniform temperature change were developed earlier by the authors. In the present paper, the authors have extended these solutions to treat bending deformation. Bending and torsion moments are combined to yield a deformation state without twisting curvature and with transverse curvature due only to the laminate Poisson effect. This state of deformation is termed anticlastic bending. The approximate elasticity solution for this bending deformation is shown to recover laminated plate theory predictions at interior regions of the laminate and thereby illustrates the boundary layer character of this interlaminar phenomenon. The results exhibit the anticipated response in congruence with the solutions for uniform axial extension and uniform temperature change, where divergence of the interlaminar shearing stress is seen to occur at the intersection of the free edge and planes between lamina of +θ and –θ orientation. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem and thereby provide an efficient and compact solution available for parametric studies of the influence of geometry and material properties. Finally, the solution was exercised to determine the dimensions of the boundary layer in bending for very large numbers of layers.

Accuracy of automated software-guided detection of significant coronary artery stenosis by CT angiography: comparison with invasive catheterisation

True automated detection of coronary artery stenoses might be useful whenever expert evaluation is not available, or as a "second reader" to enhance diagnostic confidence. We evaluated the accuracy of a PC-based stenosis detection tool alone and combined with expert interpretation. One hundred coronary CT angiography datasets were evaluated with the automated software alone, by manual interpretation (axial images, multiplanar reformations and maximum intensity projections in free double-oblique planes), and by expert interpretation aware of the automated findings. Stenoses ≥ 50 % were noted per-vessel and per-patient, and compared with invasive angiography. Automated post-processing was successful in 90 % of patients (88 % of vessels). When excluding uninterpretable datasets, per-patient sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) were 89 %, 79 %, 74 % and 92 % (per-vessel: 82 %, 85 %, 48 % and 96 %). All 100 datasets were evaluable by expert interpretation. Per-patient sensitivity, specificity, PPV and NPV were 95 %, 95 %, 93 % and 97 % (per-vessel: 89 %,98 %, 88 % and 98 %). Knowing the results of automated interpretation did not improve the performance of expert readers. Automated off-line post-processing of coronary CT angiography shows adequate sensitivity, but relatively low specificity in coronary stenosis detection. It does not increase accuracy of expert interpretation. Failure of post-processing in 10 % of all patients necessitates additional manual image work-up. • Coronary CT angiography is increasingly used for detection of coronary artery stenosis • Computer assisted diagnosis might facilitate and speed up interpretation • Performance in properly segmented cases compared favourably with manual image interpretation • However, automated segmentation failed in about 10 % of cases • Manual reading is still mandatory; computer assisted diagnosis can provide a useful second read.

Thermodynamics of metal reactants for ammonia synthesis from steam, nitrogen and biomass at atmospheric pressure

AbstractCatalytic ammonia synthesis at approximately 30 MPa and 800 K consumes about 5% of the global annual natural gas production causing significant CO2 emissions. A conceptual solar thermochemical reaction cycle to produce NH3 at near atmospheric pressure without natural gas is explored here and compared to solar thermochemical steam/air reforming to provide H2 used in the Haber‐Bosch process for NH3 synthesis. Mapping of Gibbs free energy planes quantifies the tradeoff between the yield of N2 reduction via metal nitridation, and NH3 liberation via steam hydrolysis vs. the temperatures required for reactant recovery from undesirably stable metal oxides. Equilibrium composition simulations suggest that reactants combining an ionic nitride‐forming element (e.g., Mg or Ce) with a transition metal (e.g., MgCr2O4, MgFe2O4, or MgMoO4) may enable the concept near 0.1 MPa (at maximum 64 mol % yield of Mg3N2 through nitridation of MgFe2O4 at 1,300 K, and 72 mol % of the nitrogen in Mg3N2 as NH3 during hydrolysis at 500 K). © 2011 American Institute of Chemical Engineers AIChE J, 58: 3203–3213, 2012

Block theory on the complex combinations of free planes

The core problem of block theory is to determine the finiteness, removability and mechanical stability of various blocks under different engineering structures based on dip angles, dip direction angles of discontinuities, frictional angles and the direction of the active resultant force. The practices of the classical block theory focus mainly on the convex blocks, assuming that joint surfaces and excavation faces are planar and extended infinitely in the rock mass. However, in practical engineering structures, the concave combinations of free planes (natural of excavated surfaces) are common. For example, the non-convex blocks usually exist in underground edges, corners and portals, and some of them are quite dangerous. In this paper, the characteristics of the non-convex blocks with complex combinations of free planes are analysed deeply based on the classical block theory. First, a non-convex block is seen as a combination of a series of convex blocks, then the criteria for finiteness and removability of the non-convex blocks are proposed, and finally, the identification algorithm is designed and validated by some cases. The results show that the method is effective and feasible and has important theoretical significance and practical value.

Experimental Studies on the Changes in Resistivity and Its Anisotropy Using Electrical Resistivity Tomography

Three measuring lines were arranged on one of free planes of magnetite cuboid samples. Apparent resistivity data were acquired by MIR-2007 resistivity meter when samples were under uniaxial compression of servocontrol YAW-5000F loadingmachine in laboratory. Then we constructed the residual resistivity images using electrical resistivity tomography (ERT) and plotted the diagrams of apparent resistivity anisotropy coefficient (ARAC)λ∗and the included angleαbetween the major axis of apparent resistivity anisotropy ellipse and the axis of load with pressure and effective depth. Our results show that with increasing pressure, resistivity and the decreased (D region) and increased (I region) resistivity regions have complex behaviors, but when pressure is higher than a certain value, the average resistivity decrease and the area of D region expand gradually in all time with the increase of pressure, which may be significant to the monitoring and prediction of earthquake, volcanic activities, and large-scale geologic motions. The effects of pressure onλ∗andαare not very outstanding for dry magnetite samples.

말뚝 간격에 따른 에너지 파일의 열적 거동분석

본 논문에서는 지열을 이용한 PHC 말뚝형 에너지 파일의 계절별 유속변화에 따른 열교환율과 단독말뚝의 열교환율을 100시간 운용 시 포화지반 조건에 한정하여 수치해석을 수행하였다. 해석결과 동절기 및 하절기일 때 100시간 운용 시 평균 열교환율은 약 55 W/m, 47 W/m로 나타났으며, 순환수 유속이 증가할수록 전체적인 열교환율이 상승하였다. 동절기에 말뚝간격 3D 및 5D(D:말뚝직경) 배치 시 0.6m/s의 순환수 유속에 따른 열적거동을 분석결과 지반과의 열적 자유면이 많은 외곽부일수록 열효율이 증가하였다. 또한, 3D 및 5D 간격의 평균 열교환율은 약 48.5 W/m, 51 W/m로 말뚝간격이 증가할수록 열교환율이 향상되는 것으로 나타났으며, 단독말뚝의 열교환율 대비 상대적으로 3D 및 5D 간격의 군말뚝은 각각 89% 및 93%보 떨어지는 것을 알 수 있었다. This study was conducted to analyze the thermal behavior of a PHC energy pi1e system in saturated soil conditions, various seasonal and flow-speed conditions during 100 hours of operation through numerical analysis. The examination was a1so conducted with a single pile as well as with group pils. For the operation of 100 hours, the average heat exchange rate appeared 55 W/m, 47 W/m during winter and summer respectively. An increase in flow-speed was associated with a rise in the heat exchange rate. And thermal behavior analysis results during winter season show that thermal efficiency has increased when there are more free thermal planes. For the operation in group pile as 3D and 5D pile spacing (D: pile diameter), average heat exchange rate increased as pile spacing grows. Compared with the heat exchange rate of single pile, thermal exchange efficiency of group pile decreased by 89% (for 3D spacing) and 93% (for 5D spacing).

Interlaminar stresses in composite laminates: Thermoelastic deformation

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4]. In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σ x over the laminate cross-section in the y– z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of + θ and − θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.

Short term wind speed prediction using support vector machine model

Wind speed prediction in short term is required to asses the effect of wind on different objects in action in free space, like rockets, navigating ships and planes, guided missiles satellites in launch etc. Forecasting also helps in usage of wind energy as an alternative source of energy in Electrical power generation plants. The wind speed depends on the values of other atmospheric variables, such as pressure, moisture content, humidity, rainfall etc. This paper reports a Support Vector Machine model for short term wind speed prediction. The model uses the values of these parameters, obtained from a nearest weather station, as input data. The trained model is validated using a part of data. The model is then used to predict the wind speed, using the same meteorological information.

Stabilization of surface reaction intermediates by added metal atoms on metal surfaces of low free energy

Dynamic restructuring of the Ag(111) surface occurs during the reaction of sulfur dioxide with Ag(111)-p(4 x 4)-O at 300 K, resulting in the incorporation of added silver atoms into the unit cells of both adsorbed sulfite and sulfate. This result clearly demonstrates that incorporation of metal atoms into the structures of adsorbates and reaction intermediates is not restricted to more open, higher free energy single crystal planes. These observations indicate that the participation of added metal atoms must be considered in the theoretical treatment of metal catalyzed reactions.

A semi‐analytic approach for direct slicing of free form surfaces for layered manufacturing

PurposeThis paper aims to develop an efficient surface‐plane intersection (SPI) algorithm for direct slicing of free‐form surfaces to be produced by layered manufacturing.Design/methodology/approachA semi‐analytical method for direct slicing has been formulated and tested on Bezier and B‐spline surfaces commonly used in CAD modeling. This method solves for the intersection points by a “root” finding procedure and establishes their connectivity, unlike the conventional “marching” procedures.FindingsThe proposed algorithm solves intersection contours between free form surfaces and planes. The solution procedure is efficient with respect to computational time and accuracy (feature detection) over some of the conventional SPI strategies. The method involves a global solution procedure in contention with the traditional methodologies which are generally spatially distinctive in approach.Research limitations/implicationsUse of higher order terms in the representation of parametric surfaces makes the algorithm computationally intensive and time‐expensive.Practical implicationsThis algorithm would be of practical use in the direct slicing of free form surfaces used in CAD modeling. Direct slicing methods solve for the actual intersection of surface and plane without resorting to “tessellation.” Reducing the computation time and detection of features within a given resolution is of primary importance for developing commercial rapid prototyping software, which is achieved in the present paper.Originality/valueA novel method has been developed for SPI for use in direct slicing of CAD models. While a major proportion of the direct slicing strategies employ the “marching” procedure involving determination of “critical points,” the proposed method utilizes the evaluation of “roots” of a surface in a global manner to determine the intersection points with proper connectivity. Hence, it is effective in reducing the computation time and is simple but generic in approach. Although Bezier and B‐spline surfaces are used as the representative cases, the algorithm can be extended for any parametric surface for direct slicing.

Die sonomorphologische Topographie des weiblichen Beckens

Achieving a high quality gynaecological ultrasound examination requires thorough knowledge of topographic anatomy. To date, there are no guidelines for a standardised course of the examination. The goal of the study was to define exact planes by means of cross-sectional anatomy and then to standardise the gynaecological ultrasound examination with the transabdominal, introital and transvaginal technique. We developed a software tool based on IDL (Interactive Data Language) for the female data set of the Visible Human Project which generates free determinable planes in the volume. The organs of the female pelvis were divided into landmark- and target structures according to the ultrasonic visibility and the variability of the position, shape and structure. From this, a course for the gynaecological ultrasound examination was created and verified on 65 patients each with an inconspicuous ultrasound finding. In addition, the average duration of the examination was determined. The landmark structures could be demonstrated in all patients. Five planes were defined for each technique, and the course of the whole examination with 15 exact planes was described. The average duration of the examination was 4.5 minutes. As of now, the digitally reconstructed anatomical illustrations have achieved the best image resolution and quality regardless of the position of the plane in the examination volume. The standardised course of the gynaecological ultrasound examination can serve as a basis for the improvement of training quality and the evaluation of a general gynaecological ultrasound screening.

Free Planes in Lattice Sphere Packings

Abstract We show that for every lattice packing of n-dimensional spheres there exists an (n/log2(n))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large enough. Such an affine plane is called a free plane and our result improves on former bounds.