Solution of the Ornstein–Zernike Equation in the Critical Region

A new numerical scheme for the solution of liquid state integral equations using the Baxter factorization of the Ornstein–Zernike equation is proposed. For short range potentials the method yields reliable results over the whole fluid region, including the vicinity of the critical point, and opens up new possibilities for numerical study of the critical behavior of integral equation approximations. To demonstrate the effectiveness of the method, numerical results are compared with the analytical solution of the mean spherical approximation for a hard-core plus Yukawa tail interaction potential. Accurate results for the critical exponents δ, γ, and η for this model are obtained.     

Thermoactive coating as a means for controlled action on the temperature field of an infinite solid body with a spherical heating source

A mathematical model of the process of formation of a temperature field in an infinite isotropic solid body containing a spherical heating source with a thermally thin thermoactive coating of its surface has been proposed. The obtained analytical solution of the corresponding problem of nonstationary heat conduction has been used for substantiation of the possibility of acting on the temperature field of the system under study in a controlled manner. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 12–19, May–June, 2006.     

基于一致性几何绕射理论的曲面表面绕射声场解

提出了一种基于一致性几何绕射理论的理想刚性光滑曲面表面绕射声场高频近似计算方法。分别以圆球和无限长圆柱为例,计算了其表面绕射声场,并将计算结果与解析解进行了比较。结果表明,该方法具有计算简单明确,物理概念清晰,计算结果精确的特点。     

Resistance of spherical fills in the case of flow of single- and two-phase media

The results of experimental investigations of the hydrodynamic resistance in spherical fills as applied to the cores of nuclear reactors with spherical fuel elements are presented. The experimental setup and the procedures of preparation of models, measurement, and processing of experimental data are described. The criterial dependences satisfactorily describing data on resistance in motion of single- and two-phase media in spherical fills are obtained. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 283–288, March–April, 2009.     

真实空气中TNT装药爆炸近区冲击波传播特性研究

本文基于点源爆炸理论,建立了面源、线源和点源TNT装药强爆炸解,填补了面源与线源强爆炸解的空白;采用真实空气状态方程进行分析计算,研究了真实空气条件下球形TNT装药爆炸近区冲击波的传播特性。通过算例分析,计算结果与已有文献资料数据吻合较好。本文的研究成果对爆炸力学和防护工程研究起到了重要的参考作用。     

The secondary splitting of zero-gradient points in a scalar field

The mechanisms related to the secondary splitting of zero-gradient points of scalar fields are analyzed using the two-dimensional case of a scalar extreme point lying in a region of local strain. The velocity field is assumed to resemble a stagnation-point flow, cf. Gibson (Phys Fluids 11:2305–2315, 1968), which is approximated using a Taylor expansion up to third order. The temporal evolution of the scalar field in the vicinity of the stagnation point is derived using a series expansion, and it is found that the splitting can only be explained when the third-order terms of the Taylor expansion of the flow field are included. The non-dimensional splitting time turns out to depend on three parameters, namely the local Péclet number Pe _δ based on the initial size of the extreme point δ and two parameters which are measures of the rate of change of the local strain. For the limiting casePe _δ → 0, the splitting time is found to be finite but Péclet-number independent, while for the case of Pe _δ → ∞ it increases logarithmically with the Péclet number. The physical implications of the two-dimensional mathematical solution are discussed and compared with the splitting times obtained numerically from a Taylor–Green vortex.     

旋转点声源声场的数值仿真计算

旋转声源辐射声场的计算是利用点源模型预测风扇离散噪声的关键所在,对叶片式机械气动噪声的研究具有重要参考价值.提供了在任意边界条件下计算旋转点声源辐射卢场的数值仿真计算方法.将连续的旋转声源离散化,处理为分布于旋转轨迹上的有限个固定点声源.利用离散化处理后的声源,通过边界元法分别计算旋转单极子和旋转点力源的辐射声场.在自由空间内的计算结果与理论解进行了对比验证,得到较为理想的结果:另外进行了有限长圆管内旋转点声源辐射声场的数值计算,由此对不同长度圆管的结果进行对比,分析了管道长度对声场分布以及指向性的影响规律.     

Theoretical study of the curve of the melting point of iron with allowance for ionization by pressure

A curve of the melting point of iron up to 200 GPa is constructed on the basis of the Lindemann criterion. The transverse velocity of sound, needed for determining the Debye temperature, is calculated with allowance for ionization by pressure. The compression dependence of the concentration of free electrons is ascertained via the band structure of the metal obtained for various compression ratios by solving the Hartree-Fock-Slater equations of a self-consistent field in the Wigner—Seitz approximation of spherical cells. The calculated curve is compared with the experimental melting-point curve.     

Preparation and characterisation of calcium-phosphate porous microspheres with a uniform size for biomedical applications

In the present work, a novel route for the preparation of porous ceramic microspheres is described. Two ceramic powders, calcium-titanium-phosphate (CTP) and hydroxyapatite (HAp), were mixed with a sodium alginate solution that enabled the preparation of spherical particles, using the droplet extrusion method combined with ionotropic gelation in the presence of Ca²⁺. The spherical particles were subsequently sintered, to burn-off the polymer and obtain calcium-phosphate microspheres with a uniform size and an interconnected porous network. CTP microspheres with diameters ranging from 513 ± 24 μm to 792 ± 35 μm and with pores of approximately 40 μm were obtained. HAp microspheres presented diameters of 429 ± 46 μm and 632 ± 40 μm and pores of ca. 2 μm. Depending on the formulations tested, the structure of both calcium phosphates may become altered during the sintering process, suggesting that the ratio between the ceramic phase and the polymer solution is a critical parameter. Porous microspheres prepared using the described methodology are promising candidates as bone defect fillers and scaffolds for bone tissue regeneration.     

New superelements for singular derivative problems of arbitrary order

The paper describes a new method for development of singular elements through optimal positioning of offset mid‐side nodes using adjacent six‐ and eight‐noded isoparametric elements. By joining the two elements to form a superelement, an attempt to rectify a known problem with existing approaches proves successful. Calculations are made to optimize the mid‐side node positions and the relative size of the two elements for a wide range of singular orders. By way of example, the approach is applied to two different forms of singular stress field in a bimaterial joint in a three‐point‐bend test. Numerical solutions for the singular fields existing at both ends of the material interface compare favourably with those obtained with the more usual refined mesh approach. Copyright © 2001 John Wiley & Sons, Ltd.     

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 10⁵) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov–Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L ₂ and L _∞, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.     

Acoustic scattering of spherical waves incident on a long fluid-saturated poroelastic cylinder

Acoustic scattering of spherical waves generated by a monopole point source in a perfect (inviscid and ideal) compressible fluid by a fluid-saturated porous cylinder of infinite length is studied theoretically in the present study. The formulation utilizes the Biot theory of dynamic poroelasticity along with the appropriate wave-field expansions, the translational addition theorem for spherical wave functions, and the pertinent boundary conditions to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a monopole point source within water is located near a porous cylinder with a water-saturated Ridgefield sandstone formation. The numerical results reveal the effects of source excitation frequency, the cylinder interface permeability condition, and the location of the point source and the field point on the backscattered pressure magnitudes. Limiting cases are considered, and the obtained numerical results are validated by already well-known solutions.     

Stress singularity for a crack with an arbitrarily curved front

To investigate the possibility of a point of a crack front propagating in a direction not in the normal plane of the crack front, the three-dimensional form of the crack front stress field is obtained. To simplify comparisons of the states of stress at various points lying on a spherical surface centered at a point of the crack front, a local spherical coordinate system is used. It is found that the crack propagation will be from each point of the crack front in a direction lying in the normal plane.The results are used in conjunction with the strain energy density fracture criterion for the problem of an elliptical crack. The plane of the flat elliptical crack makes an arbitrry angle with the field of uniform applied tensile stress. Crack growth directions for various positions along the crack front are determined, and loads required for fracture for various angles are obtained.     

Diffraction of SH-waves on interface cracks under the action of concentrated forces

In the mathematically rigorous statement, we solve the problem of diffraction of elastic SH-waves on a finite (semiinfinite) crack located on the plane boundary of two perfectly joined materials. As a sounding field, we consider the field of a point source. The problem is reduced to the Wiener – Hopf functional equation, which is solved by the method of factorization. An approximate solution of this equation is obtained. We numerically study the distribution of the field in the radiation zone and the distinctive features of its formation depending on the location of the source of radiation. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 67–77, November–December, 2008.     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

Elastic Wave Propagation in a Class of Cracked,Functionally Graded Materials by BIEM

Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson’s ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ (x)=μ ₀ exp (2ax ₂), where μ ₀ is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green’s function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case     

Coupled P and SV waves propagating in spherical elastic layers: Exact solution and interpretation

We study the propagation of coupled P and SV waves emitted by a source point placed outside a given finite set of concentric elastic spherical layers. We show that the system of boundary conditions of this pattern is a linear combination of the boundary conditions of the simpler problem of reflectionrefraction phenomenon of a wave at a spherical surface. From this result the exact solution follows for all regions of the multilayered structure without using Cramer's technique. This solution is written as a series of which each element is interpreted directly in terms of multiple reflection-refraction. It gives a simple explanation for triggering of resonance phenomena. The solution contains many particular bases of which several are investigated.     

An improved boundary distributed source method for two-dimensional Laplace equations

In this work, the boundary distributed source (BDS) method [EABE 34(11): 914-919] based on the method of fundamental solutions (MFS) is considered for the solution of two-dimensional Laplace equations. The BDS is a truly mesh-free method and quite easy to implement since the source points and field points are collocated on the domain boundary while the conventional MFS requires a fictitious boundary where the source points locate. The main idea of the BDS is that to avoid the singularities of the fundamental solutions the concentrated point sources in the conventional MFS are replaced by distributed sources over circles centered at the source points. In the original BDS, all elements of the system matrix can be derived analytically in a very simple form for the Dirichlet boundary conditions and off-diagonal elements for the Neumann boundary conditions, while the diagonal elements for the Neumann boundary conditions can be obtained indirectly from the constant potential field. This work suggests a simple way to determine the diagonal elements for the Neumann boundary conditions by invoking that the boundary integration of the normal gradient of the potential should vanish. Several numerical examples are addressed to show the feasibility and the accuracy of the proposed method.     

An analysis of the temperature field of the workpiece in dry continuous grinding

The recent model for heat transfer during intermittent grinding described in Skuratov, Ratis, Selezneva, Pérez, Fernández de Córdoba and Urchueguía (Appl Math Model 31:1039–1047, 2007) is considered. This model is particularized to the case of continuous dry grinding, where an alternative solution is obtained in the steady state. This alternative solution is analytically equivalent to the well-known formula of Jaeger (Proc R Soc NSW 76:204–224, 1942) for the steady–state temperature field created by an infinite moving source of heat and proves to be very useful for evaluating the maximum point of the temperature.