Rheological and dynamic thermomechanical propert ies of epoxy composites reinforced with single- and multiwalled carbon nanotubes

An epoxy resin (Epon 828) was filled with single- and multiwalled carbon nanotubes (SWCNT and MWCNT) in two steps by using the high shear mixing and ultrasonication techniques. The melt flow of the composites was characterized in a plate/plate rheometer. The thermomechanical properties of the composites were determined in dynamic mechanical analysis tests performed at various frequencies and temperatures. It was found that the incorporation of SWCNT or MWCNT increased the viscosity and stiffness of epoxy above its glass-transition temperature. The time-temperature superposition principle was employed to estimate the storage modulus of the composites as a function of frequency (f = 10^–33–10³ Hz) in the form of master curves.     

Investigating Asymptotic Suction Boundary Layers using a One-Dimensional Stochastic Turbulence Model

The one-dimensional turbulence model (ODT) is applied to study turbulent asymptotic suction boundary layers for a Reynolds number of Re = u_∞/v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively. In here we will demonstrate that a large eddy suppression mechanism may reduce the influence of ODT model parameters, such as the viscous cut-off parameter Z. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On one contact problem of plane elasticity theory with partially unknown boundary

Applications of elastic plates weakened with full-strength holes are of great interest in several mechanical constructions (building practice, in mechanical engineering, shipbuilding, aircraft construction, etc). It's proven that in case of infinite domains the minimum of tangential normal stresses (tangential normal moments) maximal values will be obtained on such contours, where these values maintain constant(the full strength holes). The solvability of these problems allow to control stress optimal distribution at the hole boundary via appropriate hole shape selection. The paper addresses a problem of plane elasticity theory for a doubly connected domain S on the plane z = x + iy, which external boundary is an isosceles trapezoid boundary; the internal boundary is required full-strength hole including the origin of coordinates. In the provided work the unknown full-strength contour and stressed state of the body were determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of round jets with nozzle-dependent inflow conditions using the k−ε turbulence model

In view of the “round jet initial condition anomaly”, discussed in literature, we investigate the effect of inflow conditions resulting from the use of different nozzle geometries to form the jet. RANS simulations in the framework of OpenFOAM using the k − ε turbulence model are performed. As the standard model coefficient C_ε1 = 1.44 is known to overpredict spreading rates for round jets, a value of C_ε1 = 1.6 was recommended for this case already in the 1970's. While this works well for jets issuing from long pipes, it does not give satisfactory results for other nozzle geometries. To overcome this deficiency while keeping the k − ε model, we suggest modified coefficients C_ε1 based on profiles of mean flow and turbulence at the nozzle exit. We determine optimal values of C_ε1 for three different nozzle geometries, and test them at various Reynolds numbers. Good agreement with experimental data is obtained. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sums of Magnetic Eigenvalues are Maximal on Rotationally Symmetric Domains

The sum of the first n ≥ 1 energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)³ on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n = 1).     

Analysis of the operator splitting scheme for the Cahn‐Hilliard equation with a viscosity term

In this paper, we consider a second‐order fast explicit operator splitting method for the viscous Cahn‐Hilliard equation, which includes a viscosity term αΔu_t (α ∈ (0, 1)) described the influences of internal micro‐forces. The choice α = 0 corresponds to the classical Cahn‐Hilliard equation whilst the choice α = 1 recovers the nonlocal Allen‐Cahn equation. The fundamental idea of our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using a pseudo‐spectral method, and thus an ordinary differential equation is obtained. The nonlinear one is solved via TVD‐RK method. The stability and convergence are discussed in L²‐norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Besides, a detailed comparison is made for the dynamics and the coarsening process of the metastable pattern for various values of α. Moreover, energy degradation and mass conservation are also verified.     

Diffraction of a magnetoelastic wave on stress concentrators in conducting bodies (antiplanar deformation)

We consider a two-dimensional boundary-value problem of magnetoelasticity for a half-space weakened by tunnel stress concentrators (cracks, holes) in the presence of a static magnetic field. The mechanical stimulus is taken as a magnetoelastic shear wave incident from infinity or a shear load that varies harmonically in time and is prescribed on the edges of the crack or hole. The problem reduces to a singular integral equation that can be solved numerically by the method of mechanical quadratures. We give the results of computation of the coefficient of stress intensity K₁₁₁ for a slit and the stress concentration on the edge of a hole. We conclude that it is necessary to take account of electromagnetic effects in estimating the strength of diamagnetic or paramagnetic bodies. Four figures. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 103–110 1991.     

Identification of Viscoelastic Properties and Damaging Effects of Highly Extensible Polyurea

The present work aims particular at the experimental identification of the viscoelastic properties of polyurea as well as on the onset of the damage. For the viscoelastic part, several relaxation experiments are performed. From the measured data a general viscoelastic model is derived where we use two different approaches. At first we identify a general Maxwell model (combining spring and damping elements for finite deformations) to use a prony series with N elements, which requires the identification of 2N + 1 parameters. At second, a model of generalized fractional elements [3] is employed. Both approaches are studied in detail and are compared to data from literature; furthermore a comparison concerning the effort is presented. Damaging effects of Polyurea are investigated using tensile tests with and without cyclic loading. In particular we focus on the the onset of damage by cavitation. To this end the recovered specimens were analyzed using a laser microscope; the surfaces of the ruptured areas are compared in terms of quantity and size of voids. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of an external magnetic field on the dynamic stress of an elastic conducting one-sided layer with a longitudinal shear crack

We study the interaction of a magnetoelastic shear wave with a curvilinear tunnel crack in an ideally conducting diamagnetic (resp. paramagnetic) one-sided (resp. two-sided) layer in the presence of an external static magnetic field. The bases of the one-sided layer are free of mechanical load, and the rim of the face is clamped or free. The corresponding linearized boundary-value problem of magnetoelasticity is reduced to a singular integrodifferential equation with subsequent implementation on a computer. We give numerical results that characterize the influence of the size of the preliminary magnetic field, the frequencies of the load, the curvature, and the orientation of the crack on the stress intensity factor. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 96–102.     

Multiobjective Optimization of the Flow Around a Cylinder Using Model Order Reduction

In this article an efficient numerical method to solve multiobjective optimization problems for fluid flow governed by the Navier Stokes equations is presented. In order to decrease the computational effort, a reduced order model is introduced using Proper Orthogonal Decomposition and a corresponding Galerkin Projection. A global, derivative free multiobjective optimization algorithm is applied to compute the Pareto set (i.e. the set of optimal compromises) for the concurrent objectives minimization of flow field fluctuations and control cost. The method is illustrated for a 2D flow around a cylinder at Re = 100. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The standard model physical degrees of freedom interpretation of the electromagnetic fine structure coupling

The present short note gives for the first time a derivation of the inverse electromagnetic fine structure constant from the elementary particles content of the standard model plus graviton and the Higgs. It is the first derivation ever to interpret as the familiar N_f = (2)(48) = 96 Fermions and N_B = (2)(15) = 30 Bosons of the standard model plus the eleven dimensions D = 11 of super gravity spacetime . The exact theoretical value 137.082039325 and the accurate experimental results are also given clear mathematical derivation showing that all of the 137 and not only the 96 + 30 = 126 may be interpreted as physical particles so that in a sense elementary particles create and span spacetime.     

A new bound for the distance to singularity of a regular matrix pencil

For regular matrix pencils 𝒜(s) = sE − A the distance to the nearest singular pencil in the Frobenius norm of the coefficients is called the distance to singularity. We derive a new lower bound for this distance by using the spectral theory of tridiagonal Toeplitz matrices. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boundary Layer Heat Transport in turbulent Rayleigh-Bénard Convection in Air

We study the convective heat transfer in a large-scale Rayleigh-Bénard (RB) experiment which is called the “Barrel of Ilmenau”. We present the results of flow visualization and Particle Image Velocimetry (PIV) measurements of the near wall flow field in a plane perpendicular to the surface of the heated bottom plate. The experiment was run in a smaller rectangular inset that was placed inside the larger barrel. The Rayleigh number amounts to Ra = 1.4 × 10¹⁰. The aspect ratios were Γ_x = 1 in flow direction and Γ_y = 0.26 perpendicular to the vertical flow plane. The measurements have been undertaken using a 2 W continuous wave Laser in combination with a light sheet optics and various cameras. Due to the slender geometry of the cell, the mean wind is confined in one direction where the Laser light sheet is aligned parallel. The flow was seeded with droplets of 1...2 µm size generated using an ordinary fog machine. Flow visualization as well as the PIV data clearly show the intermittent character of the boundary layer flow field that permanently switches between “laminar” and “turbulent” phases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transforming algebraic Riccati equations into unilateral quadratic matrix equations

The problem of reducing an algebraic Riccati equation XCX − AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX ² + QX + R = 0 is analyzed. New transformations are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm (SDA) of Anderson (Int J Control 28(2):295–306, 1978) is in fact the cyclic reduction algorithm of Hockney (J Assoc Comput Mach 12:95–113, 1965) and Buzbee et al. (SIAM J Numer Anal 7:627–656, 1970), applied to a suitable UQME. A new algorithm obtained by complementing our transformations with the shrink-and-shift technique of Ramaswami is presented. The new algorithm is accurate and much faster than SDA when applied to some examples concerning fluid queue models.     

On the number of affine equivalence classes of spherical tube hypersurfaces

We consider Levi non-degenerate tube hypersurfaces in \mathbbCⁿ⁺¹{\mathbb{C}^{n+1}} that are (k, n − k)-spherical, i.e. locally CR-equivalent to the hyperquadric with Levi form of signature (k, n − k), with n ≤ 2k. We show that the number of affine equivalence classes of such hypersurfaces is infinite (in fact, uncountable) in the following cases: (i) k = n − 2, n ≥ 7; (ii) k = n − 3, n ≥ 7; (iii) k ≤ n − 4. For all other values of k and n, except for k = 3, n = 6, the number of affine classes was known to be finite. The exceptional case k = 3, n = 6 has been recently resolved by Fels and Kaup who gave an example of a family of (3, 3)-spherical tube hypersurfaces that contains uncountably many pairwise affinely non-equivalent elements. In this paper we deal with the Fels–Kaup example by different methods. We give a direct proof of the sphericity of the hypersurfaces in the Fels–Kaup family, and use the j-invariant to show that this family indeed contains an uncountable subfamily of pairwise affinely non-equivalent hypersurfaces.     

On quasi-symmetric designs with intersection difference three

In a recent paper, Pawale (Des Codes Cryptogr, 2010) investigated quasi-symmetric 2-(v, k, λ) designs with intersection numbers x > 0 and y = x + 2 with λ > 1 and showed that under these conditions either λ = x + 1 or λ = x + 2, or D{\mathcal{D}} is a design with parameters given in the form of an explicit table, or the complement of one of these designs. In this paper, quasi-symmetric designs with y − x = 3 are investigated. It is shown that such a design or its complement has parameter set which is one of finitely many which are listed explicitly or λ ≤ x + 4 or 0 ≤ x ≤ 1 or the pair (λ, x) is one of (7, 2), (8, 2), (9, 2), (10, 2), (8, 3), (9, 3), (9, 4) and (10, 5). It is also shown that there are no triangle-free quasi-symmetric designs with positive intersection numbers x and y with y = x + 3.     

Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels

Variable stepsize algorithms for the numerical solution of nonlinear Volterra integral and integro-differential equations of convolution type are described. These algorithms are based on an embedded pair of Runge–Kutta methods of order p=5 and p=4 proposed by Dormand and Prince with interpolation of uniform order p=4. They require O(N) number of kernel evaluations, where N is the number of steps. The cost of the algorithms can be further reduced for equations that have rapidly vanishing convolution kernels, by using waveform relaxation iterations after computing the numerical approximation by variable stepsize algorithm on some initial interval. AMS subject classification (2000)  65R20, 45L10, 93C22     

Analysis of wave propagation in the fluid-saturated porous media

In the present work, a so-called hybrid two-phase model composed of a materially incompressible solid and a compressible pore fluid is studied. The mechanical behavior is described by the thermodynamically consistent Theory of Porous Media (TPM). Numerical experiments were performed with the space-time coupled discontinuous galerkin (DGT)-method. The existence of two compressional waves (P-waves) and one shear wave (S-wave) was confirmed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Attractors and Long Time Behavior of von Karman Thermoelastic Plates

This paper undertakes a study of asymptotic behavior of solutions corresponding to von Karman thermoelastic plates. A distinct feature of the work is that the model considered has no added dissipation—particularly mechanical dissipation typically added to plate equation when long time-behavior is considered. Thus, the model consists of undamped oscillatory plate equation strongly coupled with heat equation. Nevertheless we are able to show that the ultimate (asymptotic) behavior of the von Karman evolution is described by finite dimensional global attractor. In addition, the obtained estimate for the dimension and the size of the attractor are independent of the rotational inertia parameter γ and heat/thermal capacity κ, where the former is known to change the character of dynamics from hyperbolic (γ>0) to parabolic like (γ=0). Other properties of attractors such as additional smoothness and upper-semicontinuity with respect to parameters γ and κ are also established. The main ingredients of the proofs are (i) sharp regularity of Airy’s stress function, and (ii) newly developed (Chueshov and Lasiecka in Memoirs of AMS, in press) “compensated” compactness methods applicable to non-compact dynamics. I. Lasiecka’s research partially supported by the NSF Grant DMS-0104305 and ARO Grant DAAD19-02-10179.