Simulation of cross-flow-induced vibration of cylinder arrays by surface vorticity method

The surface vorticity method (SVM), which is a fast and practical grid-free two-dimensional (2-D) method, and a fluid–structure interaction model incorporating the effects of cylinder motions and displacements is used to simulate the vortex-induced vibration of cylinder arrays at sub-critical Reynolds number Re=2.67×10⁴. The SVM is found to be most suitable for simulating a 2-D cylinder row with large-amplitude vibrations where the vorticity field and the fluid forces of the cylinder row change drastically, and the effect of the stream on the transverse direction vibration is very significant. The fluidelastic instability of a flexible cylinder row at small pitch ratio is also investigated, and the critical reduced velocity of the cylinder row at a reduced damping parameter S_G=1.29 is calculated, which is in good agreement with experimental and analytical results of the unsteady model. Vortex-induced vibration of a staggered cylinder array is simulated using different structural parameters. When the cylinders are relatively more flexible, the flow pattern changes dramatically and the fluid–structure interaction has a dominant impact on the flow field. Compared with grid-based methods, the grid-free SVM is a fast and practical method for the simulation of the FIV of cylinder arrays due to vortex shedding at sub-critical Reynolds numbers.     

Rheological analysis of highly concentrated w/o emulsions

A series of highly concentrated lipophilic cosmetic emulsions were analysed, in order to determine their rheological and textural properties, as a function of their microstructure. The originality of this study lies in the methodology used, especially the shear-stress scanning analysis. The results of a very powerful and comprehensive dynamic rheological analysis suggest the existence of two critical volume fraction values: besides the “close-packed” value φ _c , a “slack-packed” value φ₀, close to 0.60 could be demonstrated. It has been shown that the close-packed structure is stable under shear; in constrast, the slack-packed configuration, defined as φ₀<φ<φ _c is unstable under shear. A comparison with theoretical models, especially that of Princen, showed good agreement and allowed the close-packed value φ _c to be defined more precisely as 0.67. The gap between 0.67 and 0.74 is probably indicative of a highly polydisperse distribution, as confirmed by microscopic analysis. Flow experiments confirmed the validity of Princen‘s model. Received: 20 February 1997 Accepted: 20 January 1998     

Micro-mechanical modeling of anisotropic inelastic response of soft tissues under supra-physiological loading

Under supra-physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro-mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature.     

Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition

In this paper, we prove the existence of nontrivial nonnegative solutions to a class of elliptic equations and systems which do not satisfy the Ambrosetti–Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth at ∞. The known results without the AR condition in the literature only involve nonlinear terms of polynomial growth. We will use suitable versions of the Mountain Pass Theorem and Linking Theorem introduced by Cerami (Istit. Lombardo Accad. Sci. Lett. Rend. A, 112(2):332–336, 1978 Ann. Mat. Pura Appl., 124:161–179, 1980). The Moser–Trudinger inequality plays an important role in establishing our results. Our theorems extend the results of de Figueiredo, Miyagaki, and Ruf (Calc. Var. Partial Differ. Equ., 3(2):139–153, 1995) and of de Figueiredo, do Ó, and Ruf (Indiana Univ. Math. J., 53(4):1037–1054, 2004) to the case where the nonlinear term does not satisfy the AR condition. Examples of such nonlinear terms are given in Appendix A. Thus, we have established the existence of nontrivial nonnegative solutions for a wider class of nonlinear terms.     

Global asymptotic stability of a second-order system of difference equations

In this paper a sufficient condition is obtained for the global asymptotic stability of the following system of difference equations $$x_{n + 1} = \frac{{x_n y_{n - 1}^b + 1}} {{x_n + y_{n - 1}^b }}, y_{n + 1} = \frac{{y_n x_{n - 1}^b + 1}} {{y_n + x_{n - 1}^b }}n = 0,1,2 \ldots$$ where the parameter b ∈ [0, ∞) and the initial values (x _k , y _k ) ∈ (0, ∞) (for k = ?1, 0).     

A Frank–Wolfe type theorem for nondegenerate polynomial programs

In this paper, we study the existence of optimal solutions to a constrained polynomial optimization problem. More precisely, let \(f_0\) and \(f_1, \ldots , f_p :{\mathbb {R}}^n \rightarrow {\mathbb {R}}\) be convenient polynomial functions, and let \(S := \{x \in {\mathbb {R}}^n \ : \ f_i(x) \le 0, i = 1, \ldots , p\} \ne \emptyset .\) Under the assumption that the map \((f_0, f_{1}, \ldots , f_{p}) :{\mathbb {R}}^n \rightarrow {\mathbb {R}}^{p + 1}\) is non-degenerate at infinity, we show that if \(f_0\) is bounded from below on \(S,\) then \(f_0\) attains its infimum on \(S.\)      

A solution method for linear variational relation problems

In this paper, we consider a particular class of variational relation problem namely linear variational relation problem wherein the sets are defined by linear inequalities. The purpose is to study the existence of the solution set and its nature for this class of problem. Using these results, we provide algorithms to obtain the solutions of the problem based on which we present some numerical illustrations.     

A vacuum-ultraviolet laser pulsed field ionization-photoelectron study of sulfur monoxide (SO) and its cation (SO+)

Vacuum ultraviolet (VUV) laser pulsed field ionization-photoelectron (PFI-PE) spectroscopy has been applied to the study of the sulfur monoxide radical (SO) prepared by using a supersonically cooled radical beam source based on the 193 nm excimer laser photodissociation of SO(2). The vibronic VUV-PFI-PE bands for the photoionization transitions SO(+)(X(2)Π(1∕2); v(+) = 0) ← SO(X(3)Σ(-); v = 0); and SO(+)((2)Π(3∕2); v(+) = 0) ← SO(X(3)Σ(-); v = 0) have been recorded. On the basis of the semiempirical simulation of rotational branch contours observed in these PFI-PE bands, we have obtained highly precise ionization energies (IEs) of 83,034.2 ± 1.7 cm(-1) (10.2949 ± 0.0002 eV) and 83,400.4 ± 1.7 cm(-1) (10.3403 ± 0.0002 eV) for the formation of SO(+)(X(2)Π(1∕2); v(+) = 0) and SO(+)((2)Π(3∕2); v(+) = 0), respectively. The present VUV-PFI-PE measurement has enabled the direct determination of the spin-orbit coupling constant (A(0)) for SO(+)(X(2)Π(1∕2,3∕2)) to be 365.36 ± 0.12 cm(-1). We have also performed high-level ab initio quantum chemical calculations at the coupled-cluster level up to full quadruple excitations and complete basis set (CBS) extrapolation. The zero-point vibrational energy correction, the core-valence electronic correction, the spin-orbit coupling, and the high-level correction are included in the calculation. The IE[SO(+)(X(2)Π(1∕2,3∕2))] and A(0) predictions thus obtained are found to be in remarkable agreement with the experimental determinations.