Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

Comparative analysis of shape memory-based self-healing coatings

Self-healing materials exhibit the ability to repair and to recover their functionality upon damage. Here, we report on an investigation into preparation and characterization of shape memory assisted self-healing coatings. We built on past work in which poly(ε-caprolactone) electrospun fibers were infiltrated with a shape memory epoxy matrix and delve into fabricating and characterizing a coating with the same materials, but employing a blending approach, polymerization induced phase separation. After applying controlled damage, the ability of both coatings to self-heal upon heating was investigated. In both methods, coatings showed excellent thermally induced crack closure and protection against corrosion, with the blend approach being more suitable for large-scale applications given its process simplicity. Two different approaches to the preparation of shape memory-based self-healing coatings were compared for their ability to heal structurally and functionally by heating. These two approaches, electrospinning versus polymerization-induced phase separation were found to feature comparable and quite complete healing, with the latter system offering the advantage of facile processing. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1415–1426     

Synthesis of 4-unsubstituted 2H-1,2,3-benzothiadiazine 1,1-dioxides via ortho lithiation of protected benzaldehyde derivatives

Variously substituted 2-phenyl-1,3-dioxolanes and 2-(2-bromophenyl)-1,3-dioxolanes, prepared from the corresponding benzaldehydes, were lithiated ortho to the acetal group. Reaction of the lithio derivatives with sulfur dioxide led to the lithium sulfinate salts, which gave, upon oxidative chlorination with sulfuryl chloride, the corresponding benzenesulfonyl chlorides. Then, depending on the aromatic substitution pattern of the molecule, several protocols were elaborated for the functional group transformations leading to the target compounds. Ring closure was performed with hydrazine hydrate or acetylhydrazine, in the latter case with one-pot removal of the acetyl group. The 4-unsubstituted 2H-1,2,3-benzothiadiazine 1,1-dioxides thus obtained are potential drug candidates based on their structural similarity to biologically active phthalazinones.     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Homogeneous turbulence subjected to rotation-dominated plane distortion

A new configuration of distorted homogeneous turbulence is investigated in the domain of rotation-dominated elliptical flows. The experimental results are compared with exact numerical solutions obtained in Fourier space for the linear part of the problem. The inherently periodic character of the flow results in typical oscillatory variations of the anisotropy and the pressure-strain correlations. A new two-point closure approach of the EDQNM type is proposed for the nonlinear problem; it is based on a representation of the spectral tensor by scalar functions expanded in terms of spherical harmonics.     

A two-scale second-moment turbulence closure based on weighted spectrum integration

A two-scale second-moment turbulence closure has been derived based on the weighted integration of the dynamic equation for the covariance spectrum. The goal is to close the Reynolds stress equations with two additional scalar equations that provide separately the scales of the spectral energy transfer and of the turbulence energy dissipation rate. Such a model should provide better prediction of nonequilibrium turbulent flows. The derivation consists of analytical integration of the wave-number-weighted covariance spectrum using a model of the spectral equations with an assumed simple representation of the shape of the energy spectrum. The resulting closure consists of a set of three tensorial equations, one for the Reynolds stress and two for length scale tensors, the latter representing the energy containing- and dissipative eddies respectively. The trace of the two tensor-scale equations leads to a set of two scalar scale parameters. In the equilibrium limit, the model reduces to the standard second-moment single-scale closure. The approach makes it also possible to derive the scale equations in a more systematic manner as compared with the common single-scale and other multi-scale models. The performance of the model in capturing the scale dynamics is illustrated by predictions of several generic homogeneous and inhomogeneous unsteady flows, demonstrating the expected response of the two scale equations. PACS 03.50.De, 04.20-q, 42.65-k     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

Nonlinear random coupled motions of structural elements with quadratic nonlinearities

The second-order closure method is used to analyze the nonlinear response of two-degree-of-freedom systems with quadratic nonlinearities. The excitation is assumed to be the sum of a deterministic harmonic component and a random component. The case of primary resonance of the second mode in the presence of a two-to-one internal (autoparametric) resonance is investigated. The method of multiple scales is used to obtain four first-order ordinary-differential equations that describe the modulation of the amplitudes and phases of the two modes. Applying the second-order closure method to the modulation equations, we determine the stationary mean and mean-square responses. For the case of a narrow-band random excitation, the results show that the presence of the nonlinearity causes multi-valued mean-square responses. The multi-valuedness is responsible for a jump phenomenon. Contrary to the results of the linear analysis, the nonlinear analysis reveals that the directly excited second mode takes a small amount of the input energy (saturates) and spills over the rest of the input energy into the first mode, which is indirectly excited through the autoparametric resonance.     

Modelling of inhomogeneous turbulence in the absence of mean velocity gradients

In this paper we propose a new rational model for turbulent transport of Reynolds stresses and dissipation. For this purpose we first analyse some properties of diffused turbulence i.e. turbulence where dissipation is balanced by turbulent diffusion arising from inhomogeneity. Then we use some of these results to deduce some mathematical requirements that must be satisfied by any rational model and we show that they are not verified by available models. Consequently we derive a more general model taking into account the various properties of diffused turbulence.