Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Solutions of a system of forced Burgers equation

In this article, we obtain explicit solutions of a system of forced Burgers equation subject to some classes of bounded and compactly supported initial data and also subject to certain unbounded initial data. In a series of papers, Rao and Yadav (2010) 1-3] obtained explicit solutions of a nonhomogeneous Burgers equation in one dimension subject to certain classes of bounded and unbounded initial data. Earlier Kloosterziel (1990) 4] represented the solution of an initial value problem for the heat equation, with initial data in L-2 (R-n, e(vertical bar x vertical bar 2/2)), as a series of self-similar solutions of the heat equation in R-n. Here we express the solutions of certain classes of Cauchy problems for a system of forced Burgers equation in terms of self-similar solutions of some linear partial differential equations. (C) 2013 Elsevier Inc. All rights reserved.

Hydrogen-Bond-Driven Controlled Molecular Marriage in Covalent Cages

A supramolecular approach that uses hydrogen-bonding interaction as a driving force to accomplish exceptional self-sorting in the formation of imine-based covalent organic cages is discussed. Utilizing the dynamic covalent chemistry approach from three geometrically similar dialdehydes (A, B, and D) and the flexible triamine tris(2-aminoethyl)amine (X), three new 3+2] self-assembled nanoscopic organic cages have been synthesized and fully characterized by various techniques. When a complex mixture of the dialdehydes and triamine X was subjected to reaction, it was found that only dialdehyde B (which has OH groups for H-bonding) reacted to form the corresponding cage B3X2 selectively. Surprisingly, the same reaction in the absence of aldehyde B yielded a mixture of products. Theoretical and experimental investigations are in complete agreement that the presence of the hydroxyl moiety adjacent to the aldehyde functionality in B is responsible for the selective formation of cage B3X2 from a complex reaction mixture. This spectacular selection was further analyzed by transforming a nonpreferred (non-hydroxy) cage into a preferred (hydroxy) cage B3X2 by treating the former with aldehyde B. The role of the H-bond in partner selection in a mixture of two dialdehydes and two amines has also been established. Moreover, an example of unconventional imine bond metathesis in organic cage-to-cage transformation is reported.

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Sunlight-Induced Covalent Marriage of Two Triply Interlocked Pd-6 Cages and Their Facile Thermal Separation

A template-free triply interlocked Pd-6 cage (2) was synthesized by two-component self-assembly of cis-blocked 90 degrees acceptor cis-(tmen)Pd(NO3)(2) (M) and 1,3,5-tris((E)-2-(pyridin-3-yl)vinyl)benzene (L). Assembly 2 was characterized by H-1 NMR and ESI-MS, and the structure was confirmed by X-ray crystallography, which revealed a parallel conformation of the olefin double bonds belonging to the adjacent cages in the solid state at a distance of 3.656 angstrom, thereby indicating the feasibility of 2+2] photochemical reaction. Two adjacent interlocked cages were covalently married together by intermolecular 2+2] cycloaddition in a single crystal-to-single crystal fashion upon exposure to sunlight/UV irradiation. Most surprisingly, the covalently married pair was easily separated thermally in aqueous medium under mild reaction conditions.

Experimental studies on evaporation of fuel droplets under forced convection using spray in crossflow methodology

Experimental data on evaporation of droplets of decane, Jet-A1, and Jet-A1 surrogate are generated using a spray in crossflow configuration. The advantage of a crossflow configuration is that it enables us to study droplet evaporation under forced convective conditions involving droplet diameters of size relevant in practical combustors. Specifically, spray from an airblast atomizer is injected into a preheated crossflow of air and the resulting spray is characterized in terms of spray structure along with droplet size and velocity. An existing correlation for the spray trajectory is modified to incorporate the effect of elevated temperature, and is found to be in good agreement with the experimental data. Droplet sizes and velocities are measured at different locations along the crossflow direction to assess droplet evaporation. Specifically, droplets having size less than 25-mu m are selected for further analysis since these droplets are observed to exhibit velocities which are aligned with the crossflow. By comparing the droplet diameter profiles at upstream and downstream locations, the evaporation constant k for the d(2)-law is obtained iteratively. To assess the efficacy of the values of k obtained, the calculated droplet size distribution using the proposed k values at the downstream location is compared with the measured droplet size distribution at that location. A reasonably good match is found for all the three liquids confirming the validity of the analysis. (C) 2015 Elsevier Ltd. All rights reserved.

Mechano-Chemical Coupling at Molecular Level: Forced Dissociation of Selectin/Ligand Binding

Mechano-chemical coupling is a common phenomenon that exists in various biological processes at different physiological levels. Bone tissue remodeling strongly depends on the local mechanical load. Leukocytes are sheared to form the transient aggregates with platelets or other leukocytes in the circulation. Flow pattern affects the signal transduction pathways in endothelial cells. Receptor/ligand interactions are important to cell adhesion since they supply the physical linkages...

Forced Dissociation of Selectin-ligand Complexes Using Steered Molecular Dynamics Simulation

Selectin-ligand interactions are crucial to such biological processes as inflammatory cascade or tumor metastasis. How transient formation and dissociation of selectin-ligand bonds in blood flow are coupled to molecular conformation at atomic level, however, has not been well understood. In this study, steered molecular dynamics (SMD) simulations were used to elucidate the intramolecular and intermolecular conformational evolutions involved in forced dissociation of three selectin-ligand systems: the construct consisting of P-selectin lectin (Lec) and epidermal growth factor (EGF)-like domains (P-LE) interacting with synthesized sulfoglycopeptide or SGP-3, P-LE with sialyl Lewis X (sLeX), and E-LE with sLeX. SMD simulations were based on newly built-up force field parameters including carbohydrate units and sulfated tyrosine(s) using an analogy approach. The simulations demonstrated that the complex dissociation was coupled to the molecular extension. While the intramolecular unraveling in P-LESGP-3 system mainly resulted from the destroy of the two anti-parallel sheets of EGF domain and the breakage of hydrogen-bond cluster at the Lec-EGF interface, the intermolecular dissociation was mainly determined by separation of fucose (FUC) from Ca2+ ion in all three systems. Conformational changes during forced dissociations depended on pulling velocities and forces, as well as on how the force was applied. This work provides an insight into better understanding of conformational changes and adhesive functionality of selectin-ligand interactions under external forces.

Influence of Forced Convection on Columnar Microstructure During Directional Solidification of Al-Ni Alloys

This paper presents a summary of cellular and dendritic morphologies resulting from the upward directional solidification of Al - Ni alloys in a cylindrical crucible. We analysed the coupling of solid-liquid interface morphology with natural and forced convection. The influence of natural convection was first analyzed as a function of growth parameters (solute concentration, growth rate and thermal gradient). In a second step, the influence of axial vibrations on solidification microstructure was investigated by varying vibration parameters (amplitude and frequency). Experimental results were compared to preliminary numerical simulations and a good agreement is found for natural convection. In this study, the critical role of the mushy zone in the interaction between fluid flow and solidification microstructure is pointed out.

Forced extension of P-selectin construct using steered molecular dynamics

P-selectin, a 70-nm-long cellular adhesive molecule, possesses elastic and extensible properties when neutrophils roll over the activated endotheliam of blood vessel in inflammatory reaction. Transient formation and dissociation of P-selectin/ligand bond on applied force of blood flow induces the extension of P-selectin and relevant ligands. Steered molecular dynamics simulations were performed to stretch a single P-selectin construct consisting of a lectin (Lec) domain and an epithelial growth factor (EGF)-like domain, where P-selectin construct was forced to extend in water with pulling velocities of 0.005-0.05 nm/ps and with constant forces of 1000-2500 pN respectively. Resulting force-extension profiles exhibited a dual-peak pattern on various velocities, while both plateaus and shoulders appeared in the extension-time profiles on various forces. The force or extension profiles along stretching pathways were correlated to the conformational changes, suggesting that the structural collapses of P-selectin Lec/EGF domains were mainly attributed to the burst of hydrogen bonds within the major beta sheet of EGF domain and the disruptions of two hydrophobic cores of Lee domain. This work furthers the understanding of forced dissociation of P-selectin/ligand bond.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.