Closed-form solutions for non-uniform Euler–Bernoulli free–free beams

In this paper, the free vibration of a non-uniform free–free Euler–Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free–free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free–free beam numerical codes.     

Information geometry,phase transitions,and the Widom line: Magnetic and liquid systems

We study information geometry of the thermodynamics of first and second order phase transitions, and beyond criticality, in magnetic and liquid systems. We establish a universal microscopic characterization of such phase transitions via a conjectured equality of the correlation lengths ξ$\xi$ in co-existing phases, where ξ$\xi$ is related to the scalar curvature of the equilibrium thermodynamic state space. The 1-D Ising model, and the mean-field Curie–Weiss model are discussed, and we show that information geometry correctly describes the phase behavior for the latter. The Widom lines for these systems are also established. We further study a toy model for the thermodynamics of liquid–liquid phase co-existence, and show that our method provides a simple and direct way to obtain its phase behavior and the location of the Widom line. Our analysis points towards the possibility of multiple Widom lines in liquid systems.     

Holographic Dark Energy Model with Quintessence in Bianchi Type-I Space-Time

In this paper, we have studied a homogeneous and anisotropic universe filled with matter and holographic dark energy components. Assuming deceleration parameter to be a constant, an exact solution to Einstein’s field equations in axially symmetric Bianchi type-I line element is obtained. A correspondence between the holographic dark energy models with the quintessence dark energy models is also established. Quintessence potential and the dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe.     

Independent Component Analysis to enhance performances of Karhunen–Loeve expansions for non-Gaussian stochastic processes: Application to uncertain systems

In the context of engineering systems, an essential step in uncertainty quantification is the development of accurate and efficient representation of the random input parameters. For such input parameters modeled as stochastic processes, Karhunen–Loeve expansion is a classical approach providing efficient representations using a set of uncorrelated, but generally statistically dependent random variables. The dependence structure among these random variables may be difficult to estimate statistically and is thus ignored in many practical applications. This simplifying assumption of independence may lead to considerable errors in estimating the variability in the system state, thus limiting the effectiveness of Karhunen–Loeve expansion in certain cases. In this paper, Independent Component Analysis is exploited to linearly transform the random variables used in Karhunen–Loeve expansion resulting into a set of random variables exhibiting higher order decorrelation. The stochastic wave equation is investigated for numerical illustration whereby the random stiffness coefficient is modeled as a non-Gaussian stochastic process. Under the assumption of independence among the random variables used in the Karhunen–Loeve expansion and Independent Component Analysis representations, the latter provides more accurate statistical characterization of the output process for the specific cases examined.     

Tandem C-3/C-2 annulation of indole,benzofuran, and benzothiophene with 2-alkynyl benzylalcohol: an efficient approach to the diverse tetracyclic heteroazulene ring systems

We demonstrate an efficient and flexible strategy toward the synthesis of a library of biologically and pharmaceutically important tetracyclic heteroazulene derivatives in the presence of inexpensive and less toxic molecular iodine. The present strategy involves a sequential alkylation and alkenylation of indole/benzofuran/benzothiophene with o-alkynyl benzyl alcohols derivatives to obtain tetracyclic heteroazulene derivatives in moderate to good yields. Compared to other methodologies, the present strategy is more general, versatile, and environmentally friendly.     

Alcohol oxidation reactions catalyzed by ruthenium–carbonyl complexes of thioarylazoimidazoles

Alcohols are oxidized by N‐methylmorpholine‐N‐oxide (NMO), Bu^tOOH and H₂O₂ to the corresponding aldehydes or ketones in the presence of catalyst, [RuH(CO)(PPh₃)₂(SRaaiNR′)]PF₆ ( 2 ) and [RuCl(CO)(PPh₃)(S_κRaaiNR′)]PF₆ ( 3 ) (SRaaiNR′ ( 1 ) = 1‐alkyl‐2‐{(o‐thioalkyl)phenylazo}imidazole, a bidentate N(imidazolyl) (N), N(azo) (N′) chelator and S_κRaaiNR′ is a tridentate N(imidazolyl) (N), N(azo) (N′), S_κ‐R is tridentate chelator; R and R′ are Me and Et). The single‐crystal X‐ray structures of [RuH(CO)(PPh₃)₂(SMeaaiNMe)]PF₆ ( 2a ) (SMeaaiNMe = 1‐methyl‐2‐{(o‐thioethyl)phenylazo}imidazole) and [RuH(CO)(PPh₃)₂(SEtaaiNEt)]PF₆ ( 2b ) (SEtaaiNEt = 1‐ethyl‐2‐{(o‐thioethyl)phenylazo}imidazole) show bidentate N,N′ chelation, while in [RuCl(CO)(PPh₃)(S_κEtaaiNEt)]PF₆ ( 3b ) the ligand S_κEtaaiNEt serves as tridentate N,N′,S chelator. The cyclic voltammogram shows Ru^III/Ru^II (~1.1 V) and Ru^IV/Ru^III (~1.7 V) couples of the complexes 2 while Ru^III/Ru^II (1.26 V) couple is observed only in 3 along with azo reductions in the potential window +2.0 to ?2.0 V. DFT computation has been used to explain the spectra and redox properties of the complexes. In the oxidation reaction NMO acts as best oxidant and [RuCl(CO)(PPh₃)(S_κRaaiNR′)](PF₆) ( 3 ) is the best catalyst. The formation of high‐valent Ru^IV=O species as a catalytic intermediate is proposed for the oxidation process. Copyright © 2014 John Wiley & Sons, Ltd.