Three-dimensional nonlinear vibrations of composite beams — II. flapwise excitations

The nonlinear equations of motion derived in Part I are used to investigate the response of an inextensional, symmetric angle-ply graphite-epoxy beam to a harmonic base-excitation along the flapwise direction. The equations contain bending-twisting couplings and quadratic and cubic nonlinearities due to curvature and inertia. The analysis focuses on the case of primary resonance of the first flexural-torsional (flapwise-torsional) mode when its frequency is approximately one-half the frequency of the first out-of-plane flexural (chordwide) mode. A combination of the fundamental-matrix method and the method of multiple scales is used to derive four first-order ordinary-differential equations to describe the time variation of the amplitudes and phases of the interacting modes with damping, nonlinearity, and resonances. The eigenvalues of the Jacobian matrix of the modulation equations are used to determine the stability and bifurcations of their constant solutions, and Floquet theory is used to determine the stability and bifurcations of their limit-cycle solutions. Hopf bifurcations, symmetry-breaking bifurcations, period-multiplying sequences, and chaotic solutions of the modulation equations are studied. Chaotic solutions are identified from their frequency spectra, Poincaré sections, and Lyapunov's exponents. The results show that the beam motion may be nonplanar although the input force is planar. Nonplanar responses may be periodic, periodically modulated, or chaotically modulated motions.     

An analytical study of linear and non-linear double diffusive convection with Soret and Dufour effects in couple stress fluid

The onset of double diffusive convection in a two component couple stress fluid layer with Soret and Dufour effects has been studied using both linear and non-linear stability analysis. The linear theory depends on normal mode technique and non-linear analysis depends on a minimal representation of double Fourier series. The effect of couple stress parameter, the Soret and Dufour parameters, and the Prandtl number on the stationary and oscillatory convection are presented graphically. The Dufour parameter enhances the stability of the couple stress fluid system in case of both stationary and oscillatory mode. The effect of positive Soret parameter is to destabilize the system in case of stationary mode while it stabilizes the system in case of oscillatory mode. The negative Soret parameter enhances the stability in both stationary and oscillatory mode. The couple stress parameter enhances the stability of the system in both stationary and oscillatory modes. The Dufour parameter increases the heat transfer while the couple stress parameter has reverse effect. The Soret parameter has negligible influence on heat transfer. Both Dufour and Soret parameters increases the mass transfer while the couple stress parameter has dual effect depending on the value of the Rayleigh number.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

Numerical Solution of Large Scale Sparse Matrix Equations in Python

The M.E.S.S. software suite for solving large scale matrix equations and related problems is the successor of the obsolete LyaPack MATLAB® toolbox. The software suite consists of a new MATLAB toolbox and a separate C library C-M.E.S.S. which works independent from MATLAB. Due to the fact that many scientists use Python with NumPy and SciPy for their computations, we want to provide the key algorithms of M.E.S.S. there as well. In this paper, we describe and compare two possible approaches for the implementation, with special focus on their multicore performance. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Julia Sets of Joukowski-Exponential Maps

Let $h$ be a transcendental entire function of finite type such that all the coefficients in its Taylor series about the origin are non-negative, $h(x)\! >\!0 \hbox { for } x \!<~0,\,h(0)\ge 1$ and each finite singular value of $h$ is either real or is with unit modulus. For $J(z) = z + (1/z)\hbox { and } n \in \mathbb {N}$ , we define $f_{\lambda }(z)=\lambda J^n(h(z))$ . It is proved that there exists a $\lambda ^{*}$ such that the Julia set of $f_\lambda $ is a nowhere dense subset of $\widehat{\mathbb {C}}\hbox { for }0< \lambda \le \lambda ^*$ whereas it becomes equal to $\widehat{\mathbb {C}}$ for $\lambda >\lambda ^*$ . A detailed study of the Julia sets of Joukowski-exponential maps $\lambda J( e^z+1)$ is undertaken when it is not equal to the whole sphere. Such a Julia set consists of a non-singleton, unbounded and forward invariant component, infinitely many non-singleton bounded components and singleton components. A bounded component of the Julia set eventually not mapped into the unbounded Julia component is singleton if and only if it is not expanding. The Julia set contains two topologically as well as dynamically distinct completely invariant subsets.     

Multimodal imaging probes based on Gd-DOTA conjugated quantum dot nanomicelles

Recently, multimodal nanoparticles integrating dual- or tri-imaging modalities into a single hybrid nanosystem have attracted plenty of attention in biomedical research. Here, we report the fabrication of two types of multimodal micelle-encapsulated nanoparticles, which were systematically characterized and thoroughly evaluated in terms of their imaging potential and biocompatibility. Optical and magnetic resonance (MR) imaging probes were integrated by conjugating DOTA-gadolinium (Gd) derivative to quantum dot based nanomicelles. Two amphiphilic block copolymer micelles, amine-terminated mPEG-phospholipid and amine-modified Pluronic F127, were chosen as the capping agents because of their excellent biocompatibility and ability to prevent opsonization and prolong circulation time in vivo. Owing to their different hydrophobic-hydrophilic structure, the micellar aggregates exhibited different sizes and protection of core QDs. This work revealed the differences between these nanomicelles in terms of the stability over a wide range of pH, along with their cytotoxicity and the capacity for chelating gadolinium, thus providing a useful guideline for tailor-making multimodal nanoparticles for specific biomedical applications.     

Concise Synthesis of JN403, a Novel Nicotinic Acetylcholine Receptor α7 Selective Agonist

A three-step method for the synthesis of (S)-(1-aza-bicyclo[2.2.2]oct-3-yl)carbamic acid (S)-1-(2-fluorophenyl)ethyl ester HCl salt (12) was developed, starting from alcohol 3 and resulting in an overall yield of 50%. A key feature of the present study is the need to use a strong base such as n-butyllithium for neutralizing the HCl salt of 5 during the condensation of 4 with 5.     

Asymmetric Synthesis of Unnatural Amino Acids and Tamsulosin Chiral Intermediate

An efficient and enantioselective hydrogenation of N-acetylamino phenyl acrylic acids was successfully developed by using ruthenium catalyst. This methodology is important in the field of pharmaceuticals and provides a new process for the preparation of unnatural amino acids and tamsulosin chiral intermediate.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource: Full experimental and spectral details.]     

Thermal and Microwave‐Assisted Conjugate Additions of Indole on Electron‐Deficient Nitro‐olefins

Conjugate addition of indole on nitro‐olefins was carried out by three different methods: (i) thermal heating in a sealed tube, (ii) reaction with indolyl magnesium iodide, and (iii) microwave irradiation. Comparison of the results indicated that the microwave technique is most efficient.