The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.

Longitudinal Magnetic Field Effect on Nonlocal Ultrasonic Vibration Analysis of Single-Walled Carbon Nanotubes Based on Wave Propagation Approach

This paper studies the effect of longitudinal magnetic field on ultrasonic vibration in single walled carbon nanotubes (CNTs) based on nonlocal continuum medium theory. Governing partial differential equations of CNTs are derived by considering the Lorentz magnetic forces applied on CNTs induced by a longitudinal magnetic field through Maxwell equations. The vibration characteristics of CNTs under a longitudinal magnetic field are obtained by solving the governing equations via wave propagation approach. The effects of longitudinal magnetic field on vibration of CNTs are discussed through numerical experiments. The present analysis show that vibration frequencies of CNTs drops dramatically in the presence of the magnetic field for various circumferential wavenumbers. Such effect is also observed for various boundary conditions of the CNT. New features for the effect of longitudinal magnetic field on ultrasonic vibration of CNTs, presented in this paper are useful in the design of nano-drive device, nano-oscillator and actuators and nano-electron technology, where carbon nanotubes act as basic elements.

Analysis of current voltage characteristics of MWIR homojunction photodiodes for uncooled operation

Dark currents n(+)/v/p(+) Hg0.69Cd0.Te-31 mid wave infrared photodiodes were measured at room temperature. The diodes exhibited negative differential resistance at room-temperature, but with increasing leakage currents as a function of reverse bias. The current-voltage characteristics were simulated and fitted by incorporating trap assisted tunneling via traps and Shockley-Read-Hall generation recombination process due to dislocations in the carrier transport equations. The thermal suppression of carriers was simulated by taking energy level of trap (E-t), trap density (N-t) and the doping concentrations of n(+) and v regions as fitting parameters. Values of E-t and N-t were 0.78E(g) and similar to 6-9 x 10(14) cm(-3) respectively for most of the diodes. Variable temperature current voltage measurements on variable area diode array (VADA) structures confirmed the fact that variation in zero bias resistance area product (R(0)A) is related to g-r processes originating from variation in concentration and kind of defects that intersect a junction area. (C) 2012 Elsevier B.V. All rights reserved.

Causality analysis of groundwater dynamics based on a Vector Autoregressive model in the semi-arid basin of Gundal (South India)

Causal relationships existing between observed levels of groundwater in a semi-arid sub-basin of the Kabini River basin (Karnataka state, India) are investigated in this study. A Vector Auto Regressive model is used for this purpose. Its structure is built on an upstream/downstream interaction network based on observed hydro-physical properties. Exogenous climatic forcing is used as an input based on cumulated rainfall departure. Optimal models are obtained thanks to a trial approach and are used as a proxy of the dynamics to derive causal networks. It appears to be an interesting tool for analysing the causal relationships existing inside the basin. The causal network reveals 3 main regions: the Northeastern part of the Gundal basin is closely coupled to the outlet dynamics. The Northwestern part is mainly controlled by the climatic forcing and only marginally linked to the outlet dynamic. Finally, the upper part of the basin plays as a forcing rather than a coupling with the lower part of the basin allowing for a separate analysis of this local behaviour. The analysis also reveals differential time scales at work inside the basin when comparing upstream oriented with downstream oriented causalities. In the upper part of the basin, time delays are close to 2 months in the upward direction and lower than 1 month in the downward direction. These time scales are likely to be good indicators of the hydraulic response time of the basin which is a parameter usually difficult to estimate practically. This suggests that, at the sub-basin scale, intra-annual time scales would be more relevant scales for analysing or modelling tropical basin dynamics in hard rock (granitic and gneissic) aquifers ubiquitous in south India. (c) 2012 Elsevier B.V. All rights reserved.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Generation and analysis of drought stressed subtracted expressed sequence tags from safflower (Carthamus tinctorius L.)

Drought is the most crucial environmental factor that limits productivity of many crop plants. Exploring novel genes and gene combinations is of primary importance in plant drought tolerance research. Stress tolerant genotypes/species are known to express novel stress responsive genes with unique functional significance. Hence, identification and characterization of stress responsive genes from these tolerant species might be a reliable option to engineer the drought tolerance. Safflower has been found to be a relatively drought tolerant crop and thus, it has been the choice of study to characterize the genes expressed under drought stress. In the present study, we have evaluated differential drought tolerance of two cultivars of safflower namely, A1 and Nira using selective physiological marker traits and we have identified cultivar A1 as relatively drought tolerant. To identify the drought responsive genes, we have constructed a stress subtracted cDNA library from cultivar A1 following subtractive hybridization. Analysis of similar to 1,300 cDNA clones resulted in the identification of 667 unique drought responsive ESTs. Protein homology search revealed that 521 (78 %) out of 667 ESTs showed significant similarity to known sequences in the database and majority of them previously identified as drought stress-related genes and were found to be involved in a variety of cellular functions ranging from stress perception to cellular protection. Remaining 146 (22 %) ESTs were not homologous to known sequences in the database and therefore, they were considered to be unique and novel drought responsive genes of safflower. Since safflower is a stress-adapted oil-seed crop this observation has great relevance. In addition, to validate the differential expression of the identified genes, expression profiles of selected clones were analyzed using dot blot (reverse northern), and northern blot analysis. We showed that these clones were differentially expressed under different abiotic stress conditions. The implications of the analyzed genes in abiotic stress tolerance are discussed in our study.

Synthesis, structural analysis and solvatochromic behaviour of 4,6-bis (4-butoxyphenyl)-2-methoxynicotinonitrile mesogen

In this communication, we report the synthesis and characterisation of a new luminescent liquid crystalline material, 4,6-bis (4-butoxyphenyl)-2-methoxynicotinonitrile (3). We have confirmed its structure by Fourier transform infrared and 1H nuclear magnetic resonance spectroscopy, elemental analysis and X-ray single crystal diffraction studies. The newly synthesised compound crystallises in a monoclinic system with the space group C2/c and its cell parameters are found to be a?=?25.181(4) angstrom, b?=?15.651(4)angstrom, c?=?12.703(19) angstrom, V?=?4880.4 (16) angstrom, Z?=?8. The results indicate that the presence of weak CH center dot center dot center dot O and CH center dot center dot center dot N hydrogen bonding as short-range intermolecular interactions are responsible for the formation of its crystal assembly. The measured torsion angle shows the existence of a distorted structure for the molecule wherein 4-butoxyphenylene ring substituent at the fourth position of the central pyridine ring forms a torsion angle chiC(4), C(3), C(10), C(19)] of 40.55 degrees. Its liquid crystalline behaviour was investigated with the aid of polarised optical microscopy and differential scanning calorimetry. The study reveals that the compound displays a broad nematic phase in the range of 78112 degrees C. Further, solution phase optical studies indicate that it is a blue light emitter in different non-polar and polar organic solvents at a concentration of 10-5M.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Evaluation of the accuracy of an impact load cell using lumped parameter modeling and analysis

The objective of the current study is to evaluate the fidelity of load cell reading during impact testing in a drop-weight impactor using lumped parameter modeling. For the most common configuration of a moving impactor-load cell system in which dynamic load is transferred from the impactor head to the load cell, a quantitative assessment is made of the possible discrepancy that can result in load cell response. A 3-DOF (degrees-of-freedom) LPM (lumped parameter model) is considered to represent a given impact testing set-up. In this model, a test specimen in the form of a steel hat section similar to front rails of cars is represented by a nonlinear spring while the load cell is assumed to behave in a linear manner due to its high stiffness. Assuming a given load-displacement response obtained in an actual test as the true behavior of the specimen, the numerical solution of the governing differential equations following an implicit time integration scheme is shown to yield an excellent reproduction of the mechanical behavior of the specimen thereby confirming the accuracy of the numerical approach. The spring representing the load cell, however,predicts a response that qualitatively matches the assumed load-displacement response of the test specimen with a perceptibly lower magnitude of load.

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

Performance analysis of FSO links under strong atmospheric turbulence conditions using various modulation schemes

Strong atmospheric turbulence is a major hindrance in wireless optical communication systems. In this paper, the performance of a wireless optical communication system is analyzed using different modulation formats such as, binary phase shift keying-subcarrier intensity modulation (BPSK-SIM), differential phase shift keying (DPSK), differential phase shift keying-subcarrier intensity modulation (DPSK-SIM), Mary pulse position modulation (M-PPM) and polarization shift keying (PoISK). The atmospheric channel is modeled for strong atmospheric turbulences with combined effect of turbulence and pointing errors. Novel closed-form analytical expressions for average bit error rate (BER), channel capacity and outage probability for the various modulation techniques, viz. BPSK-SIM, DPSK, DPSK-SIM, PoISK and M-PPM are derived. The simulated results for BER, channel capacity and outage probability of various modulation techniques are plotted and analyzed. (C) 2014 Elsevier GmbH. All rights reserved.

Wave propagation analysis in adhesively bonded composite joints using the wavelet spectral finite element method

A wavelet spectral finite element (WSFE) model is developed for studying transient dynamics and wave propagation in adhesively bonded composite joints. The adherands are formulated as shear deformable beams using the first order shear deformation theory (FSDT) to obtain accurate results for high frequency wave propagation. Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle. The adhesive layer is modeled as a line of continuously distributed tension/compression and shear springs. Daubechies compactly supported wavelet scaling functions are used to transform the governing partial differential equations from time domain to frequency domain. The dynamic stiffness matrix is derived under the spectral finite element framework relating the nodal forces and displacements in the transformed frequency domain. Time domain results for wave propagation in a lap joint are validated with conventional finite element simulations using Abaqus. Frequency domain spectrum and dispersion relation results are presented and discussed. The developed WSFE model yields efficient and accurate analysis of wave propagation in adhesively-bonded composite joints. (C) 2014 Elsevier Ltd. All rights reserved.

Differential response of cholesterol based pyrimidine systems with oxyethylene type spacers to gelation and mesogen formation in the presence of alkali metal ions

A new series of lipophilic cholesteryl derivatives of 2,4,6-trichloro-pyrimidine-5-carbaldehyde has been synthesized. Oxyethylene spacers of variable lengths were inserted between the hydrogen bonding promoting pyrimidine core and the cholesteryl tail in order to understand their effect on the selfassembly of these compounds. Only compound 1a with the shortest spacer formed a gel in organic solvents such as n-butanol and n-dodecane. While other members (1b and c) having longer spacers led to sol formation and precipitation in n-butanol and n-dodecane respectively. The self-assembly phenomena associated with the gelation process were investigated using temperature-dependent UVVis and CD-spectroscopy. The morphological features of the freeze-dried gels obtained from different organic solvents were examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM). The solid phase behaviours of these molecules and their associated alkali metal ion complexes were explored using polarized optical microscopy (POM) and differential scanning calorimetry (DSC). The molecular arrangements in the xerogel and in the solid state were further probed using a wide-angle Xray diffraction (WAXD) technique. Analysis of the wide-angle X-ray diffraction data reveals that this class of molecules adopts a hexagonal columnar organization in the gel and in the solid state. Each slice of these hexagonal columnar structures is composed of a dimeric molecular-assembly as a building block. Significant changes in the conformation of the oxyethylene chains could be triggered via the coordination of selected alkali metal ions. This led to the production of interesting metal ion promoted mesogenic behaviour.