Nonlinear surface acoustic waves on an isotropic solid

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

Crystal and molecular structure of 15-bromolongibornane-8,9-dione

The crystal and molecular structure of the title compound (1) has been determined by the heavy-atom method from 1038 observed three-dimensional photographic data. Crystals are orthorhombic, with a = 20.07 ± 0.02, b= 10.05 ± 0.02, c= 7.31 ± 0.01 Å, space group P212121, with Z= 4. The structure was refined by block diagonal leastsquares to R 0.099. The conformation of the norbornane moiety is discussed. The seven-membered ring portion of the molecule adopts an approximate chair conformation. The packing of the molecules in the crystal is mainly a consequence of van der Waals interactions.

Vibration of generally orthotropic skew plates

Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Sterochemical studies on cyclic peptides-VIII. Conformational analysis of hydrogen bonded cyclohexaglycyl molecule with a centre of inversion symmetry

A study on the conformational aspects of cyclo-hexaglycyl having inversion symmetry has been made. The cyclic backbone has been assumed to have two internal 4→1 types of NH... O hydrogen bonds. This molecule has been found to take up two types of conformations designated asA* andB* having nearly the same energy values. The theoretical conformations have been compared with the conformations of cyclohexaglycyl hemihydrate observed in the crystal structure. Two molecules with an approximate inversion symmetry are close to the conformation of the typeB* and two other molecules with exact inversino symmetry correspond nearly to the typesB* andA*. comparison with the theoretically possible conformations of cyclohexaglycyl molecule with 2-fold symmetry has been made. The preference of inversion symmetry and preferred ranges ofψ for glycyl molecules is discussed.

Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Purification and properties of Image -mandelate-4-hydroxylase from Pseudomonas convexa

An inducible Image -mandelate-4-hydroxylase has been partially purified from crude extracts of Pseudomonas convexa. This enzyme catalyzed the hydroxylation of Image -mandelic acid to 4-hydroxymandelic acid. It required tetrahydropteridine, NADPH, Fe2+, and O2 for its activity. The approximate molecular weight of the enzyme was assessed as 91,000 by gel filtration on Sephadex G-150. The enzyme was optimally active at pH 5.4 and 38 °C. A classical Michaelis-Menten kinetic pattern was observed with Image -mandelate, NADPH, and ferrous sulfate and Km values for these substrates were found to be 1 × 10−4, 1.9 × 10−4, and 4.7 × 10−5 Image , respectively. The enzyme is very specific for Image -mandelate as substrate. Thiol inhibitors inhibited the enzyme reaction, indicating that the sulfhydryl groups may be essential for the enzyme action. Treatment of the partially purified enzyme with denaturing agents inactivated the enzyme.

Open source computer-vision based guidance system for UAVs on-board decision making

The use of UAVs for remote sensing tasks; e.g. agriculture, search and rescue is increasing. The ability for UAVs to autonomously find a target and perform on-board decision making, such as descending to a new altitude or landing next to a target is a desired capability. Computer-vision functionality allows the Unmanned Aerial Vehicle (UAV) to follow a designated flight plan, detect an object of interest, and change its planned path. In this paper we describe a low cost and an open source system where all image processing is achieved on-board the UAV using a Raspberry Pi 2 microprocessor interfaced with a camera. The Raspberry Pi and the autopilot are physically connected through serial and communicate via MAVProxy. The Raspberry Pi continuously monitors the flight path in real time through USB camera module. The algorithm checks whether the target is captured or not. If the target is detected, the position of the object in frame is represented in Cartesian coordinates and converted into estimate GPS coordinates. In parallel, the autopilot receives the target location approximate GPS and makes a decision to guide the UAV to a new location. This system also has potential uses in the field of Precision Agriculture, plant pest detection and disease outbreaks which cause detrimental financial damage to crop yields if not detected early on. Results show the algorithm is accurate to detect 99% of object of interest and the UAV is capable of navigation and doing on-board decision making.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.

Conformational analysis of cyclo (l-cystine

Conformational analysis of cyclo(L-cystine) shows that the diketopiperazine ring has to exist only in the boat form. With this geometry, the molecule can adopt two distinct forms differing mainly in the chirality of the disulphide bridge. In both the P- and M-models, corresponding to dihedral angles of nearly + 90° and —90° respectively about the S-S bond, the molecule displays an approximate two-fold symmetry. According to our semi-empirical energy calculations, the minimum energy of the M-model is —9.2 kcal/mol, only 0.3 kcal/mol lower than that of the P-model. Because the difference between the two minima is so small, neither form is clearly superior to the other. However, the number of low energy conformations of the M-model in the allowed conformational space is significantly larger than that of the P-model by a ratio of 3 to 1, and therefore the former is likely to be thermodynamically favoured.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Purification and properties of an NADP+-specific isocitrate dehydrogenase from Rhizobium meliloti

An NADP+-specific isocitrate dehydrogenase has been purified and characterized from Rhizobium meliloti. The enzyme showed Mn++ or Mg++ requirement. The apparent Km values were 2.00×10-5 m and 1.51×10-5 m for dl-isocitrate and NADP+, respectively. The enzyme was inhibited by ATP, to a lesser extent by ADP and AMP. agr-Ketoglutarate also inhibited the enzyme activity. Oxalacetate and glyoxylate together inhibited the enzyme activity. The inhibition was competitive. Studies with thiol inhibitors suggested that the enzyme contained a sulfhydryl group at or near the active site. The enzyme has an approximate molecular weight of 60 000. Fluorescence studies suggested that the enzyme contained tryptophan.

Stresses in a thick plate with a circular hole under axisymmetric loading

An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results.