Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

1H and 13C NMR spectra of some unsymmetric N,N-dipyridyl ureas: spectral assignments and molecular conformation

Abstract: The H-1 NMR spectra of N-(2-pyridyl), N'-(3-pyridyl)ureas and N-(2-pyridyl), N'-(4-pyridyl)ureas in CDCl3 and (CD3)(2)CO have been assigned with the aid of COSY and NOE experiments and chemical shift and coupling constant correlations, The C-13 NMR spectra in CDCl3 were analysed utilizing the HETCOR and proton coupled spectra, The H-1 NMR spectra, NOE effects and MINDO/3 calculations have been utilized to show that the molecular conformation of these compounds has the 2-pyridyl ring coplanar with the urea plane with the N-H group hydrogen bonded to the nitrogen of the 2-pyridyl group on the other urea nitrogen while the 3/4-pyridyl group rotates rapidly about the N-C-3/N-C-4 bond.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

Broadband Suspended Microstrip Antenna For Circular Polarization

In this paper we propose a circularly polarized (CP) microstrip antenna on a suspended substrate with a coplanar capacitive feed and a slot within the rectangular patch. The antenna has an axial ratio bandwidth (< 3 dB) of 7.1%. The proposed antenna exhibits a much higher impedance bandwidth of about 49% (S11 < -10 dB) and also yields return loss better than -15 dB in the useful range of circular polarization. Measured characteristics of the antenna are in good agreement with the simulated results. The radiation patterns indicate good cross polarization rejection and low back lobe radiations. The design proposed here can be scaled to any frequency of interest.

1-(2,4-Dichlorophenyl)-3-[4-(dimethylamino)-phenyl]prop-2-enone

In the title compound, C17H15Cl2NO, the dimethylaminophenyl group is close to coplanar with the central propenone group [dihedral angle =13.1 (1)degrees between the mean planes], while the dichlorophenyl group is twisted from the plane [dihedral angle = 64.0 (1)degrees].In the crystal, C-H center dot center dot center dot O and weak C-H center dot center dot center dot pi interactions are formed between molecules.

The structure of monopotassium phosphoenolpyruvate

CaH406P-.K +, M r = 206.10, is orthorhombic, space group Pbca (from systematic absences), a = 14.538(4), b = 13.364(5), c = 6.880 (6)A, U = 1383.9 A 3, D x = 2.07 Mg m -a, Z = 8, ~.(Mo Ka) = 0.7107/~, p(MO Ka) = 1.015 mm -1. The final R value is 0.042 for a total of 1397 reflections. The high energy P-O(13) and the enolic C(1)-O(13) bonds are 1.612 and 1.374 A respectively. The enolpyruvate moiety is essentially planar. The orientation of the phosphate with respect to the pyruvate group in PEP.K is distinctly different from that in the PEP-cyclohexylammonium salt, the torsion angle C (2)-C (1)-O(13)- P being -209.1 in the former and -90 ° in the latter. The K + ion binds simultaneously to both the phosphate and carboxyl ends of the same PEP molecule. The ester O(13) is also a binding site for the cation. The K + ion is coplanar with the pyruvate moiety and binds to 0(22) and O(13) almost along their lone-pair directions. The carbonyl 0(22) prefers to bind to the K + ion rather than take part in the formation of hydrogen bonds usually observed in carboxylic acid structures.

Structure of 4-Hydroxymonophenylbutazone

4-Butyl-4-hydroxy-l-phenyl-3,5-pyrazolidinedione, ClaH16N20 a, Mr=248.3, monoclinic, P21/n, a = 22.357 (5), b = 5.014 (2), c = 11.350 (4)/~,, //=91.88(3) °, V=1272(1)A 3, Z=4, D,,=1.296(3), D x = 1.297 Mg m -3, 2(Cu Ka) = 1.5418/~, a = 0.777 mm -~, F(000) = 528, T= 293 K. Final R - 0.059 for 1668 observed reflections. The hetero nitrogen which carries the six-membered ring is planar in the structure while the other unsubstituted one is pyramidal. The five- and six-membered rings are almost coplanar. The crystal is made up of infinite columns of hydrogen-bonded molecules.

Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Structure of a new crystal form of 2- ([3-(trifluoromethyl)phenyl] amino)benzoic acid (flufenamic acid)

C14Ht0F3NO2, P2.Jc, a = 12.523 (4), b = 7.868(6), c = 12.874 (3)A, fl = 95.2 (2) ° , O,,, = 1.47 (4), D e = 1.47 Mg m -3, Z = 4. Final R = 0.074 for 2255 observed reflections. The carboxyl group and the phenyl ring bearing the carboxyl group are nearly coplanar whereas the two phenyl rings are inclined with respect to each other at 52.8 ° . The difference between the two polymorphs of flufenamic acid lies in the geometrical disposition of the [3-(trifluoromethyl)- phenyl]amino moiety with respect to the benzoic acid moiety. As in other fenamate structures, the carboxyl group and the imino N atom are connected through an intramolecular hydrogen bond; also, pairs of centrosymmetrically related molecules are connected through hydrogen bonds involving carboxyl groups.

Structure of a new crystal form of 2-{[3-(trifluoromethyl)phenyl]amino}benzoic acid (flufenamic acid)

C14Ht0F3NO2, P2.Jc, a = 12.523 (4), b = 7.868(6), c = 12.874 (3)A, fl = 95.2 (2) ° , O,,, = 1.47 (4), D e = 1.47 Mg m -3, Z = 4. Final R = 0.074 for 2255 observed reflections. The carboxyl group and the phenyl ring bearing the carboxyl group are nearly coplanar whereas the two phenyl rings are inclined with respect to each other at 52.8 ° . The difference between the two polymorphs of flufenamic acid lies in the geometrical disposition of the [3-(trifluoromethyl)- phenyl]amino moiety with respect to the benzoic acid moiety. As in other fenamate structures, the carboxyl group and the imino N atom are connected through an intramolecular hydrogen bond; also, pairs of centrosymmetrically related molecules are connected through hydrogen bonds involving carboxyl groups.

Structural Crystallography and Crystal Chemistry

CaH406P-.K +, M r = 206.10, is orthorhombic, space group Pbca (from systematic absences), a = 14.538(4), b = 13.364(5), c = 6.880 (6)A, U = 1383.9 A 3, D x = 2.07 Mg m -a, Z = 8, ~.(Mo Ka) = 0.7107/~, p(MO Ka) = 1.015 mm -1. The final R value is 0.042 for a total of 1397 reflections. The high energy P-O(13) and the enolic C(1)-O(13) bonds are 1.612 and 1.374 A respectively. The enolpyruvate moiety is essentially planar. The orientation of the phosphate with respect to the pyruvate group in PEP.K is distinctly different from that in the PEP-cyclohexylammonium salt, the torsion angle C (2)-C (1)-O(13)- P being -209.1 in the former and -90 ° in the latter. The K + ion binds simultaneously to both the phosphate and carboxyl ends of the same PEP molecule. The ester O(13) is also a binding site for the cation. The K + ion is coplanar with the pyruvate moiety and binds to 0(22) and O(13) almost along their lone-pair directions. The carbonyl 0(22) prefers to bind to the K + ion rather than take part in the formation of hydrogen bonds usually observed in carboxylic acid structures.

Application of the Conjugate Gradient Method to a Problem on Minimum Time Orbit Transfer

This correspondence considers the problem of optimally controlling the thrust steering angle of an ion-propelled spaceship so as to effect a minimum time coplanar orbit transfer from the mean orbital distance of Earth to mean Martian and Venusian orbital distances. This problem has been modelled as a free terminal time-optimal control problem with unbounded control variable and with state variable equality constraints at the final time. The problem has been solved by the penalty function approach, using the conjugate gradient algorithm. In general, the optimal solution shows a significant departure from earlier work. In particular, the optimal control in the case of Earth-Mars orbit transfer, during the initial phase of the spaceship's flight, is found to be negative, resulting in the motion of the spaceship within the Earth's orbit for a significant fraction of the total optimized orbit transfer time. Such a feature exhibited by the optimal solution has not been reported at all by earlier investigators of this problem.

2-Chloro-3-hydroxymethyl-6-methoxyquinoline

All the non-H atoms of the title compound, C11H10ClNO2, are roughly coplanar (r.m.s. deviation = 0.058 angstrom). In the crystal, adjacent molecules are linked by an O-H center dot center dot center dot N hydrogen bond, generating chains running along the a axis.

Design and analysis of ARROW-based racetrack resonator vibration sensor for inertial navigation application

In this paper we propose and analyze a novel racetrack resonator based vibration sensor for inertial grade application. The resonator is formed with an Anti Resonance Reflecting Optical Waveguide (ARROW) structure which offers the advantage of low loss and single mode propagation. The waveguide is designed to operate at 1310nm and TM mode of propagation since the Photo-elastic co-efficient is larger than TE mode in a SiO2/ Si3N4/ SiO2. The longer side of the resonator is placed over a cantilever beam with a proof mass. A single bus waveguide is coupled to the resonator structure. When the beam vibrates the resonator arm at the foot of the cantilever experiences maximum stress. Due to opto-mechanical coupling the effective refractive index of the resonator changes hence the resonance wavelength shifts. The non uniform cantilever beam has a dimension of 1.75mm X 0.45mm X 0.020mm and the proof mass has a dimension of 3mm X 3mm X 0.380mm. The proof mass lowers the natural frequency of vibration to 410Hz, hence designed for inertial navigation application. The operating band of frequency is from DC to 100Hz and acceleration of less than 1g. The resonator has a Free Spectral Range (FSR) of 893pm and produces a phase change of 22.4mrad/g.

(2-Chlorobenzo[h]quinolin-3-yl)methanol

In the title molecule, C14H10ClNO, all non-H atoms are coplanar (r.m.s deviation = 0.0266 angstrom). In the crystal, symmetry-related molecules are hydrogen bonded via intermolecular O-H center dot center dot center dot O interactions, forming chains along the b axis.