Toward a Mean Field Formulation of the Babcock-Leighton Type Solar Dynamo. I. α-Coefficient versus Durney's Double-Ring Approach

We develop a model of the solar dynamo in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes, such as the production of poloidal field from the decay of active regions, and, on the other hand, we attempt to develop a mean field theory that can be studied in quantitative detail. One of the main challenges in developing such models is to treat the buoyant rise of the toroidal field and the production of poloidal field from it near the surface. A previous paper by Choudhuri, Schüssler, & Dikpati in 1995 did not incorporate buoyancy. We extend this model by two contrasting methods. In one method, we incorporate the generation of the poloidal field near the solar surface by Durney's procedure of double-ring eruption. In the second method, the poloidal field generation is treated by a positive α-effect concentrated near the solar surface coupled with an algorithm for handling buoyancy. The two methods are found to give qualitatively similar results.

Capturing higher modes of vibration of micromachined resonators

MEMS resonators have potential applications in the areas of RF-MEMS, clock oscillators, ultrasound transducers, etc. The important characteristics of a resonator are its resonant frequency and Q-factor (a measure of damping). Usually large damping in macro structures makes it difficult to excite and measure their higher modes. In contrast, MEMS resonators seem amenable to excitation in higher modes. In this paper, 28 modes of vibration of an electrothermal actuator are experimentally captured–perhaps the highest number of modes experimentally captured so far. We verify these modes with FEM simulations and report that all the measured frequencies are within 5% of theoretically predicted values.

Microwave spectrum and structure of C(6)H(5)CCH center dot center dot center dot H(2)S complex

Rotational spectra of C(6)H(5)CCH center dot center dot center dot H(2)S, C(6)H(5)CCH center dot center dot center dot H(2)(34)S, C(6)H(5)CCH center dot center dot center dot HDS, C(6)H(5)CCH center dot center dot center dot D(2)S and C(6) H(5)CCD center dot center dot center dot H(2)S complexes have been observed using a pulsed nozzle Fourier transform microwave spectrometer. The observed spectrum is consistent with a structure in which hydrogen sulfide is located over the phenyl ring pi cloud and the distance between the centers of masses of the two monomers is 3.74 +/- 0.01 angstrom. In the complex, the H(2)S unit is shifted from the phenyl ring center towards the acetylene group. The vibrationally averaged structure has an effective Cs symmetry. Ab initio calculations were performed at MP2/aug-cc-pVDZ level of theory to locate the possible geometries of the complex. The calculations reveal the experimentally observed structure to be more stable than a coplanar arrangement of the monomers, which was observed for the C(6)H(5)CCH center dot center dot center dot H(2)O complex. Atoms in molecule theoretical analysis shows the presence of S-H center dot center dot center dot pi hydrogen bond. For the parent isotopologue, each transition frequency was found to split into two resulting from an interchange of the equivalent hydrogens of H(2)S unit in the complex. (C) 2011 Elsevier Inc. All rights reserved.

Enantiospecific synthesis of the ABC and ABD ring systems of the marine diterpenes aberraranes

Enantiospecific synthesis of the ABC and ABD ring systems present in the marine diterpenes aberraranes, starting from the readily available (S)-campholenaldehyde, has been accomplished. (C) 2011 Elsevier Ltd. All rights reserved.

Phase Characterization and Study of Molecular Order of a Three-Ring Mesogen by (13)C NMR in Smectic C and Nematic Phases

Molecules exhibiting a thermotropic liquid-crystalline property have acquired significant importance due to their sensitivity to external stimuli such as temperature, mechanical forces, and electric and magnetic fields. As a result, several novel mesogens have been synthesized by the introduction of various functional groups in the vicinity of the aromatic core as well as in the side chains and their properties have been studied. In the present study, we report three-ring mesogens with hydroxyl groups at one terminal. These mesogens were synthesized by a multistep route, and structural characterization was accomplished by spectral techniques. The mesophase properties were studied by hot-stage optical polarizing microscopy, differential scanning calorimetry, and small-angle X-ray scattering. An enantiotropic nematic phase was noticed for lower homologues, while an additional smectic C phase was found for higher homologues. Solid-state high-resolution natural abundance (13)C NMR studies of a typical mesogen in the solid phase and in the mesophases have been carried out. The (13)C NMR spectrum of the mesogen in the smectic C and nematic phases indicated spontaneous alignment of the molecule in the magnetic field. By utilizing the two-dimensional separated local field (SLF) NMR experiment known as SAMPI4, (13)C-(1)H dipolar couplings have been obtained, which were utilized to determine the orientational order parameters of the mesogen.

The single ring theorem

We study the empirical measure LA of the eigenvalues of nonnormal square matrices of the form A(n) = U(n)T(n)V(n), with U(n), V(n) independent Haar distributed on the unitary group and T(n) diagonal. We show that when the empirical measure of the eigenyalues of T(n) converges, and T(n) satisfies some technical conditions, L(An) converges towards a rotationally invariant measure mu on the complex plane whose support is a single ring. In particular, we provide a complete proof of the Feinberg-Zee single ring theorem [6]. We also consider the case where U(n), V(n) are independently Haar distributed on the orthogonal group.

Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.

Alkylation of toluene by methanol over alkali exchanged zeolite-X: side chain versus ring alkylation

The ring versus side-chain alkylation of toluene with methanol over alkali-exchanged zeolite-X of differing basicity has been investigated by in situ infrared spectroscopy and TPD measurements. Over the basic Cs-exchanged zeolite the product of alkylation is styrene/ethylbenzene while over the acidic Li-exchanged zeolite ring alkylation occurs to give mainly xylene as the product. FTIR and TPD investigations reveal that, the key difference in the two types of alkylation processes lies in the state of the adsorbed methanol present at higher temperatures in the zeolite. In basic zeolites, methanol decomposes to formaldehyde and formates. The former is the key ‘side-chain’ alkylating species that leads to the formation of styrene. In the acidic zeolites it is shown that methanol bound to the acid sites plays an active role in the ‘ring alkylation’ of toluene to xylene.

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.

Novel De-Acylative Ring Opening of 3-Acetyl and 3-Bromo Acetyl Coumarins

Reaction of 3-acetyl and 3-bromoacetyl coumarins with hydrazine hydrate has resulted in the ring opening of the coumarin moiety. The reaction was attempted with a view to obtain some new pyridazinones and pyrazolones. The reaction did not proceed via the expected pathway instead led to the formation of salicyl azines, the structure of which has been confirmed by single crystal X-ray studies.