Determination of C-13 Chemical Shift Anisotropy Tensors and Molecular Order of 4-Hexyloxybenzoic Acid

4-Alkoxy benzoic acids belong to an important class of thermotropic liquid crystals that are structurally simple and often used as starting materials for many novel mesogens. 4-Hexyloxybenzoic acid (HBA) is a homologue of the same series and exhibits an enantiotropic nematic phase. As this molecule could serve as an ideal model compound, high resolution C-13 NMR studies of HEA in solution, solid, and liquid crystalline phases have been undertaken. In the solid state, two-dimensional separation of undistorted powder patterns by effortless recoupling (2D SUPER) experiments have been carried out to estimate the magnitude of the components of the chemical shift anisotropy (GSA) tensor of all the aromatic carbons. These values have been used subsequently for calculating the orientational order parameters in the liquid crystalline phase. The GSA values computed by density functional theory (DFT) calculations showed good agreement with the 2D SUPER values. Additionally, C-13-H-1 dipolar couplings in the nematic phase have been determined by separated local field (SLF) spectroscopy at various temperatures and were used for computing the order parameters, which compared well with those calculated by using the chemical shifts. It is anticipated that the CSA values determined for MBA would be useful for the assignment of carbon chemical shifts and for the study of order and dynamics of structurally similar novel mesogens in their nematic phases.

On the Role of Higher-Order Evanescent Modes in End-Offset Inlet and End-Centered Outlet Elliptical Flow-Reversal Chamber Mufflers

This paper deals with the role of the higher-order evanescent modes generated at the area discontinuities in the acoustic attenuation characteristics of an elliptical end-chamber muffler with an end-offset inlet and end-centered outlet. It has been observed that with an increase in length, the muffler undergoes a transition from being acoustically short to acoustically long. Short end chambers and long end chambers are characterized by transverse plane waves and axial plane waves, respectively, in the low-frequency range. The nondimensional frequency limit k(0)(D-1/2) or k(0)R(0) as well as the chamber length to inlet/outlet pipe diameter ratio, i.e., L/d(0), up to which the muffler behaves like a short chamber and the corresponding limit beyond which the muffler is acoustically long are determined. The limits between which neither the transverse plane-wave model nor the conventional axial plane-wave model gives a satisfactory prediction have also been determined, the region being called the intermediate range. The end-correction expression for this muffler configuration in the acoustically long limit has been obtained using 3-D FEA carried on commercial software, covering most of the dimension range used in the design exercise. Development of a method of combining the transverse plane wave model with the axial plane wave model using the impedance Z] matrix is another noteworthy contribution of this work.

Premixed flame response to equivalence ratio fluctuations: Comparison between reduced order modeling and detailed computations

Combustion instability events in lean premixed combustion systems can cause spatio-temporal variations in unburnt mixture fuel/air ratio. This provides a driving mechanism for heat-release oscillations when they interact with the flame. Several Reduced Order Modelling (ROM) approaches to predict the characteristics of these oscillations have been developed in the past. The present paper compares results for flame describing function characteristics determined from a ROM approach based on the level-set method, with corresponding results from detailed, fully compressible reacting flow computations for the same two dimensional slot flame configuration. The comparison between these results is seen to be sensitive to small geometric differences in the shape of the nominally steady flame used in the two computations. When the results are corrected to account for these differences, describing function magnitudes are well predicted for frequencies lesser than and greater than a lower and upper cutoff respectively due to amplification of flame surface wrinkling by the convective Darrieus-Landau (DL) instability. However, good agreement in describing function phase predictions is seen as the ROM captures the transit time of wrinkles through the flame correctly. Also, good agreement is seen for both magnitude and phase of the flame response, for large forcing amplitudes, at frequencies where the DL instability has a minimal influence. Thus, the present ROM can predict flame response as long as the DL instability, caused by gas expansion at the flame front, does not significantly alter flame front perturbation amplitudes as they traverse the flame. (C) 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws

A computational tool called ``Directional Diffusion Regulator (DDR)'' is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax-Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson-Schmidt-Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework. (C) 2012 Elsevier Inc. All rights reserved.

Power Controlled Reverse Channel Training Achieves an Infinite Diversity Order in a TDD-SIMO System with Perfect CSIR

In this letter, we analyze the Diversity Multiplexinggain Tradeoff (DMT) performance of a training-based reciprocal Single Input Multiple Output (SIMO) system. Assuming Channel State Information (CSI) is available at the Receiver (CSIR), we propose a channel-dependent power-controlled Reverse Channel Training (RCT) scheme that enables the transmitter to directly estimate the power control parameter to be used for the forwardlink data transmission. We show that, with an RCT power of (P) over bar (gamma), gamma > 0 and a forward data transmission power of (P) over bar, our proposed scheme achieves an infinite diversity order for 0 <= g(m) < L-c-L-B,L-tau/L-c min(gamma, 1) and r > 2, where g(m) is the multiplexing gain, L-c is the channel coherence time, L-B,L-tau is the RCT duration and r is the number of receive antennas. We also derive an upper bound on the outage probability and show that it goes to zero asymptotically as exp(-(P) over bar (E)), where E (sic) (gamma - g(m)L(c)/L-c-L-B,L-tau), at high (P) over bar. Thus, the proposed scheme achieves a significantly better DMT performance compared to the finite diversity order achieved by channel-agnostic, fixed-power RCT schemes.

Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

Influence of Side-Chain on Structural Order and Photophysical Properties in Thiophene Based Diketopyrrolopyrroles: A Systematic Study

In this work, we have synthesized a series of TDPP derivatives with different alkyl groups such as n-hexyl (-C6H13) 3a, 2-ethylhexyl (-(2-C2H5)C6H12) 3b, triethylene glycol mono methyl ether (-(CH2CH2O)(3c)H-3, TEG) 3c, and octadodecyl (-(8-C8H17)C12H22) 3d. N,N dialkylation of Othiophene-diketopyrrolopyrrole (TDPP, 1) strongly influences its solubility, solid state packing, and structural order. These materials allow us to explicitly study the influence of alkyl chain on solid state packing and photophysical properties. TDPP moiety containing two different alkyl groups 3e (TEG and 2-ethylhexyl) and 3f (TEG and n-hexyl) were synthesized for the first time. The absorption spectra of all derivatives exhibited a red shift in solid state when compared to their solution spectra. The type of alkyl chains leads to change in the optical band gaps in solid state. The fluorescence study reveals that TDPP derivatives have strong pi-pi interaction in the solid state and the extent of bathochromic shift is due to combination of intramolecular interaction and formation of aggregates in solid state. This behavior strongly depends on the nature of alkyl chain. The presence of strong C-H center dot center dot center dot O inter chain interactions and CH-pi interactions in solid state exhibits strong influence on the photophysical properties of TDPP chromophore.

Multiuser detection in large-dimension multicode MIMO-CDMA systems with higher-order modulation

In this paper, we are interested in high spectral efficiency multicode CDMA systems with large number of users employing single/multiple transmit antennas and higher-order modulation. In particular, we consider a local neighborhood search based multiuser detection algorithm which offers very good performance and complexity, suited for systems with large number of users employing M-QAM/M-PSK. We apply the algorithm on the chip matched filter output vector. We demonstrate near-single user (SU) performance of the algorithm in CDMA systems with large number of users using 4-QAM/16-QAM/64-QAM/8-PSK on AWGN, frequency-flat, and frequency-selective fading channels. We further show that the algorithm performs very well in multicode multiple-input multiple-output (MIMO) CDMA systems as well, outperforming other linear detectors and interference cancelers reported in the literature for such systems. The per-symbol complexity of the search algorithm is O(K2n2tn2cM), K: number of users, nt: number of transmit antennas at each user, nc: number of spreading codes multiplexed on each transmit antenna, M: modulation alphabet size, making the algorithm attractive for multiuser detection in large-dimension multicode MIMO-CDMA systems with M-QAM.

Electronically tunable zero order resonator based on CRLH-TLs

Composite Right/Left Handed (CRLH) transmission line (TL) based electronically tunable 1.5 cell zero order resonator (ZOR) is demonstrated with microstrip technology by use of varactors. A novel mechanism for DC bias for the varactor is proposed. This is achieved by patterning the ground plane of microstrip thereby reducing the complexity of DC feed mechanism. This approach also mitigates the effect of parasitics arising from DC feed choke appearing in the RF signal path.

Live Soap: Stability, Order, and Fluctuations in Apolar Active Smectics

We construct a hydrodynamic theory of noisy, apolar active smectics in bulk suspension or on a substrate. Unlike purely orientationally ordered active fluids, active apolar smectics can be dynamically stable in Stokesian bulk suspensions. Smectic order in these systems is quasilong ranged in dimension d = 2 and long ranged in d = 3. We predict reentrant Kosterlitz-Thouless melting to an active nematic in our simplest model in d = 2, a nonzero second-sound speed parallel to the layers in bulk suspensions, and that there are no giant number fluctuations in either case. We also briefly discuss possible instabilities in these systems. DOI: 10.1103/PhysRevLett.110.118102

A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4790845]

Anisotropy induced crossover from weakly to strongly first order melting of two dimensional solids

Melting and freezing transitions in two dimensional (2D) systems are known to show highly unusual characteristics. Most of the earlier studies considered atomic systems: the melting of 2D molecular solids is still largely unexplored. In order to understand the role of anisotropy as well as multiple energy and length scales present in molecular systems, here we report computer simulation studies of melting of 2D molecular systems. We computed a limited portion of the solid-liquid phase diagram. We find that the interplay between the strength of isotropic and anisotropic interactions can give rise to rich phase diagram consisting of isotropic liquid and two crystalline phases-honeycomb and oblique. The nature of the transition depends on the relative strength of the anisotropic interaction and a strongly first order melting turns into a weakly first order transition on increasing the strength of the isotropic interaction. This crossover can be attributed to an increase in stiffness of the solid phase free energy minimum on increasing the strength of the anisotropic interaction. The defects involved in melting of molecular systems are quite different from those known for the atomic systems.

Structural characterization and molecular order of rodlike mesogens with three- and four-ring core by XRD and C-13 NMR spectroscopy

Structural characterizations using XRD and C-13 NMR spectroscopy of two rodlike mesogens consisting of (i) three phenyl ring core with a polar cyano terminal and (ii) four phenyl ring core with flexible dodecyl terminal chain are presented. The three-ring-core mesogen with cyano terminal exhibits enantiotropic smectic A phase while the four-ring mesogen reveals polymesomorphism and shows enantiotropic nematic, smectic C, and tilted hexatic phases. The molecular organization in the three-ring mesogen is found to be partial bilayer smectic Ad type, and the interdigitation of the molecules in the neighboring layers is attributed to the presence of the polar terminal group. For the four-ring mesogen, the XRD results confirm the existence of the smectic C and the tilted hexatic mesophases. A thermal variation of the layer spacing across the smectic C phase followed by a discrete jump at the transition to the tilted hexatic phase is also observed. The tilt angles have been estimated to be about 45 degrees in the smectic C phase and about 40 degrees in tilted hexatic phase. C-13 NMR results indicate that in the mesophase the molecules are aligned parallel to the magnetic field. From the C-13-H-1 dipolar couplings determined from the 2D experiments, the overall order parameter for the three-ring mesogen in its smectic A phase has been estimated to be 0.72 while values ranging from 0.88 to 0.44 have been obtained for the four-ring mesogen as it passes from the tilted hexatic to the nematic phase. The orientations of the different rings of the core unit with respect to each other and also with respect to the long axis of the molecule have also been obtained.