Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

An a priori error analysis of discontinuous Galerkin methods for a general elliptic problem is derived under a mild elliptic regularity assumption on the solution. This is accomplished by using some techniques from a posteriori error analysis. The model problem is assumed to satisfy a GAyenrding type inequality. Optimal order L (2) norm a priori error estimates are derived for an adjoint consistent interior penalty method.

Comparative study of different formulations and solution methods for two phase flow in saturated porous media

Six models (Simulators) are formulated and developed with all possible combinations of pressure and saturation of the phases as primary variables. A comparative study between six simulators with two numerical methods, conventional simultaneous and modified sequential methods are carried out. The results of the numerical models are compared with the laboratory experimental results to study the accuracy of the model especially in heterogeneous porous media. From the study it is observed that the simulator using pressure and saturation of the wetting fluid (PW, SW formulation) is the best among the models tested. Many simulators with nonwetting phase as one of the primary variables did not converge when used along with simultaneous method. Based on simulator 1 (PW, SW formulation), a comparison of different solution methods such as simultaneous method, modified sequential and adaptive solution modified sequential method are carried out on 4 test problems including heterogeneous and randomly heterogeneous problems. It is found that the modified sequential and adaptive solution modified sequential methods could save the memory by half and as also the CPU time required by these methods is very less when compared with that using simultaneous method. It is also found that the simulator with PNW and PW as the primary variable which had problem of convergence using the simultaneous method, converged using both the modified sequential method and also using adaptive solution modified sequential method. The present study indicates that pressure and saturation formulation along with adaptive solution modified sequential method is the best among the different simulators and methods tested.

X-ray studies on crystalline complexes involving amino acids and peptides XIX. Effects of change in chirality in the complexes of succinic acid with dl- and l-arginine

Crystals of dl-arginine hemisuccinate dihydrate (I)(monoclinic; P21/c; a = 5.292, b = 16.296, c = 15.203 Å; α= 92.89°; Z = 4) and l-arginine hemisuccinate hemisuccinic acid monohydrate (II) (triclinic; P1; a = 5.099; b = 10.222, c = 14.626 Å; α= 77.31, β= 89.46, γ= 78.42°; Z = 2) were grown under identical conditions from aqueous solutions of the components in molar proportions. The structures were solved by direct methods and refined to R = 0.068 for 2585 observed reflections in the case of (I) and R = 0.036 for 2154 observed reflections in the case of (11). Two of the three crystallographically independent arginine molecules in the complexes have conformations different from those observed so far in the crystal structures containing arginine. The succinic acid molecules and the succinate ions in the structures are centrosymmetric and planar. The crystal structure of (II) is highly pseudosymmetric. Arginine-succinate interactions in both the complexes involve specific guanidyl-carboxylate interactions. The basic elements of aggregation in both the structures are ribbons made up of alternating arginine dimers and succinate ions. However, the ribbons pack in different ways in the two structures. (II) presents an interesting case in which two ionisation states of the same molecule coexist in a crystal. The two complexes provide a good example of the effect of change in chirality on stoichiometry, conformation, aggregation, and ionisation state in the solid state.

Phenyl-Ring-Bearing Cationic Surfactants: Effect of Ring Location on the Micellar Structure

A series of isomeric cationic surfactants (S1-S5) bearing a long alkyl chain that carries a 1,4-phenylene unit and a trimethyl ammonium headgroup was synthesized; the location of the phenyl ring within the alkyl tail was varied in an effort to understand its influence on the amphiphilic properties of the surfactants. The cmc's of the surfactants were estimated using ionic conductivity measurements and isothermal calorimetric titrations (ITC); the values obtained by the two methods were found to be in excellent agreement. The ITC measurements provided additional insight into the various thermodynamic parameters associated with the micellization process. Although all five surfactants have exactly the same molecular formula, their micellar properties were seen to vary dramatically depending on the location of the phenyl ring; the cmc was seen to decrease by almost an order of magnitude when the phenyl ring was moved from the tail end (cmc of S1 is 23 mM) to the headgroup region (cmc of S5 is 3 mM). In all cases, the enthalpy of micellization was negative but the entropy of micellization was positive, suggesting that in all of these systems the formation of micelles is both enthalpically and entropically favored. As expected, the decrease in cmc values upon moving the phenyl ring from the tail end to he headgroup region is accompanied by an increase in the thermodynamic driving force (Delta G) for micellization. To understand further the differences in the micellar structure of these surfactants, small-angle neutron scattering (SANS) measurements were carried out; these measurements reveal that the aggregation number of the micelles increases as the cmc decreases. This increase in the aggregation number is also accompanied by an increase in the asphericity of the micellar aggregate and a decrease in the fractional charge. Geometric packing arguments are presented to account for these changes in aggregation behavior as a function of phenyl ring location.

CD and NMR studies on the aggregation of amphotericin-B in solution

We report in this paper the aggregation properties of amphotericin-B (amp-B) in solution using CD and 1H-NMR techniques. Our results indicate that the preferred structure of amp-B in dimethylsulfoxide is a monomer at low concentrations (10−4M and below) and a stable dimer at higher concentrations (range 5 · 103 M to 10−2M). In a DMSO/ethanol mixture (1:1 (v/v)), the antibiotic is monomeric, irrespective of the concentration within the range studied. We propose a head-to-tail model based on NMR data. An understanding of the head-to-tail dimer, is, we believe important, particularly in view of the recent report wherein it is proposed that the drug inserts into bilayers as head-to-tail oligomers.

Lipid-amphotericin B complex structure in solution: A possible first step in the aggregation process in cell membranes

The interactions between the polyene antibiotic amphotericin B with dipalmitoylphosphatidylcholine were investigated in vesicles (using circular dichroism) and in chloroform solution (using circular dichroism and IH, I3C, and 31P nuclear magnetic resonance). The results show that amphotericin B readily aggregates in vesicles and that the extent of aggregation depends on the 1ipid:drug concentration ratio. Introduction of sterol molecules into the membrane hastens the process of aggregation of amphotericin B. In chloroform solutions amphotericin B strongly interacts with phospholipid molecules to form a stoichiometric complex. The results suggest that there are interactions between the conjugated heptene stretch of amphotericin B and the methylene groups of lipid acyl chains, while the sugar moiety interacts with the phosphate head group by the formation of a hydrogen bond. A model is proposed for the lipid-amphotericin B complex, in which amphotericin B interacts equally well with the two lipid acyl chains, forming a 1:l complex.

NDDO-based CI methods for the prediction of electronic spectra and sum-over-states molecular hyperpolarization

NDDO-based (AM1) configuration interaction (CI) calculations have been used to calculate the wavelength and oscillator strengths of electronic absorptions in organic molecules and the results used in a sum-over-states treatment to calculate second-order-hyperpolarizabilities. The results for both spectra and hyperpolarizabilities are of acceptable quality as long as a suitable CI-expansion is used. We have found that using an active space of eight electrons in eight orbitals and including all single and pair-double excitations in the CI leads to results that agree well with experiment and that do not change significantly with increasing active space for most organic molecules. Calculated second-order hyperpolarizabilities using this type of CI within a sum-over-states calculation appear to be of useful accuracy.

A study of the synthetic methods and properties of graphenes

Graphenes with varying number of layers can be synthesized by using different strategies. Thus, single-layer graphene is prepared by micromechanical cleavage, reduction of single-layer graphene oxide, chemical vapor deposition and other methods. Few-layer graphenes are synthesized by conversion of nanodiamond, arc discharge of graphite and other methods. In this article, we briefly overview the various synthetic methods and the surface, magnetic and electrical properties of the produced graphenes. Few-layer graphenes exhibit ferromagnetic features along with antiferromagnetic properties, independent of the method of preparation. Aside from the data on electrical conductivity of graphenes and graphene-polymer composites, we also present the field-effect transistor characteristics of graphenes. Only single-layer reduced graphene oxide exhibits ambipolar properties. The interaction of electron donor and acceptor molecules with few-layer graphene samples is examined in detail.

Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Finite data performance of MUSIC and minimum norm methods

In the direction of arrival (DOA) estimation problem, we encounter both finite data and insufficient knowledge of array characterization. It is therefore important to study how subspace-based methods perform in such conditions. We analyze the finite data performance of the multiple signal classification (MUSIC) and minimum norm (min. norm) methods in the presence of sensor gain and phase errors, and derive expressions for the mean square error (MSE) in the DOA estimates. These expressions are first derived assuming an arbitrary array and then simplified for the special case of an uniform linear array with isotropic sensors. When they are further simplified for the case of finite data only and sensor errors only, they reduce to the recent results given in [9-12]. Computer simulations are used to verify the closeness between the predicted and simulated values of the MSE.

Fuel drop size measurement in a carburetted induction system with 2 throttling methods

A new throttling system far SI engines is examined. The SMD of the fuel droplets in the induction system is measured to evaluate the performance of the new device with respect to the conventional throttle plate arrangement. The measurements are conducted at steady now conditions. A forward angular scattering technique with a He-Ne laser beam is used for droplet size measurement. The experiments are carried out with different mixture strength, stream velocity and throttle positions. It is observed that A/F ratio has no effect on SMD. However, stream velocity and throttle position have a significant influence on SMD. The new throttling method is found to be more effective in reducing the SMD, particularly at low throttle opening and high stream velocity compared to the conventional throttle plate.

Influence of poling methods on the orientational dynamics of 2-methyl-4-nitro-aniline in poly(methyl methacrylate) studied by second harmonic generation

The magnitude and stability of the induced dipolar orientation of 2-methyl-4-nitroaniline (MNA)/poly(methyl methacrylate) (PMMA) guest/host system is investigated. The chromophores are aligned using both the corona discharge and contact electrode poling techniques. The magnitude of order parameter (also an indicator for the second order nonlinear susceptibility) is measured by recording absorbances of the poled (by the two different techniques) and unpoled PMMA films at different concentrations of MNA. Under the same conditions the corona poling technique creates a higher alignment of molecules along the field direction. The time dependence of the second harmonic intensity of the MNA/PMMA film prepared by the two techniques can be described by a Kohlrausch-Williams-Watts stretched exponential. The temperature dependence of the decay time constant is found to generally follow a modified Williams-Landel-Ferry (WLF) or Vogel-Tamann-Fulcher (VTF) equation. The glass transition temperature seems to be the single most important parameter for determining the relaxation time tau(T).

Coordination aggregation of mesoaryl substituted porphyrins

Synthesis of the free-base tetrakis (3'-nitro/aminophenyl), (H2TNP/H(2)TAP) has been accomplished and its coordination behaviour towards Mg(II), Co(II), Zn(II) and Ag(II) ions is investigated. Optical and magnetic resonance properties of the metal derivatives MTNP and MTAP reveal that the aminoporphyrins exist as aggregates in solution. The aggregation is promoted by the coordination of the peripheral amino groups to neighbouring metalloporphyrins. Possible structures of aggregated species are proposed from the model studies.

Parallel computing concepts and methods for floquet analysis of helicopter trim and stability

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, however, it is practical neither for design applications nor for comprehensive analysis models that lead to large systems (M > 100); the run time on a sequential computer is simply prohibitive, Accordingly, a massively parallel Floquet analysis is developed with emphasis on large systems, and it is implemented on two SIMD or single-instruction, multiple-data computers with 4096 and 8192 processors, The focus of this development is a parallel shooting method with damped Newton iteration to generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are computed by a parallel QR method, and thereby stability results are generated, For illustration, flap and flap-lag stability of isolated rotors are treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasisteady airfoil aerodynamics and a finite-state three-dimensional wake model are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition numbers of the eigenvalues and the residual errors of the eigenpairs, and reliability figures are comparable in both the parallel and sequential analyses, Compared to the sequential analysis, the parallel analysis reduces the run time of large systems dramatically, and the reduction increases with increasing system order; this finding offers considerable promise for design and comprehensive-analysis applications.