Extended self-similarity works for the Burgers equation and why

Extended self-similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier-Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the IR and UV end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

Self-consistent microscopic treatment of the effects of self-motion of the probe on ionic and dipolar solvation dynamics

A simple but self-consistent microscopic theory for the time dependent solvation energy of both ions and dipoles is presented which includes, for the first time, the details of the self-motion of the probe on its own solvation dynamics. The theory leads to several interesting predictions. The most important of them is that, for dipolar solvation, both the rotational and the translational motions of the dipolar solute probe can significantly accelerate the rate of solvation. In addition, the rotational self-motion of the solute can also give rise to an additional mechanism of nonexponentiality in solvation time correlation functions in otherwise slow liquids. A comparison between the present theoretical predictions and the recent experimental studies of Maroncelli et al. on solvation dynamics of aniline in l-propanol seems to indicate that the said experiments have missed the initial solvent response up to about 45 ps. After mapping the experimental results on the redefined time scale, the theoretical results can explain the experimental results for solvation of aniline in 1-propanol very well. For ionic solvation, the translational motion is significant for light solutes only. For example, for Li+ in water, translational motion speeds up the solvation by about 20%. The present theory demonstrates that in dipolar solvation the partial quenching of the self-motion due to the presence of specific solute-solvent interactions (such as H-bonding) may lead to a much slower solvation than that when the self-motion is present. This point has been discussed. In addition, we present the theoretical results for solvation of aniline in propylene carbonate, Here, the solvation is predicted to be complete within 15-20 ps.

Some recent advances in the theory of homogeneous isotropic turbulence

We review some advances in the theory of homogeneous, isotropic turbulence. Our emphasis is on the new insights that have been gained from recent numerical studies of the three-dimensional Navier Stokes equation and simpler shell models for turbulence. In particular, we examine the status of multiscaling corrections to Kolmogorov scaling, extended self similarity, generalized extended self similarity, and non-Gaussian probability distributions for velocity differences and related quantities. We recount our recent proposal of a wave-vector-space version of generalized extended self similarity and show how it allows us to explore an intriguing and apparently universal crossover from inertial- to dissipation-range asymptotics.

Strong shock approximation in the new theory of shock dynamics

This paper investigates the propagation of a strong shock into an inhomogeneous medium using the new theory of shock dynamics. The equations are simple to solve and involve no trial-and-error method commonly used in this case. The results compare favourably with earlier results obtained in the case of self-similar flows, which arise as a special case of this theory.

The log delta log t method for the determination of the coefficient of consolidation

The behaviour of saturated soils undergoing consolidation is very complex, It may not follow Terzaghi's theory over the entire consolidation process, Different soils may behave in such a way as to fit into Terzaghi's theory over some specific stages of the consolidation process (percentage of consolidation), This may be one of the reasons for the difficulties faced by the existing curve-fitting procedures in obtaining the coefficient of consolidation, c(v). It has been shown that the slope of the initial linear portion of the theoretical log U-log T curve is constant over a wider range of degree of consolidation, U, when compared with the other methods in use, This initial well-defined straight line in the log U-log T plot intersects the U = 100% line at T = pi/4, which corresponds to U = 88.3%, The proposed log delta-log t method is based on this observation, which gives the value of c(v) through simple graphical construction, In the proposed method, which is more versatile, identification of the characteristic straight lines is very clear; the intersection of these lines is more precise and the method does not depend upon the initial compression for the determination of c(v).

Ab initio, DFT and transition state theory calculations on 1,2-HF, HCI and CIF elimination reactions from CH2F-CH2Cl

This paper reports ab intio, DFT and transition state theory (TST) calculations on HF, HCI and CIF elimination reactions from CH2Cl-CH2F molecule. Both the ground state and the transition state for HX elimination reactions have been optimized at HF, MP2 and DFT calculations with 6-31G*, 6-31G** and 6-311++G** basis sets. In addition, CCSD(T) single point calculations were carried out with MP2/6-311++G** optimized geometry for more accurate determination of the energies of the minima and transition state, compared to the other methods employed here. Classical barriers are converted to Arrhenius activation energy by TST calculations for comparisons with experimental results. The pre-exponential factors, A, calculated at all levels of theory are significantly larger than the experimental values. For activation energy, E-a DFT gives good results for HF elimination, within 4-8 W mol(-1) from experimental values. None of the methods employed, including CCSD(T), give comparable results for HCI elimination reactions. However, rate constants calculated by CCSD(T) method are in very good agreement with experiment for HCI elimination and they are in reasonable agreement for HF elimination reactions. Due to the strong correlation between A and E., the rate constants could be fit to a lower A and E-a (as given by experimental fitting, corresponding to a tight TS) or to larger A and E-a (as given by high level ab initio calculations, corresponding to a loose TS). The barrier for CIF elimination is determined to be 607 U mol(-1) at HF level and it is unlikely to be important for CH2FCH2Cl. Results for other CH2X-CH2Y (X,Y = F/Cl) are included for comparison.

Theoretical determination of HI vertical scale heights in the dwarf galaxies DDO 154, Ho II, IC 2574 and NGC 2366

In this paper, we model dwarf galaxies as a two-component system of gravitationally coupled stars and atomic hydrogen gas in the external force field of a pseudo-isothermal dark matter halo, and numerically obtain the radial distribution of HI vertical scale heights. This is done for a group of four dwarf galaxies (DDO 154, Ho II, IC 2574 and NGC 2366) for which most necessary input parameters are available from observations. The formulation of the equations takes into account the rising rotation curves generally observed in dwarf galaxies. The inclusion of self-gravity of the gas into the model at par with that of the stars results in scale heights that are smaller than what was obtained by previous authors. This is important as the gas scale height is often used for deriving other physical quantities. The inclusion of gas self-gravity is particularly relevant in the case of dwarf galaxies where the gas cannot be considered a minor perturbation to the mass distribution of the stars. We find that three out of four galaxies studied show a flaring of their HI discs with increasing radius, by a factor of a few within several disc scale lengths. The fourth galaxy has a thick HI disc throughout. This flaring arises as a result of the gas velocity dispersion remaining constant or decreasing only slightly while the disc mass distribution declines exponentially as a function of radius.

Analog/RF Built-in-Self-Test Subsystem for a Mobile Broadcast Video Receiver in 65-nm CMOS

A built-in-self-test (BIST) subsystem embedded in a 65-nm mobile broadcast video receiver is described. The subsystem is designed to perform analog and RF measurements at multiple internal nodes of the receiver. It uses a distributed network of CMOS sensors and a low bandwidth, 12-bit A/D converter to perform the measurements with a serial bus interface enabling a digital transfer of measured data to automatic test equipment (ATE). A perturbation/correlation based BIST method is described, which makes pass/fail determination on parts, resulting in significant test time and cost reduction.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Coordination-driven self-assembly of 2D-metallamacrocycles using a shape-selective Pt(2)(II)-organometallic 90 degrees acceptor: design, synthesis and sensing study

Synthesis of a series of two-dimensional metallamacrocycles via coordination-driven self-assembly of a shape-selective Pt(2)(II)-molecular building unit incorporating carbazole-ethynyl functionality is described. An equimolar (1 : 1) combination of a Pt(2)(II)-organometallic 90 degrees acceptor, 1, with rigid linear ditopic donors (L(a) and L(b)) afforded [4 + 4] self-assembled octanuclear molecular squares, 2 and 3, in quantitative yields, respectively [L(a) = 4,4'-bipyridine; L(b) = trans-1,2-bis(4-pyridyl)ethylene]. Conversely, a similar treatment of 1 with an amide-based unsymmetrical flexible ditopic donor, L(c), resulted in the formation of a [2 + 2] self-sorted molecular rhomboid (4a) as a single product [L(c) = N-(4-pyridyl)isonicotinamide]. Despite the possibility of several linkage isomeric macrocycles (rhomboid, triangle and square) due to the different connectivity of L(c), the formation of a single and symmetrical molecular rhomboid (4a) as the only product is an interesting observation. All the self-assembled macrocycles (2, 3 and 4a) were fully characterized by multinuclear NMR ((1)H and (31)P) and ESI-MS analysis. Further structural insights about the size and shape of the macrocycles were obtained through energy minimization using density functional theory (DFT) calculations. Decoration of the starting carbazole building unit with Pt-ethynyl functionality enriches the assemblies to be more p-electron rich and luminescent in nature. Macrocycles 2 and 3 could sense the presence of electron deficient nitroaromatics in solution by quenching of the initial intensity upon gradual addition of picric acid (PA). They exhibited the largest quenching response with high selectivity for nitroaromatics compared to several other electron deficient aromatics tested.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

Self-diffusion of colloids at freezing

This is an introduction to the theory of interacting Brownian particles, as applied to charge-stabilised colloidal suspensions near their equilibrium liquid-solid transition. The density functional approach to the statics of the transition is reviewed briefly, and the generalised Langevin equation method for the dynamics presented in detail. Work with A.V. Indrani [1] on a self-consistent approach for calculating the excess single-particle friction is presented, which explains the observed [2] ''universal'' suppression of self-diffusion at freezing as a consequence of the universal structure-factor height at this transition. Criticisms, open questions, and challenges to theory are discussed.