Semi-similar solutions of the unsteady compressible second-order boundary layer flow at the stagnation point

Semi-similar solutions of the unsteady compressible laminar boundary layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer are studied for all the second-order boundary layer effects when the free stream velocity varies arbitrarily with time. The set of partial differential equations governing the unsteady compressible second-order boundary layers representing all the effects are derived for the first time. These partial differential equations are solved numerically using an implicit finite-difference scheme. The results are obtained for two particular unsteady free stream velocity distributions: (a) an accelerating stream and (b) a fluctuating stream. It is observed that the total skin friction and heat transfer are strongly affected by the surface mass transfer and wall temperature. However, their variation with time is significant only for large times. The second-order boundary layer effects are found to be more pronounced in the case of no mass transfer or injection as compared to that for suction. Résumé Des solutions semi-similaires d'écoulement variable compressible de couche limite sur des corps bi-dimensionnels thermique, sont étudiées pour tous les effets de couche limite du second ordre, lorsque la vitesse de l'écoulement libre varie arbitrairement avec le temps. Le systéme d'équations aux dérivées partielles représentant tous les effets est écrit pour la premiére fois. On le résout numériquement á l'aide d'un schéma implicite aux différences finies. Les résultats sont obtenus pour deux cas de vitesse variable d'écoulement libre: (a) un écoulement accéléré et (b) un écoulement fluctuant. On observe que le frottement pariétal total et le transfert de chaleur sont fortement affectés par le transfert de masse et la température pariétaux. Néanmoins, leur variation avec le temps est sensible seulement pour des grandes durées. Les effets sont trouvés plus prononcés dans le cas de l'absence du transfert de masse ou de l'injection par rapport au cas de l'aspiration.

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Neel order, quantum spin liquids, and quantum criticality in two dimensions

This paper is concerned with the possibility of a direct second-order transition out of a collinear Neel phase to a paramagnetic spin liquid in two-dimensional quantum antiferromagnets. Contrary to conventional wisdom, we show that such second-order quantum transitions can potentially occur to certain spin liquid states popular in theories of the cuprates. We provide a theory of this transition and study its universal properties in an epsilon expansion. The existence of such a transition has a number of interesting implications for spin-liquid-based approaches to the underdoped cuprates. In particular it considerably clarifies existing ideas for incorporating antiferromagnetic long range order into such a spin-liquid-based approach.

An Accurate Model For Interference From Spatially Distributed Shadowed Users in CDMA Uplinks

A detailed characterization of interference power statistics in CDMA systems is of considerable practical and theoretical interest. Such a characterization for uplink inter-cell interference has been difficult because of transmit power control, randomness in the number of interfering mobile stations, and randomness in their locations. We develop a new method to model the uplink inter-cell interference power as a lognormal distribution, and show that it is an order of magnitude more accurate than the conventional Gaussian approximation even when the average number of mobile stations per cell is relatively large and even outperforms the moment-matched lognormal approximation considered in the literature. The proposed method determines the lognormal parameters by matching its moment generating function with a new approximation of the moment generating function for the inter-cell interference. The method is tractable and exploits the elegant spatial Poisson process theory. Using several numerical examples, the accuracy of the proposed method in modeling the probability distribution of inter-cell interference is verified for both small and large values of interference.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Superharmonic vibrations of order 3 in stretched strings

Superharmonic vibrations of order 3 in stretched strings driven by a single-mode planar simple-harmonic force are investigated. It is shown that planar as well as nonplanar superharmonic resonances can occur. After giving a few analytical results, the problem is thoroughly investigated numerically. The stability analysis shows that the region of stable nonplanar oscillations is much smaller than that of stable planar oscillation. It is observed in the case of nonplanar oscillations that the amplitude of the superharmonic in the plane normal to the plane of excitation is larger than that in the plane of excitation.

On higher order shear deformation theory of laminated composite panels

In this paper we examine the suitability of higher order shear deformation theory based on cubic inplane displacements and parabolic normal displacements, for stress analysis of laminated composite plates including the interlaminar stresses. An exact solution of a symmetrical four layered infinite strip under static loading has been worked out and the results obtained by the present theory are compared with the exact solution. The present theory provides very good estimates of the deflections, and the inplane stresses and strains. Nevertheless, direct estimates of strains and stresses do not display the required interlaminar stress continuity and strain discontinuity across the interlaminar surface. On the other hand, ‘statically equivalent stresses and strains’ do display the required interlaminar stress continuity and strain discontinuity and agree very closely with the exact solution.

The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behavior of collections of active particles-active matter-with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogs. Theory and experiment are discussed side by side.

Sign Of The Order Parameter In Oriented Systems And Its Utility In The Study Of The Dynamic Properties Of Molecules

Novel one and two dimensional NMR techniques are proposed and utilized for the determination of the signs of the order parameters used for the study of the mobility of the fatty acid chains. The experiments designed to extract this information involve the use of the intensities of the side bands in the spectra of oriented systems spinning at the magic angle. Advantages of the two dimensional technique over the one dimensional method are discussed. The utility of the method in the study of the dynamic properties of membranes and model systems is pointed out.

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

An infrared spectroscopic study of the low-spin-high-spin transition in FexMn1-x(Phen)2(NCS)2: A composition-induced change in the order of the spin-state transition

Infrared spectroscopy provides a valuable tool to investigate the spin-state transition in Fe(II) complexes of the type Fe(Phen)2(NCS)2. With progressive substitution of Fe by Mn, the first-order transition changes over to a second-order transition, with a high residual population of the high-spin state even at very low temperatures

Padé approach to potential transients: Part 1. Electron transfer without and with coupling to first-order homogeneous reactions at planar electrodes

Potential transients are obtained by using “Padé approximants” (an accurate approximation procedure valid globally — not just perturbatively) for all amplitudes of concentration polarization and current densities. This is done for several mechanistic schemes under constant current conditions. We invert the non-linear current-potential relationship in the form (using the Lagrange or the Ramanujan method) of power series appropriate to the two extremes, namely near reversible and near irreversible. Transforming both into the Pad́e expressions, we construct the potential-time profile by retaining whichever is the more accurate of the two. The effectiveness of this method is demonstrated through illustrations which include couplings of homogeneous chemical reactions to the electron-transfer step.