An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

High frequency millimetre wave absorbers derived from polymeric nanocomposites

The world has dominated by automation, wireless communication and various electronic equipments, which has led to the most undesirable offshoots like electromagnetic (EM) pollution. The rationale is environmental concern and the necessity to develop EM absorbing materials. This paper reviews the state of the art of designing polymer based nanocomposites containing nanoscopic particles with high electrical conductivity and complex microwave properties for enhanced EM attenuation. Given the brevity of this review article, herein we have summarized the high frequency millimetre wave absorbing properties of polymer nanocomposites consisting of various nanoparticles that either reflect or absorb microwave radiation like electrically conducting carbon nanotubes (CNTs) and graphene nanosheets (GNs), high dielectric constant ceramic nanoparticles that show relaxation loss in the microwave frequency and magnetic metal and ferrite nanoparticles that absorb microwave radiation through natural resonance, eddy current and hysteresis losses. Furthermore, we have stressed the necessity and impact of hybrid nanoparticles consisting of magnetic and dielectric nanoparticles along with conducting inclusions like CNT and GNs in this review. Electromagnetic interference (EMI) theory and necessary criterion for attenuation has been briefly discussed. The emphasis is made on various mechanisms towards EM attenuation controlled by these nanoparticles. Various structures developed using polymer nanocomposites like bulk, foam and layered structures and their effect on EM attenuation has been elaborately discussed. In addition, various covalent/non-covalent modifications on nanoparticles have been juxtaposed in context to EM attenuation. In addition, we have highlighted important facets and direction for enhancing the microwave attenuation. (C) 2016 Elsevier Ltd. All rights reserved.

EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Three-dimensional warping in strip-based composite four-bar mechanisms

This work intends to demonstrate the effect of geometrically non-linear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting the three-dimensional warping of the cross-section. The only restriction in the present analysis is that the strains within each elastic body remain small (i.e., this work does not deal with materials exhibiting non-linear constitutive laws at the 3-D level). Here, all component bars of the mechanism are made of fiber-reinforced laminates. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction, results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis, the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here. The representative cross-sections of all component bars are analyzed using two different approaches: (1) Numerical Model and (2) Analytical Model. Four-bar mechanisms are analyzed using the above two approaches for Omega = 20 rad/s and Omega = pi rad/s and observed the same behavior in both cases. The noticeable snap-shots of the deformation shapes of the mechanism about 1000 frames are also reported using commercial software (I-DEAS + NASTRAN + ADAMS). The maximum out-of-plane warping of the cross-section is observed at the mid-span of bar-1, bar-2 and bar-3 are 1.5 mm, 250 mm and 1.0 mm, respectively, for t = 0:5 s. (C) 2015 Elsevier Ltd. All rights reserved.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

Four- and five-component molecular solids: crystal engineering strategies based on structural inequivalence

A synthetic strategy is described for the co-crystallization of four-and five-component molecular crystals, based on the fact that if any particular chemical constituent of a lower cocrystal is found in two different structural environments, these differences may be exploited to increase the number of components in the solid. 2-Methylresorcinol and tetramethylpyrazine are basic template molecules that allow for further supramolecular homologation. Ten stoichiometric quaternary cocrystals and one quintinary cocrystal with some solid solution character are reported. Cocrystals that do not lend themselves to such homologation are termed synthetic dead ends.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.

Electro-Osmotic Flow and Mixing in Heterogeneous Microchannels

Analytical and numerical studies of secondary electro-osmotic flow EOF and its mixing in microchannels with heterogeneous zeta potentials are carried out in the present work. The secondary EOFs are analyzed by solving the Stokes equation with heterogeneous slip velocity boundary conditions. The analytical results obtained are compared with the direct numerical simulation of the Navier-Stokes equations. The secondary EOFs could transport scalar in larger areas and increase the scalar gradients, which significantly improve the mixing rate of scalars. It is shown that the heterogeneous zeta potentials could generate complex flow patterns and be used to enhance scalar mixing.

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF4 premixed in the test gas. The final product C2F4 is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C2F4 is correlated to the temperature of the reflected shock wave with the initial pressure P-1 and test time tau as parameters in the temperature range 3 300 K < T < 5 600 K, pressure range 5 kPa < P1 <12 kPa and tau similar or equal to 0.4 ms.

Wave Propagation Analysis in a Pressure-Wave-Refrigerator

Pressure wave refrigerators (PWR) refrigerate the gas through periodical expansion waves. Due to its simple structure and robustness, PWR may have many potential applications if the efficiency becomes competitive with existing alternative devices. In order to improve the efficiency, the characteristics of wave propagation in a PWR are studied by experiment, numerical simulation and theoretical analysis. Based on the experimental results and numerical simulation, a simplified model is suggested, which includes the assumptions of flux-equilibrium and conservation of the free energy. This allows the independent analysis of the operation parameters and design specifics. Furthermore, the optimum operation condition can be deduced. Some considerations to improve the PWR efficiency are also given.

Capillary Effect on Vertically Excited Surface Wave in Circular Cylindrical Vessel

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension.

Interferometric Measurement of Density in Nonstationary Shock Wave Reflection Flow and Comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.

Mixing process in estuaries

A theoretical expression for vertical profile-of horizontal velocity in terms of its depth-average is derived based on oscillatory boundary layer theory and estuarine flow characteristics. The derived theoretical profile is then incorporated into a vertical quasi-two-dimensional model, which is proved advantageous in more physical implications and less CPU time demand. To validate the proposed model, the calculated results are compared to the field data in the Yangtze River Estuary, exhibiting good agreement with observations. The proposed quasi-two-dimensional vertical model is used to study mixing process, especially dependence of salinity distribution and salt front strength on runoff and tides in estuaries.

The cellular structure of a two-dimensional H2/O2/Ar detonation wave

In this paper, the cellular structure of a two-dimensional detonation wave in a low pressure H2/O2/Ar mixture calculated with a detailed chemical reaction model, high order scheme and high resolution grids is investigated. The regular cellular structure is produced about 1 ms after introducing perturbations in the reaction zone of a steady one-dimensional detonation wave. It is found from the present resolution study that the discrepancies concerning the structure type arising from the coarser grid employed can be resolved using a sufficiently fine grid size of 0.05 mm and below and shows a double-Mach-like strong-type configuration. During the structure evolution process, the structure configuration does not change much in the periods before and after the triple point collision. Through the triple point collision, three regular collision processes are observed and are followed by a quick change to the double-Mach-like configuration. The simulated structure tracks show that there are three different tracks associated with different triple points or the kink on the transverse wave. Comparisons with previous work and experiments indicate the presence of a strong structure for an ordinary detonation.