On the achievable rates of sources having a group alphabet in a distributed source coding setting

We consider the problem of compression via homomorphic encoding of a source having a group alphabet. This is motivated by the problem of distributed function computation, where it is known that if one is only interested in computing a function of several sources, then one can at times improve upon the compression rate required by the Slepian-Wolf bound. The functions of interest are those which could be represented by the binary operation in the group. We first consider the case when the source alphabet is the cyclic Abelian group, Zpr. In this scenario, we show that the set of achievable rates provided by Krithivasan and Pradhan [1], is indeed the best possible. In addition to that, we provide a simpler proof of their achievability result. In the case of a general Abelian group, an improved achievable rate region is presented than what was obtained by Krithivasan and Pradhan. We then consider the case when the source alphabet is a non-Abelian group. We show that if all the source symbols have non-zero probability and the center of the group is trivial, then it is impossible to compress such a source if one employs a homomorphic encoder. Finally, we present certain non-homomorphic encoders, which also are suitable in the context of function computation over non-Abelian group sources and provide rate regions achieved by these encoders.

Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Nonlocal continuum mechanics based ultrasonic flexural wave dispersion characteristics of a monolayer graphene embedded in polymer matrix

Wave propagation in graphene sheet embedded in elastic medium (polymer matrix) has been a topic of great interest in nanomechanics of graphene sheets, where the equivalent continuum models are widely used. In this manuscript, we examined this issue by incorporating the nonlocal theory into the classical plate model. The influence of the nonlocal scale effects has been investigated in detail. The results are qualitatively different from those obtained based on the local/classical plate theory and thus, are important for the development of monolayer graphene-based nanodevices. In the present work, the graphene sheet is modeled as an isotropic plate of one-atom thick. The chemical bonds are assumed to be formed between the graphene sheet and the elastic medium. The polymer matrix is described by a Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation of the surrounding elastic medium. When the shear effects are neglected, the model reduces to Winkler foundation model. The normal pressure or Winkler elastic foundation parameter is approximated as a series of closely spaced, mutually independent, vertical linear elastic springs where the foundation modulus is assumed equivalent to stiffness of the springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of flexural wave propagation model is also derived and the results of the wave dispersion analysis are shown for both local and nonlocal elasticity calculations. From this analysis we show that the elastic matrix highly affects the flexural wave mode and it rapidly increases the frequency band gap of flexural mode. The flexural wavenumbers obtained from nonlocal elasticity calculations are higher than the local elasticity calculations. The corresponding wave group speeds are smaller in nonlocal calculation as compared to local elasticity calculation. The effect of y-directional wavenumber (eta(q)) on the spectrum and dispersion relations of the graphene embedded in polymer matrix is also observed. We also show that the cut-off frequencies of flexural wave mode depends not only on the y-direction wavenumber but also on nonlocal scaling parameter (e(0)a). The effect of eta(q) and e(0)a on the cut-off frequency variation is also captured for the cases of with and without elastic matrix effect. For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(0)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this article. (c) 2012 Elsevier Ltd. All rights reserved.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Effect of spatial dispersion of the dielectric on the binding energy of D- ion in Si and Ge

Using a multivalley effective mass theory, we obtain the binding energy of a D- ion in Si and Ge taking into account the spatial variation of the host dielectric function. We find that on comparison with experimental results the effect of spatial dispersion is important in the estimation of binding energy for the D- formed by As in Si and Ge. The effect is less significant for the case of D- formed by P and Sb donors.

Numerical prediction of load-displacement behaviors of adhesively bonded joints at different extension rates and temperatures

The present work focuses on simulation of nonlinear mechanical behaviors of adhesively bonded DLS (double lap shear) joints for variable extension rates and temperatures using the implicit ABAQUS solver. Load-displacement curves of DLS joints at nine combinations of extension rates and environmental temperatures are initially obtained by conducting tensile tests in a UTM. The joint specimens are made from dual phase (DP) steel coupons bonded with a rubber-toughened adhesive. It is shown that the shell-solid model of a DLS joint, in which substrates are modeled with shell elements and adhesive with solid elements, can effectively predict the mechanical behavior of the joint. Exponent Drucker-Prager or Von Mises yield criterion together with nonlinear isotropic hardening is used for the simulation of DLS joint tests. It has been found that at a low temperature (-20 degrees C), both Von Mises and exponent Drucker-Prager criteria give close prediction of experimental load-extension curves. However. at a high temperature (82 degrees C), Von Mises condition tends to yield a perceptibly softer joint behavior, while the corresponding response obtained using exponent Drucker-Prager criterion is much closer to the experimental load-displacement curve.

High Oxygen Storage Capacity and High Rates of CO Oxidation and NO Reduction Catalytic Properties of Ce1-xSnxO2 and Ce0.78Sn0.2Pd0.02O2-delta

Ce1-xSnxO2 (x = 0.1-0.5) solid solution and its Pd substituted analogue have been prepared by a single step solution combustion method using tin oxalate precursor. The compounds were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM), and H-2/temperature programmed redution (TPR) studies. The cubic fluorite structure remained intact up to 50% of Sri substitution in CeO2, and the compounds were stable up to 700 C. Oxygen storage capacity of Ce1-xSnxO2 was found to be much higher than that of Ce1-xZrxO2 due to accessible Ce4+/Ce3+ and Sn4+/Sn2+ redox couples at temperatures between 200 and 400 C. Pd 21 ions in Ce0.78Sn0.2Pd0.02O2-delta are highly ionic, and the lattice oxygen of this catalyst is highly labile, leading to low temperature CO to CO2 conversion. The rate of CO oxidation was 2 mu mol g(-1) s(-1) at 50 degrees C. NO reduction by CO with 70% N-2 selectivity was observed at similar to 200 degrees C and 100% N-2 selectivity below 260 degrees C with 1000-5000 ppm NO. Thus, Pd2+ ion substituted Ce1-xSnxO2 is a superior catalyst compared to Pd2+ ions in CeO2, Ce1-xZrxO2, and Ce1-xTixO2 for low temperature exhaust applications due to the involvement of the Sn2+/Sn4+ redox couple along with Pd2+/Pd-0 and Ce4+/Ce3+ couples.

On the dielectric dispersion and absorption in nanosized manganese zinc mixed ferrites

The temperature and frequency dependence of dielectric permittivity and dielectric loss of nanosized Mn1-xZnxFe2O4 (for x = 0, 0.2, 0.4, 0.6, 0.8, 1) were investigated. The impact of zinc substitution on the dielectric properties of the mixed ferrite is elucidated. Strong dielectric dispersion and broad relaxation were exhibited by Mn1-xZnxFe2O4. The variation of dielectric relaxation time with temperature suggests the involvement of multiple relaxation processes. Cole-Cole plots were employed as an effective tool for studying the observed phenomenon. The activation energies were calculated from relaxation peaks and Cole-Cole plots and found to be consistent with each other and indicative of a polaron conduction.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

Fatigue crack growth rates and fracture toughness in electroslag refined En 52 steel

En 52 steel has been electroslag refined and the resultant effects of refining on its mechanical properties have been assessed. It was found that refining caused a decrease in fatigue crack growth rates and increases in fatigue strength, fracture toughness, Charpy fracture energy and tensile ductility. Fatigue crack growth rates in region I and in region III were found to be considerably lower in the electroslag refined steel: they were unaffected in region II. The fracture toughness values for the electroslag refined steel are nearly twice those estimated for the unrefined steel. Measurements on heat-treated samples have shown that the electroslag refined steel has a better response to heat-treatment. The improvement in the mechanical properties is explained in terms of the removal of nonmetallic inclusions and a reduction in the sulphur content of the steel.

Effect of electroslag refining on the fracture toughness and fatigue crack propagation rates in heat treated AISI 4340 steel

The AISI 4340 steel has been electroslag refined and the improvement in mechanical properties has been assessed. Electroslag refining (ESR) has improved tensile ductility, plane strain fracture toughness, Charpy fracture energy, and has decreased fatigue crack growth rates. The KIC values for the ESR steel are nearly twice those estimated in the unrefined steel and higher than those obtained in the vacuum arc remelted steel. Fatigue crack growth rates in region I and in region III are found to be decreased considerably in the ESR steel, while they are unaffected in region II. Measurements on heat treated samples have shown that the ESR steel has a better response to heat treatment. Both the suggested heat treatments namely austenitizing at 1140–1470 K as well as the conventional heat treatment of austenitizing at 1140 K have been followed. The improvement in the mechanical properties of ESR steel has been explained on the basis of removal of nonmetallic inclusions and reduction in sulfur content in the steel.

The Optical Rotatory Dispersion of Terpenes

General Properties of these Ethers.-They are colorless oils, extremely diffusible, heavier than water, insoluble in water, but soluble in fat solvents. They possess a pungent odor and undergo gradual decomposition On standing as shown by discoloration. Physiological testsI0 gave evidence that these substances are hypnotics and toxic.

Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.

Noble Metal Ionic Catalysts

Because of growing environmental concerns and increasingly stringent regulations governing auto emissions, new more efficient exhaust catalysts are needed to reduce the amount of pollutants released from internal combustion engines. To accomplish this goal, the major pollutants in exhaust-CO, NOx, and unburned hydrocarbons-need to be fully converted to CO2, N-2, and H2O. Most exhaust catalysts contain nanocrystalline noble metals (Pt, Pd, Rh) dispersed on oxide supports such as Al2O3 or SiO2 promoted by CeO2. However, in conventional catalysts, only the surface atoms of the noble metal particles serve as adsorption sites, and even in 4-6 nm metal particles, only 1/4 to 1/5 of the total noble metal atoms are utilized for catalytic conversion. The complete dispersion of noble metals can be achieved only as ions within an oxide support. In this Account, we describe a novel solution to this dispersion problem: a new solution combustion method for synthesizing dispersed noble metal ionic catalysts. We have synthesized nanocrystalline, single-phase Ce1-xMxO2-delta and Ce1-x-yTiyMxO2-delta (M = Pt, Pd, Rh; x = 0,01-0.02, delta approximate to x, y = 0.15-0.25) oxides in fluorite structure, In these oxide catalysts, pt(2+), Pd2+, or Rh3+ ions are substituted only to the extent of 1-2% of Ce4+ ion. Lower-valent noble metal ion substitution in CeO2 creates oxygen vacancies. Reducing molecules (CO, H-2, NH3) are adsorbed onto electron-deficient noble metal ions, while oxidizing (02, NO) molecules are absorbed onto electron-rich oxide ion vacancy sites. The rates of CO and hydrocarbon oxidation and NOx reduction (with >80% N-2 selectivity) are 15-30 times higher in the presence of these ionic catalysts than when the same amount of noble metal loaded on an oxide support is used. Catalysts with palladium ion dispersed in CeO2 or Ce1-xTixO2 were far superior to Pt or Rh ionic catalysts. Therefore, we have demonstrated that the more expensive Pt and Rh metals are not necessary in exhaust catalysts. We have also grown these nanocrystalline ionic catalysts on ceramic cordierite and have reproduced the results we observed in powder material on the honeycomb catalytic converter. Oxygen in a CeO2 lattice is activated by the substitution of Ti ion, as well as noble metal ions. Because this substitution creates longer Ti-O and M-O bonds relative to the average Ce-O bond within the lattice, the materials facilitate high oxygen storage and release. The interaction among M-0/Mn+, Ce4+/Ce3+, and Ti4+/Ti3+ redox couples leads to the promoting action of CeO2, activation of lattice oxygen and high oxygen storage capacity, metal support interaction, and high rates of catalytic activity in exhaust catalysis.