On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Excitation and relaxation energies of trans-stilbene: Confined singlet, triplet, and charged bipolarons

The π-electronic excitations and excited-state geometries of trans-stilbene (tS) are found by combining exact solutions of the Pariser-Parr-Pople (PPP) model and semiempirical Parametric Method 3 (PM3) calculations. Comprehensive comparisons with tS spectra are obtained and related to the fluorescence and topological alternation of poly(paraphenylenevinylene) (PPV). The one-photon absorption and triplet of tS correspond, respectively, to singlet and triplet bipolarons confined to two phenyls, while the tS2- ground state is a confined charged bipolaron. Independent estimates of the relaxation energy between vertical and adiabatic excitation show the bipolaron binding energy to depend on both charge and spin, as expected for interacting π electrons in correlated or molecular states. Complete configuration interaction within the PPP model of tS accounts for the singlet-triplet gap, for the fine-structure constants and triplet-triplet spectra, for two-photon transitions and intensities, and for one-photon spectra and the radiative lifetime, although the relative position of nearly degenerate covalent and ionic singlets is not resolved. The planar PM3 geometry and low rotational barrier of tS agree with resolved rotational and vibrational spectra in molecular beams. PM3 excitation and relaxation energies for tS bipolarons are consistent with experiment and with PPP results. Instead of the exciton model, we interpret tS excitations in terms of states that are localized on each ring or extended over an alternating chain, as found exactly in Hückel theory, and find nearly degenerate transitions between extended and localized states in the singlet, triplet, and dianion manifolds. The large topological alternation of the extended system increases the ionicity and interchanges the order of the lowest one- and two-photon absorption of PPV relative to polyenes.

Processing of Ultrasonic Signal for Transducer Characterization and for Improving Signal-To-Noise Ratio

This paper describes the work related to characterisation of an ultrasonic transducer fabricated in the laboratory. The response of the medium to the ultrasonic wave was obtained by converting the time domain signal to frequency domain, using the FFT algorithm. Cross-correlation technique was adopted to increase the S/N ratio in the raw time domain signal and subsequently, to determine the ultrasonic velocity in the medium.

Interfacial shear rheology of highly confined glassy polymers

We present results on interfacial shear rheology measurements on Langmuir monolayers of two different polymers, poly(vinyl acetate) and poly(methyl methacrylate) as a function of surface concentration and temperature. While for the high glass transition poly(methyl methacrylate) polymer we find a systematic transition from a viscous dominated regime to an elastic dominated regime as surface concentration is increased, monolayers of the low glass transition polymer, poly(vinyl acetate), remain viscous even at very high surface concentrations. We further interpret the results in terms of the soft glassy rheology model of Sollich et al. P. Sollich, F. C. Lequeux, P. Hebraud and M. E. Cates, Phys. Rev. Lett., 1997, 78, 2020-2023] and provide evidence of possible reduction in glass transition temperatures in both poly(methyl methacrylate) and poly(vinyl acetate) monolayers due to finite size effects.

High On-Off Ratio Bilayer Graphene Complementary Field Effect Transistors

In this paper, we propose a novel S/D engineering for dual-gated Bilayer Graphene (BLG) Field Effect Transistor (FET) using doped semiconductors (with a bandgap) as source and drain to obtain unipolar complementary transistors. To simulate the device, a self-consistent Non-Equilibrium Green's Function (NEGF) solver has been developed and validated against published experimental data. Using the simulator, we predict an on-off ratio in excess of 10(4) and a subthreshold slope of similar to 110mV/decade with excellent scalability and current saturation, for a 20nm gate length unipolar BLG FET. However, the performance of the proposed device is found to be strongly dependent on the S/D series resistance effect. The obtained results show significant improvements over existing reports, marking an important step towards bilayer graphene logic devices.

Probing potential energy surfaces in confined systems: behavior of mean-square displacement in zeolites

Time evolution of mean-squared displacement based on molecular dynamics for a variety of adsorbate-zeolite systems is reported. Transition from ballistic to diffusive behavior is observed for all the systems. The transition times are found to be system dependent and show different types of dependence on temperature. Model calculations on a one-dimensional system are carried out which show that the characteristic length and transition times are dependent on the distance between the barriers, their heights, and temperature. In light of these findings, it is shown that it is possible to obtain valuable information about the average potential energy surface sampled under specific external conditions.

Analysis of a long thick orthotropic circular cylindrical shell panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.

Effect of Alkyl Chain Arrangement on Conformation and Dynamics in a Surfactant Intercalated Layered Double Hydroxide: Spectroscopic Measurements and MD Simulations

The anionic surfactant dodecyl sulfate (DDS) has been intercalated in an Mg-Al layered double hydroxide (LDH). Monolayer and bilayer arrangements of the alkyl chains of the intercalated surfactant can be engineered by tuning the Al/Mg ratio of the LDH. In both arrangements the anionic headgroup of the surfactant is tethered to the LDH sheets, and consequently translational mobility of the chains is absent. The degrees of freedom of the confined alkyl chains are restricted to changes in conformation. The effects of the arrangement of the intercalated surfactant chains on conformational order and dynamics have been,investigated by spectroscopic measurements and molecular dynamics simulations. Infrared, Raman, and C-13 NMR spectroscopies were used to investigate conformation of the alkyl chains in the monolayer and bilayer arrangements and variable contact time cross-polarization magic angle spinning (VCT CPMAS) NMR measurements to probe molecular motion. The alkyl chains in the monolayer arrangement of the intercalated DDS chains showed considerably greater conformational disorder and faster dynamics as compared to chains in the bilayer arrangement, in spite of the fact that the volume available per chain in the monolayer is smaller than that in the bilayer. Atomistic MD simulations of the two arrangements of the intercalated surfactant were carried out using an isothermal-isobaric ensemble. The simulations are able to reproduce the essential results of the experiment-greater conformational disorder and faster dynamics for the alkyl chains in the monolayer arrangement of the intercalated surfactant. The MD simulations show that these results are a consequence of the fact that the nature of conformational disorder in the two arrangements is different. In the monolayer arrangement the alkyl chains can sustain isolated gauche defects, whereas in the bilayer arrangement gauche conformers occur only as part of a kink a gauche(+) trans gauche(-) sequence.

Molecular-dynamics studies of systems of confined dumbbell molecules

We present the results of molecular-dynamics simulations of systems of dumbbell molecules confined by parallel molecular walls. We have carried out systematic studies of three cases: freezing, steady flows, and stick-slip friction. We find that the molecular orientational degrees of freedom cause the surface layers to deviate from a planar configuration. Nevertheless, steady flows, in a channel as narrow as 15 molecular sizes, display continuum behavior. A range of mechanisms in the dynamics of the freezing of a confined fluid is found, as a function of the wall-fluid interactions and the bond length of the dumbbell molecules. The simple order-disorder transition associated with stick-slip motion in the presence of a layer of monoatomic lubricant molecules is supplanted by more complex behavior due to rotational degrees of freedom of the diatomic molecules.

Discontinuous shear thickening in confined dilute carbon nanotube suspensions

A monotonic decrease in viscosity with increasing shear stress is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. Here we demonstrate a discontinuous shear-thickening transition on varying shear stress where the viscosity jumps sharply by four to six orders of magnitude in flocculated suspensions of multiwalled carbon nanotubes (MWNT) at very low weight fractions (approximately 0.5%). Rheooptical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear-thickening phenomena in confined geometries is pertinent for flow-controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues.

Inverse surface melting in confined clusters: Ar-13 in zeolite L

Monte Carlo and molecular dynamics simulations on an Ar-13 cluster in zeolite L have been carried out at a series of temperatures to understand the rigid-nonrigid transition corresponding to the solid-liquid transition exhibited by the free Ar-13 cluster. The icosahedral geometry of the free cluster is no longer preferred when the cluster is confined in the zeolite. The root-mean-squared pair distance fluctuation, delta, exhibits a sharp, well-defined rigid-nonrigid transition at 17 K as compared to 27 K for the free cluster. Multiple peaks in the distribution of short-time averages of the guest-host interaction energy indicate coexistence of two phases.; It is shown that this transition is associated with the inner atoms becoming mobile at 17 K even while the outer layer atoms, which are in close proximity to the zeolitic wall, continue to be comparatively immobile. This may be contrasted with the melting of large free clusters of 40 or more atoms which exhibit surface melting. Guest-host interactions seem to play a predominant role in determining the properties of confined clusters. We demonstrate that the volume of the cluster increases rather sharply at 17 and 27 K respectively for the confined and the free cluster. Power spectra suggest that the motion of the inner atoms is generally parallel to the atoms which form the cage wall.

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carte (CBMC) simulations of n-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties of n-butane and other longer n-alkanes such as n-hexane and n-heptane when they are confined in different zeolites are presented. The changes in the conformational properties of n-butane and n-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of the gauche population as compared to the pure unconfined fluid.

California bearing ratio behavior of cement-stabilized fly ash-soil mixes

Thermal power stations using pulverized coal as fuel generate large quantities of fly ash as a byproduct, which has created environmental and disposal problems. Using fly ash for gainful applications will solve these problems. Among the various possible uses for fly ash, the most massive and effective utilization is in geotechnical engineering applications like backfill material, construction of embankments, as a subbase material, etc. A proper understanding of fly ash-soil mixes is likely to provide viable solutions for its large-scale utilization. Earlier studies initiated in the laboratory have resulted in a good understanding of the California Bearing Ratio (CBR) behavior of fly ash-soil mixes. Subsequently, in order to increase the CBR value, cement has been tried as an additive to fly ash-soil mixes. This paper reports the results.