A statistical analysis of audience sound absorption (A)

The absorption produced by the audience in concert halls is considered a random variable. Beranek's proposal [L. L. Beranek, Music, Acoustics and Architecture (Wiley, New York, 1962), p. 543] that audience absorption is proportional to the area they occupy and not to their number is subjected to a statistical hypothesis test. A two variable linear regression model of the absorption with audience area and residual area as regressor variables is postulated for concert halls without added absorptive materials. Since Beranek's contention amounts to the statement that audience absorption is independent of the seating density, the test of the hypothesis lies in categorizing halls by seating density and examining for significant differences among slopes of regression planes of the different categories. Such a test shows that Beranek's hypothesis can be accepted. It is also shown that the audience area is a better predictor of the absorption than the audience number. The absorption coefficients and their 95% confidence limits are given for the audience and residual areas. A critique of the regression model is presented.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Signal subspace approach in localization of sound source in shallow water

A new algorithm based on signal subspace approach is proposed for localizing a sound source in shallow water. In the first instance we assumed an ideal channel with plane parallel boundaries and known reflection properties. The sound source is assumed to emit a broadband stationary stochastic signal. The algorithm takes into account the spatial distribution of all images and reflection characteristics of the sea bottom. It is shown that both range and depth of a source can be measured accurately with the help of a vertical array of sensors. For good results the number of sensors should be greater than the number of significant images; however, localization is possible even with a smaller array but at the cost of higher side lobes. Next, we allowed the channel to be stochastically perturbed; this resulted in random phase errors in the reflection coefficients. The most singular effect of the phase errors is to introduce into the spectral matrix an extra term which may be looked upon as a signal generated coloured noise. It is shown through computer simulations that the signal peak height is reduced considerably as a consequence of random phase errors.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Inelastic response of beams under sinusoidal and random loads

A new analytical model has been suggested for the hysteretic behaviour of beams. The model can be directly used in a response analysis without bothering to locate the precise point where the unloading commences. The model can efficiently simulate several types of realistic softening hysteretic loops. This is demonstrated by computing the response of cantilever beams under sinusoidal and random loadings. Results are presented in the form of graphs for maximum deflection, bending moment and shear

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.

Processing and fiber content effects on the machinability of compression moulded random direction short GFRP composites

The random direction short Glass Fiber Reinforced Plastics (GFRP) have been prepared by two compression moulding processes, namely the Preform and Sheet Moulding Compound (SMC) processes. Cutting force analysis and surface characterization are conducted on the random direction short GFRPs with varying fiber contents (25 similar to 40%). Edge trimming experiments are preformed using carbide inserts with varing the depth of cut and cutting speed. Machining characteristics of the Preform and SMC processed random direction short GFRPs are evaluated in terms of cutting forces, surface quality, and tool wear. It is found that composite primary processing and fiber contents are major contributing factors influencing the cutting force magnitudes and surface textures. The SMC composites show better surface finish over the Preform composites due to less delamination and fiber pullouts. Moreover, matrix damage and fiber protrusions at the machined edge are reduced by increasing fiber content in the random direction short GFRP composites.

Light scattering in random media with wavelength-scale structures : astronomical and industrial applications

Light scattering, or scattering and absorption of electromagnetic waves, is an important tool in all remote-sensing observations. In astronomy, the light scattered or absorbed by a distant object can be the only source of information. In Solar-system studies, the light-scattering methods are employed when interpreting observations of atmosphereless bodies such as asteroids, atmospheres of planets, and cometary or interplanetary dust. Our Earth is constantly monitored from artificial satellites at different wavelengths. With remote sensing of Earth the light-scattering methods are not the only source of information: there is always the possibility to make in situ measurements. The satellite-based remote sensing is, however, superior in the sense of speed and coverage if only the scattered signal can be reliably interpreted. The optical properties of many industrial products play a key role in their quality. Especially for products such as paint and paper, the ability to obscure the background and to reflect light is of utmost importance. High-grade papers are evaluated based on their brightness, opacity, color, and gloss. In product development, there is a need for computer-based simulation methods that could predict the optical properties and, therefore, could be used in optimizing the quality while reducing the material costs. With paper, for instance, pilot experiments with an actual paper machine can be very time- and resource-consuming. The light-scattering methods presented in this thesis solve rigorously the interaction of light and material with wavelength-scale structures. These methods are computationally demanding, thus the speed and accuracy of the methods play a key role. Different implementations of the discrete-dipole approximation are compared in the thesis and the results provide practical guidelines in choosing a suitable code. In addition, a novel method is presented for the numerical computations of orientation-averaged light-scattering properties of a particle, and the method is compared against existing techniques. Simulation of light scattering for various targets and the possible problems arising from the finite size of the model target are discussed in the thesis. Scattering by single particles and small clusters is considered, as well as scattering in particulate media, and scattering in continuous media with porosity or surface roughness. Various techniques for modeling the scattering media are presented and the results are applied to optimizing the structure of paper. However, the same methods can be applied in light-scattering studies of Solar-system regoliths or cometary dust, or in any remote-sensing problem involving light scattering in random media with wavelength-scale structures.

Lypsylehmän energiataseen mallintaminen tuotoskauden alkuvaiheessa

Energiataseen mallinnus on osa KarjaKompassi-hankkeeseen liittyvää kehitystyötä. Tutkielman tavoitteena oli kehittää lypsylehmän energiatasetta etukäteen ennustavia ja tuotoskauden aikana saatavia tietoja hyödyntäviä matemaattisia malleja. Selittävinä muuttujina olivat dieetti-, rehu-, maitotuotos-, koelypsy-, elopaino- ja kuntoluokkatiedot. Tutkimuksen aineisto kerättiin 12 Suomessa tehdyistä 8 – 28 laktaatioviikon pituisesta ruokintakokeesta, jotka alkoivat heti poikimisen jälkeen. Mukana olleista 344 lypsylehmästä yksi neljäsosa oli friisiläis- ja loput ayshire-rotuisia. Vanhempien lehmien päätiedosto sisälsi 2647 havaintoa (koe * lehmä * laktaatioviikko) ja ensikoiden 1070. Aineisto käsiteltiin SAS-ohjelmiston Mixed-proseduuria käyttäen ja poikkeavat havainnot poistettiin Tukeyn menetelmällä. Korrelaatioanalyysillä tarkasteltiin energiataseen ja selittävien muuttujien välisiä yhteyksiä. Energiatase mallinnettiin regressioanalyysillä. Laktaatiopäivän vaikutusta energiataseeseen selitettiin viiden eri funktion avulla. Satunnaisena tekijänä mallissa oli lehmä kokeen sisällä. Mallin sopivuutta aineistoon tarkasteltiin jäännösvirheen, selitysasteen ja Bayesin informaatiokriteerin avulla. Parhaat mallit testattiin riippumattomassa aineistossa. Laktaatiopäivän vaikutusta energiataseeseen selitti hyvin Ali-Schaefferin funktio, jota käytettiin perusmallina. Kaikissa energiatasemalleissa vaihtelu kasvoi laktaatioviikosta 12. alkaen, kun havaintojen määrä väheni ja energiatase muuttui positiiviseksi. Ennen poikimista käytettävissä olevista muuttujista dieetin väkirehuosuus ja väkirehun syönti-indeksi paransivat selitysastetta ja pienensivät jäännösvirhettä. Ruokinnan onnistumista voidaan seurata maitotuotoksen, maidon rasvapitoisuuden ja rasva-valkuaissuhteen tai EKM:n sisältävillä malleilla. EKM:n vakiointi pienensi mallin jäännösvirhettä. Elopaino ja kuntoluokka olivat heikkoja selittäjiä. Malleja voidaan hyödyntää karjatason ruokinnan suunnittelussa ja seurannassa, mutta yksittäisen lehmän energiataseen ennustamiseen ne eivät sovellu.

Kinetics of sono-photooxidative degradation of poly(alkyl methacrylate)s

The mechano-chemical degradation of poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA) and poly(n-butyl methacrylate) (PBMA) using ultrasound (US), ultraviolet (UV) radiation and a photoinitiator (benzoin) has been investigated. The degradation of the polymers was monitored using the reduction in number average molecular weight (M-n) and polydispersity (PDI). A degradation mechanism that included the decomposition of the initiator, generation of polymer radicals by the hydrogen abstraction of initiator radicals, reversible chain transfer between stable polymer and polymer radicals was proposed. The mechanism assumed mid-point chain scission due to US and random scission due to UV radiation. A series of experiments with different initial M-n of the polymers were performed and the results indicated that, irrespective of the initial PDI, the PDI during the sono-photooxidative degradation evolved to a steady state value of 1.6 +/- 0.05 for all the polymers. This steady state evolution of PDI was successfully predicted by the continuous distribution kinetics model. The rate coefficients of polymer scission due to US and UV exhibited a linear increase and decrease with the size of the alkyl group of the poly(alkyl methacrylate)s, respectively. (C) 2010 Elsevier B.V. All rights reserved.

Temperature dependent free energy surface of polymer folding from equilibrium and quench studies

Langevin dynamics simulation studies have been employed to calculate the temperature dependent free energy surface and folding characteristics of a 500 monomer long linear alkane (polyethylene) chain with a realistic interaction potential. Both equilibrium and temperature quench simulation studies have been carried out. Using the shape anisotropy parameter (S) of the folded molecule as the order parameter, we find a weakly first order phase transition between the high-temperature molten globule and low-temperature rodlike crystalline states separated by a small barrier of the order of k(B)T. Near the melting temperature (580 K), we observe an intriguing intermittent fluctuation with pronounced ``1/f noise characteristics'' between these two states with large difference in shape and structure. We have also studied the possibilities of different pathways of folding to states much below the melting point. At 300 K starting from the all-trans linear configuration, the chain folds stepwise into a very regular fourfold crystallite with very high shape anisotropy. Whereas, when quenched from a high temperature (900 K) random coil regime, we identify a two step transition from the random coiled state to a molten globulelike state and, further, to a anisotropic rodlike state. The trajectory reveals an interesting coupling between the two order parameters, namely, radius of gyration (R-g) and the shape anisotropy parameter (S). The rodlike final state of the quench trajectory is characterized by lower shape anisotropy parameter and significantly larger number of gauche defects as compared to the final state obtained through equilibrium simulation starting from all-trans linear chain. The quench study shows indication of a nucleationlike pathway from the molten globule to the rodlike state involving an underlying rugged energy landscape. (C) 2010 American Institute of Physics. doi:10.1063/1.3509398]