Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part II. Computed results and experimental corroboration thereof

Time-domain-finite-wave analysis of engine exhaust systems is usually carried out by means of the method of characteristics. The theory and the computational details of the stationary-frame method have been worked out in the accompanying paper (part I). In this paper (part II), typical computed results are given and discussed. A setup designed for experimental corroboration is described. The results obtained from the simulation are found to be in good agreement with experimental observations.

Theoretical and Computational Analysis of Static and Dynamic Anomalies in Water-DMSO Binary Mixture at Low DMSO Concentrations

Experiments have repeatedly observed both thermodynamic and dynamic anomalies in aqueous binary mixtures, surprisingly at low solute concentration. Examples of such binary mixtures include water-DMSO, water-ethanol, water-tertiary butyl alcohol (TBA), and water-dioxane, to name a few. The anomalies have often been attributed to the onset of a structural transition, whose nature, however, has been left rather unclear. Here we study the origin of such anomalies using large scale computer simulations and theoretical analysis in water-DMSO binary mixture. At very low DMSO concentration (below 10%), small aggregates of DMSO are solvated by water through the formation of DMSO-(H2O)(2) moieties. As the concentration is increased beyond 10-12% of DMSO, spanning clusters comprising the same moieties appear in the system. Those clusters are formed and stabilized not only through H-bonding but also through the association of CH3 groups of DMSO. We attribute the experimentally observed anomalies to a continuum percolation-like transition at DMSO concentration X-DMSO approximate to 12-15%. The largest cluster size of CH3-CH3 aggregation clearly indicates the formation of such percolating clusters. As a result, a significant slowing down is observed in the decay of associated rotational auto time correlation functions (of the S = O bond vector of DMSO and O-H bond vector of water). Markedly unusual behavior in the mean square fluctuation of total dipole moment again suggests a structural transition around the same concentration range. Furthermore, we map our findings to an interacting lattice model which substantiates the continuum percolation model as the reason for low concentration anomalies in binary mixtures where the solutes involved have both hydrophilic and hydrophobic moieties.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

First-order hyperpolarizabilities and pKa of weak organic acids in protic solvents are lineraly related

Second-order nonlinearities (beta) of five weak organic acids in protic solvents have been measured by the double-quantum Rayleigh scattering (DRS) technique. beta is found to bear a linear relationship to the pK(a) of these compounds in those solvents. A direct implication of this observation is that the DRS technique can be used to determine the pK(a) of weak organic acids in any solvent.

Dissociation constants of weak organic acids in protic solvents obtained from their first hyperpolarizabilities in solution

The first hyperpolarizabilities (beta) of some weak aromatic organic acids have been measured in protic solvents by the hyper-Rayleigh scattering (HRS) technique at low concentrations. The measured hyperpolarizability (beta(m)) varies between the two extreme limits: the hyperpolarizability of the acid form (beta(HA)) at the lower side and that of the basic form (beta(A-)) at the higher side. The degree of dissociation (alpha) of the acid in a solvent is related to the measured hyperpolarizability, beta(m), by the following relationship: beta(m)(2)=(1-alpha)beta(HA)(2)+alpha beta(A-)(2). The calculated beta's including solvent effects in terms of an Onsager field do not reproduce the experimentally measured hyperpolarizabilities. Other solvent-induced effects like hydrogen bonding and van der Waals interactions seem to influence the first hyperpolarizability and, thus, indirectly the extent of dissociation of these weak acids in these protic solvents.

Irreversibility line and the hierarchy of weak links in Bi2Sr2CaCu2O8+?

The irreversibility line for H?c in a single crystal specimen of Bi2Sr2CaCu2O8+? (Bi2212) has been determined via vanishing of hysteresis in isothermal dc magnetization measurements. The hysteresis loops (H?c) in Bi2212 appear to show signatures of two-component magnetic response in several temperature regions where the temperature dependence of irreversibility field charges sharply. It is proposed that the observed behavior may be a consequence of existence of weak links of varying strength in Bi2212

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Dehydrophenylalanine zippers: strong helix-helix clamping through a network of weak interactions

A decapeptide Boc-L-Ala-(DeltaPhe)(4)-L-Ala-(DeltaPhe)(3)-Gly-OMe (Peptide I) was synthesized to study the preferred screw sense of consecutive alpha,beta-dehydrophenylalanine (DeltaPhe) residues. Crystallographic and CD studies suggest that, despite the presence of two L-Ala residues in the sequence, the decapeptide does not have a preferred screw sense. The peptide crystallizes with two conformers per asymmetric unit, one of them a slightly distorted right-handed 3(10)-helix (X) and the other a left-handed 3(10)-helix (Y) with X and Y being antiparallel to each other. An unanticipated and interesting observation is that in the solid state, the two shape-complement molecules self-assemble and interact with an extensive network of C-H...O hydrogen bonds and pi-pi interactions, directed laterally to the helix axis with amazing regularity. Here, we present an atomic resolution picture of the weak interaction mediated mutual recognition of two secondary structural elements and its possible implication in understanding the specific folding of the hydrophobic core of globular proteins and exploitation in future work on de novo design.

Dynamic shear modulus as affected by displacement amplitude

The realistic estimation of the dynamic characteristics for a known set of loading conditions continues to be difficult despite many contributions in the past. The design of a machine foundation is generally made on the basis of limiting amplitude or resonant frequency. These parameters are in turn dependent on the dynamic characteristics of soil viz., the shear modulus/stiffness and damping. The work reported herein is an attempt to relate statistically the shear modulus of a soil to its resonant amplitude under a known set of static and dynamic loading conditions as well as wide ranging soil conditions. The two parameters have been statistically related with a good correlation coefficient and low standard error of estimate.

On finding a set of healthy individuals from a large population

In this paper, we explore fundamental limits on the number of tests required to identify a given number of ``healthy'' items from a large population containing a small number of ``defective'' items, in a nonadaptive group testing framework. Specifically, we derive mutual information-based upper bounds on the number of tests required to identify the required number of healthy items. Our results show that an impressive reduction in the number of tests is achievable compared to the conventional approach of using classical group testing to first identify the defective items and then pick the required number of healthy items from the complement set. For example, to identify L healthy items out of a population of N items containing K defective items, when the tests are reliable, our results show that O(K(L - 1)/(N - K)) measurements are sufficient. In contrast, the conventional approach requires O(K log(N/K)) measurements. We derive our results in a general sparse signal setup, and hence, they are applicable to other sparse signal-based applications such as compressive sensing also.