Structural Transformations, Composition Anomalies and a Dramatic Collapse of Linear Polymer Chains in Dilute Ethanol-Water Mixtures

Water-ethanol mixtures exhibit many interesting anomalies, such as negative excess partial molar volume of ethanol, excess sound absorption coefficient at low concentrations, and positive deviation from Raoult's law for vapor pressure, to mention a few. These anomalies have been attributed to different, often contradictory origins, but a quantitative understanding is still lacking. We show by computer simulation and theoretical analyses that these anomalies arise from the sudden emergence of a bicontinuous phase that occurs at a relatively low ethanol concentration of x(eth) approximate to 0.06-0.10 (that amounts to a volume fraction of 0.17-0.26, which is a significant range!). The bicontinuous phase is formed by aggregation of ethanol molecules, resulting in a weak phase transition whose nature is elucidated. We find that the microheterogeneous structure of the mixture gives rise to a pronounced nonmonotonic composition dependence of local compressibility and nonmonotonic dependence in the peak value of the radial distribution function of ethyl groups. A multidimensional free energy surface of pair association is shown to provide a molecular explanation of the known negative excess partial volume of ethanol in terms of parallel orientation and hence better packing of the ethyl groups in the mixture due to hydrophobic interactions. The energy distribution of the ethanol molecules indicates additional energy decay channels that explain the excess sound attenuation coefficient in aqueous alcohol mixtures. We studied the dependence of the solvation of a linear polymer chain on the composition of the water-ethanol solvent. We find that there is a sudden collapse of the polymer at x(eth) approximate to 0.05-a phenomenon which we attribute to the formation of the microheterogeneous structures in the binary mixture at low ethanol concentrations. Together with recent single molecule pulling experiments, these results provide new insight into the behavior of polymer chain and foreign solutes, such as enzymes, in aqueous binary mixtures.

Flowfield Analysis of Linear Plug Nozzle

Full-length and truncated linear plug nozzle flowfields have been analyzed, using both experimental and computational tools, for pressure ratios ranging from 5 to 72, which include the transition of an open base wake to a closed base wake. A good agreement has been found between computational and experimental results on the plug surface. Considering the deficiencies of the computational tools in predicting base flows associated with truncated plug nozzles, an engineering model to predict the wake structure transition in such flows is proposed. The utility of this model in conjunction with empirical tools for the closed-wake base pressure prediction is established. The model is validated against the experimental results available in open literature.

Effects of initial height on the steady-state persistence probability of linear growth models

The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.

Flow Investigation of Linear Cluster Plug Nozzle

Computational and experimental tools have been used to understand the linear cluster plug nozzle flowfield for a range of pressure ratios. The experimental cluster configuration is arrived at from a linear plug nozzle by introducing splitter plates in the primary nozzle, and computational analysis of corresponding geometry is also carried out. The flow development on the plug surface has been analyzed for two different cluster module spacings. The interactions between the cluster module jets is a complex one with a three-dimensional shock structure because of the differential end condition the shock experiences on the plug wall and freejet boundary. A prominent streamwise vorticity resulting from curvature of the shock is also seen along the length of the plug downstream of the module junctions. The out-of-phase wave interactions occurring along the module centerline and the splitter plate centerline, resulting in a wavy surface-limiting streamline pattern, particularly at lower pressure ratios, is explained.

Transient response of coupled non-linear non-conservative systems

This paper deals with an approximate method of analysis of non-linear, non-conservative systems of two degrees of freedom. The approximate equations for amplitude and phase are obtained by a generalized averaging technique based on the ultraspherical polynomial approximation. The method is illustrated by an example of a spring-mass-damper system.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Decentralized linear quadratic power system stabilizers for multi-machine power systems

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead-lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not available in most of the power plants. Full state feedback controllers require feedback of other machine states in a multi-machine power system and necessitate block diagonal structure constraints for decentralized implementation. This paper investigates the design of Linear Quadratic Power System Stabilizers using a recently proposed modified Heffron-Phillip's model. This model is derived by taking the secondary bus voltage of the step-up transformer as reference instead of the infinite bus. The state variables of this model can be obtained by local measurements. This model allows a coordinated linear quadratic control design in multi machine systems. The performance of the proposed controller has been evaluated on two widely used multi-machine power systems, 4 generator 10 bus and 10 generator 39 bus systems. It has been observed that the performance of the proposed controller is superior to that of the conventional Power System Stabilizers (PSS) over a wide range of operating and system conditions.

Observability for a Class of Nonlinear Systems

t - N m and sufficient computable conditions are obtained for the obsemabii of systems with linear state equations and polgwmIal outputs. Based on these, initial state reconstmctors are also described.

Dissipativeness and Stability of a Class of Distributed Parameter Systems

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

BER-optimized linear parallel interference cancellers for multicarrier DS-CDMA systems

In this paper, we consider the design and bit-error performance analysis of linear parallel interference cancellers (LPIC) for multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) systems. We propose an LPIC scheme where we estimate and cancel the multiple access interference (MAT) based on the soft decision outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation. In order to choose these weights optimally, we derive exact closed-form expressions for the bit-error rate (BER) at the output of different stages of the LPIC, which we minimize to obtain the optimum weights for the different stages. In addition, using an alternate approach involving the characteristic function of the decision variable, we derive BER expressions for the weighted LPIC scheme, matched filter (MF) detector, decorrelating detector, and minimum mean square error (MMSE) detector for the considered multicarrier DS-CDMA system. We show that the proposed BER-optimized weighted LPIC scheme performs better than the MF detector and the conventional LPIC scheme (where the weights are taken to be unity), and close to the decorrelating and MMSE detectors.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.