Modeling continuous aqueous two-phase systems for control purposes

A mathematical model was proposed to allow the analysis of steady-state and transient behaviors of single-stage continuous aqueous two-phase systems. Since the complete system of simultaneous equations contains more equations than unknown variables, a program based on the method of least squares was developed to solve the problem. The methodology was tested using a system composed of thaumatin, sodium chloride, and a contaminant protein. A poly(ethylene-glycol)/phosphate salt/water system was selected to isolate the thaumatin. For the steady-state and transient operations, a constrained optimization procedure--from the Matlab Optimization Toolbox (MathWork, Inc.)--was implemented after recasting the system of equations as a minimization problem. Euler's method was used in the transient case to discretize the differential equations. The steady-state concentrations agreed with published data. An input-output model based on a 4% step change decrease in the inlet stream flow rate showed that output variables such as concentrations of sodium chloride and phosphate salt settled to their final values in different time periods. The proposed analysis may be helpful in the dynamic control of large-scale commercial extractor units using advanced control schemes.     

Comparison of Simple Particle-Radiation Coupling Models Applied on a Plasma Black Process

The effect of soot formation on the radiative heat transfer inside a plasma reactor for carbon black synthesis has been modelled. For this purpose, three methods to quantify the soot volume fraction have been tested and evaluated: (1) Assuming local thermodynamic equilibrium, (2) assuming instantaneous conversion of the hydrocarbon and (3) using a single-step soot model. These approaches have been studied using a two-dimensional axis-symmetric and a three-dimensional steady computational fluid dynamics (CFD) model based on the commercial software FLUENT (v.5.6). The CFD model includes turbulence effects (by standard k– model), an electric arc sub-model to describe the time-average and spatial-average Lorentz forces and ohmic heating generated by the three-phase power-supply, methane transport in a nitrogen plasma and radiation calculations. The calculations show that for the simulated operating conditions the resulting temperature distributions obtained are very similar with the three methods in spite of major differences in the treatment of particle formation in the different methods.     

Isothermal titration calorimetry of supramolecular polymers

A method to characterize the self-association of supramolecular polymers by isothermal titration calorimetry (ITC) has been designed. Association constants in the range 10(4)-10(6) dm(3) mol(-1) have been successfully determined from the heat exchange occurring when a supramolecular polymer solution is injected into a calorimetric cell containing pure solvent. Very good agreement with literature values has been obtained. Compared to other techniques (such as NMR or Fourier transform infrared spectroscopy), the use of ITC presents several advantages: (i) the enthalpy of association is obtained together with the association constant from the same experiment, (ii) the measurements can be performed in almost any solvent, and (iii) systems with higher association constants can be characterized.     

Reversible phase transitions in emulsified nanostructured lipid systems

Aqueous submicron-sized dispersions of the binary monolinolein/water system, which are stabilized by means of a polymer, internally possess a distinct nanostructure. Taking this as our starting point, we were able to demonstrate for the first time that the internal structure of the dispersed particles can be tuned by temperature in a reversible way. Upon increasing the temperature, the internal structure undergoes a transition from cubic via hexagonal to fluid isotropic, the so-called L2 phase, and vice versa. Intriguingly, in addition to the structural changes in topology, the particles expel (take up) water to (from) the aqueous continuous phase when increasing (decreasing) the temperature in a reversible way. At each temperature, the internal structure of the dispersed particles corresponds very well to the structure observed in nondispersed binary monolinolein with excess water. This agreement is independent of any thermal history (including phase transitions), which proves that the structures in the dispersed particles actually are in thermodynamic equilibrium with the surrounding water phase.     

Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods

Summary. The so-called multi-revolution methods were introduced in celestial mechanics as an efficient tool for the long-term numerical integration of nearly periodic orbits of artificial satellites around the Earth. A multi-revolution method is an algorithm that approximates the map _T^N of N near-periods T in terms of the one near-period map _T evaluated at few s << N selected points. More generally, multi-revolution methods aim at approximating the composition ^N of a near identity map . In this paper we give a general presentation and analysis of multi-revolution Runge-Kutta (MRRK) methods similar to the one developed by Butcher for standard Runge-Kutta methods applied to ordinary differential equations. Order conditions, simplifying assumptions, and order estimates of MRRK methods are given. MRRK methods preserving constant Poisson/symplectic structures and reversibility properties are characterized. The construction of high order MRRK methods is described based on some families of orthogonal polynomials.Mathematics Subject Classification (1991): 65L05, 65L06This material is based upon work supported by the National Science Foundation Grant No. 9983708 and by the DGI Grant BFM2001–2562     

Decay of positive waves for hyperbolic systems of balance laws

We prove Olenik-type decay estimates for entropy solutions of strictly hyperbolic systems of balance laws built out of a wave-front tracking procedure inside which the source term is treated as a nonconservative product localized on a discrete lattice.

     

Frequency specificity of distortion-product otoacoustic emissions produced by high-level tones despite inefficient cochlear electromechanical feedback

Distortion product otoacoustic emissions (DPOAEs) are thought to stem from the outer hair cells (OHCs) around the normally narrow place tuned to the primary tone stimuli. They are thus said to be frequency-specific: their local absence should accurately pinpoint local OHC damage. Yet the influence of impaired tuning on DPOAE frequency specificity is poorly documented. Mice with local damage to OHCs were examined. Their DPOAEs were frequency-specific in that audiometric notches were accurately tracked. The same cochleae were further impaired by ischemia or furosemide injection inducing strial dysfunction with flat loss of sensitivity and tuning, while the preexisting pattern of damaged OHCs remained unaltered. Despite the loss of cochlear activity, DPOAEs produced by high-level (> or =70 dB SPL) primaries remained large in about the same interval where they had been initially normal, i.e., that with nondamaged OHCs, albeit with a slight frequency shift, of -1.1 kHz on average. Thus, the ability of DPOAEs to map structurally intact OHCs cannot be a mere consequence of cochlear tuning as it largely persists in its absence. The key element for this correct mapping is likely part of intact OHC structures (e.g., stereocilia bundles) and must have some tuning of its own.     

Near-threshold reflectivity fluctuations in the independent-convective-hot-spot-model limit of a spatially smoothed laser beam

In the framework of the independent-hot-spot model, it is shown that the reflectivity resulting from scattering instabilities when a spatially smoothed laser beam interacts with a plasma exhibits large statistical fluctuations near threshold. The importance of the fluctuations is discussed in terms of a confidence interval for the reflectivity, which is more relevant to experimental measurements than the average reflectivity. An analytical model for the fluctuating reflectivity is developed and shown to be in good agreement with numerical simulations. The influence of the transverse size of the interaction region is studied.     

Optically driven spin memory in n-doped InAs-GaAs quantum dots

We show that the spin state of the resident electron in an n-doped self-assembled InAs-GaAs quantum dot can be written and read using nonresonant, circularly polarized optical pumping. A simple theoretical model is presented and accounts for the remarkable dynamics producing counterpolarized photoluminescence.     

Iodine(III)-mediated generation of nitrogen-tethered orthoquinol acetates for the construction of oxygenated indole,quinoline, and phenanthridine alkaloid motifs

Functionalized indole and quinoline derivatives are conveniently prepared from nitrogen-tethered 2-methoxyphenols via phenyliodine(III) diacetate mediated oxidative acetoxylation, followed by a fluoride- or base-induced intramolecular nucleophilic addition reaction. This regioselective Michael-type addition step is further discussed in view of the rearrangement of orthoquinol acetate intermediates into paraquinol acetates that is sometimes observed in situ. Application of this methodology to the synthesis of a functionalized phenanthridine, and its potential for the construction of polyoxygenated lycorine-type alkaloid skeleta are here described.