Blow-up and pattern formation in hyperbolic models for chemotaxis in 1-D

In this paper we study finite time blow-up of solutions of a hyperbolic model for chemotaxis. Using appropriate scaling this hyperbolic model leads to a parabolic model as studied by Othmer and Stevens (1997) and Levine and Sleeman (1997). In the latter paper, explicit solutions which blow-up in finite time were constructed. Here, we adapt their method to construct a corresponding blow-up solution of the hyperbolic model. This construction enables us to compare the blow-up times of the corresponding models. We find that the hyperbolic blow-up is always later than the parabolic blow-up. Moreover, we show that solutions of the hyperbolic problem become negative near blow-up. We calculate the zero-turning-rate time explicitly and we show that this time can be either larger or smaller than the parabolic blow-up time. The blow-up models as discussed here and elsewhere are limiting cases of more realistic models for chemotaxis. At the end of the paper we discuss the relevance to biology and exhibit numerical solutions of more realistic models.     

Microscopic selection of fluid fingering patterns

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accordance with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.     

Inverting the Motivic Bott Element

We prove a version for motivic cohomology of Thomason's theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H⁰(k,(1)) corresponding to a primitive nth root of unity.     

Analysis of electronically nonadiabatic chemical reactions: An information theoretic approach

A practical procedure for the determination of branching ratios for reactions which lead to either excited or electronically ground state products is outlined. The method is applied to four reactions which could (on energetic grounds) produce an electronically excited iodine atom. No case of a complete inversion is found, but one reaction (F + HI) is predicted to yield a statistical, (one half), I^*(²P_1/2) to I(²P_3/2) ratio.     

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.     

Determination of ethyl glucuronide in urine using reversed-phase HPLC and pulsed electrochemical detection (Part II)

A direct, versatile method for the determination of ethyl glucuronide (EtG), a biomarker of ethanol consumption, in urine has been developed using reversed-phase liquid chromatography with pulsed electrochemical detection (PED). EtG and methyl glucuronide (MetG), which serves as an internal standard, are readily separated using a mobile phase consisting of 1% acetic acid/acetonitrile (98/2, v/v). Post-column addition of NaOH allows for the detection of all glucuronides using PED at a gold working electrode. Upon optimization, EtG was found to have a limit of detection of 0.03 μg/mL (7 pmol; 50 μL injection volume) and repeatability at the limit of quantitation of 1.7%R.S.D. (relative standard deviation). Solid-phase extraction (SPE) using an aminopropyl phase was used to remove interferents in urine samples prior to their analysis. Compound recovery following SPE was approximately 50 ± 2%. The forensic utility of this method was further validated by the analysis of 29 post-mortem urine specimens, whose results agreed strongly with certified determinations.     

Pyrimido[5,4-b]quinolines. II. Reactions at the heterocyclic ring-carbon and nitrogen atoms

10-Chloro-7,8-dimethylpyrimido[5,4-b]quinolin-2,4(1H,3H)dione (I) was unreactive toward ammonia but it reacted with 2 molecules of n-butylamine, presumably via Dimroth-type ring-opening and closure, to give the N₃-butyl, N₁₀-butylamino derivative (IV). In similar reactions of 10-chloro-2,4-dimethoxy-7,8-dimethylpyrimido[5,4-b]quinoline (II) only the 4-meth-oxyl was displaced by either ammonia or n-butylamine. Alkyllithium reagents also displaced the 4-methoxyl as well as added to the 3,4 double bond of II to yield the corresponding gem-dialkyl substituted (C₄) derivatives; the C₁₀ chlorine remained unreactive. 2,4-Dimethoxy-7,8-di-methylpyrimido[5,4-b]quinoline-10-one (III) could be alkylated only in the form of the thallium salt. Treatment of the benzyl derivative of III with methylmagnesium bromide led only to the displacement of the 4-methoxyl by a methyl group.     

One- and two-particle microrheology

We study the dynamics of rigid spheres embedded in viscoelastic media and address two questions of importance to microrheology. First, we calculate the complete response to an external force of a single bead in a homogeneous elastic network viscously coupled to an incompressible fluid. From this response function we find the frequency range where the standard assumptions of microrheology are valid. Second, we study fluctuations when embedded spheres perturb the media around them and show that mutual fluctuations of two separated spheres provide a more accurate determination of the complex shear modulus than do the fluctuations of a single sphere.     

Resonance ionization mass spectrometry for precise measurements of isotope ratios

Resonance ionization mass spectrometry offers extremely high sensitivity and elemental selectivity in microanalysis, but the isotopic precision attainable by this technique has been limited. Measured isotope ratios are sensitive to small fluctuations in the pointing, pulse timing, and wavelength of the resonance lasers. We show that, by minimizing these fluctuations using feedback controls and by power-broadening the optical transitions, we are able to measure chromium isotope ratios with statistics-limited precision better than 1%. Small additional improvements in reproducibility come from careful shaping of the electric field in the region where atoms are photoionized and from minimizing pulse-to-pulse variations in the time-of-flight mass spectrometer through which the photoions travel. The increased reproducibility of isotopic measurements on standard materials has enabled us to detect anomalous chromium isotopic abundances in presolar SiC grains extracted from primitive meteorites.