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61.
T.?HillenEmail author H. A.?Levine 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):839-868
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. 相似文献
62.
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. 相似文献
63.
Marc Levine 《K-Theory》2000,19(1):1-28
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. 相似文献
64.
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. 相似文献
65.
66.
Jonathan Levine Michael R. Savina Thomas Stephan Nicolas Dauphas Andrew M. Davis Kim B. Knight Michael J. Pellin 《International journal of mass spectrometry》2009,288(1-3):36-43
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. 相似文献
67.
The geometrical approach to statistical mechanics is used to discuss changes in entropy upon sequential displacements of the state of the system. An interpretation of the angle between two states in terms of entropy differences is thereby provided. A particular result of note is that any state can be resolved into a state of maximal entropy (both states having the same expectation values for the constraints) and an orthogonal component. A cosine law for the general case is also derived. 相似文献
68.
The barrier for the hydrogen exchange reaction increases with the bend angle of H3. The implications for the dynamics of the reaction are explored on two levels. The static one uses the concept of a relaxed potential. This provides for a convenient, yet realistic representation. Itallows for the response of the molecule to the approaching atom. Among features made very evident by the relaxed potential is the possibility that hotH atoms can react by insertion. It also shows the widening of the cone of acceptance upon reagent vibrational excitation. On the dynamical level, classical trajectory computations are used to illustrate the dependence of the reactivity on the angle of attack and on the translational and vibrational excitation of the reagents. Detailed product distributions are generally not sensitive to the attack angle. An exception is the HD/H2 branching ratio in H + HD reactive collisions. 相似文献
69.
70.
A detailed mechanistic model for polystyrene pyrolysis was created that built on a modeling framework developed in our previous work and was used to probe three competing pathways to dimer formation: benzyl radical addition, 1,3-hydrogen shift, and 7,3-hydrogen shift, based on recent literature reports. To incorporate the chemistry involved in the 7,3-hydrogen shift pathway, the 1,7- and 7,3-hydrogen shift reaction families were added to the model. The updated version of the model tracks 75 species and over 3500 reactions. Rate parameters for all families were specified based on our previous work, more recent literature reports, and regression against limited experimental data. The model was able to accurately predict the experimental results for polystyrene pyrolysis for different reactor configurations for a temperature range of 100 °C and two orders of magnitude of initial molecular weight for experimental data collected in our own lab and from Bouster and coworkers and Bockhorn and coworkers. The results from our model were studied using net rate analysis to gain insight into the competitiveness of the various reaction pathways to dimer formation. The net rate analysis demonstrated that 7,3-hydrogen shift is the dominant reaction pathway to dimer formation at the temperatures studied. Benzyl radical addition becomes a more competitive reaction pathway as the temperature increases, which is caused predominantly by an increase in the benzyl radical concentration with increasing temperature. Overall, it is quantitatively shown that both 7,3-hydrogen shift and benzyl radical addition are important pathways for dimer formation, with their relative competitiveness influenced by temperature. 相似文献