Interaction Equations for Short and Long Dispersive Waves

AbstractWe show the time-local well-posedness for a system of nonlinear dispersive equations for the water wave interaction[formula]It is shown that for any initial data (u0,v0)∈Hs(R)×Hs−1/2(R) (s⩾0), the solution for the above equation uniquely exists in a subset ofC((−T,T);Hs)×C((−T,T);Hs−1/2) and depends continuously on the data. By virtue of a special structure of the nonlinear coupling, the solution is stable under a singular limiting process

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

Charge Oscillations in Debye-Hueckel Theory

The recent generalized Debye-Hueckel (GDH) theory is applied to the calculation of the charge-charge correlation function G_{ZZ}(r). The resulting expression satisfies both (i) the charge neutrality condition and (ii) the Stillinger-Lovett second-moment condition for all T and rho_N, the overall ion density, and (iii) exhibits charge oscillations for densities above a "Kirkwood line" in the (rho_N,T) plane. This corrects the normally assumed DH correlations, and, when combined with the GDH analysis of the density correlations, leaves the GDH theory as the only complete description of ionic correlation functions, as judged by (i)-(iii), (iv) exact low-density (rho_N,T) variation, and (v) reasonable behavior near criticality.Comment: 6 pages, EuroPhys.sty (now available on archive), 1 eps figur

Singular Coexistence-curve Diameters: Experiments and Simulations

Precise calculations of the coexistence-curve diameters of a hard-core square-we ll (HCSW) fluid and the restricted primitive model (RPM) electrolyte exhibit mar ked deviations from rectilinear behavior. The HCSW diameter displays a $|t|^{1- alpha}$ singularity that sets in sharply for $|t|\equiv |T-T_c|/T_c\lesssim 10^{-3}$; this compares favorably with extensive data for ${SF}_6$, also reflec ted in C$_2$H$_6$, N$_2$, etc. By contrast, the curvature of the RPM diameter va ries slowly over a wide range $|t|\lesssim 0.1$; this behavior mirrors observati ons for liquid alkali metals, specifically Rb and Cs. Amplitudes for the leading singular terms can be estimated numerically but their values cannot be taken li terally.Comment: 9 pages and 4 figure

Error-pooling-based statistical methods for identifying novel temporal replication profiles of human chromosomes observed by DNA tiling arrays

Statistical analysis on tiling array data is extremely challenging due to the astronomically large number of sequence probes, high noise levels of individual probes and limited number of replicates in these data. To overcome these difficulties, we first developed statistical error estimation and weighted ANOVA modeling approaches to high-density tiling array data, especially the former based on an advanced error-pooling method to accurately obtain heterogeneous technical error of small-sample tiling array data. Based on these approaches, we analyzed the high-density tiling array data of the temporal replication patterns during cell-cycle S phase of synchronized HeLa cells on human chromosomes 21 and 22. We found many novel temporal replication patterns, identifying about 26% of over 1 million tiling array sequence probes with significant differential replication during the four 2-h time periods of S phase. Among these differentially replicated probes, 126 941 sequence probes were matched to 417 known genes. The majority of these genes were found to be replicated within one or two consecutive time periods, while the others were replicated at two non-consecutive time periods. Also, coding regions found to be more differentially replicated in particular time periods than noncoding regions in the gene-poor chromosome 21 (25% differentially replicated among genic probes versus 18.6% among intergenic probes), while such a phenomenon was less prominent in gene-rich chromosome 22. A rigorous statistical testing for local proximity of differentially replicated genic and intergenic probes was performed to identify significant stretches of differentially replicated sequence regions. From this analysis, we found that adjacent genes were frequently replicated at different time periods, potentially implying the existence of quite dense replication origins. Evaluating the conditional probability significance of identified gene ontology terms on chromosomes 21 and 22, we detected some over-represented molecular functions and biological processes among these differentially replicated genes, such as the ones relevant to hydrolase, transferase and receptor-binding activities. Some of these results were confirmed showing >70% consistency with cDNA microarray data that were independently generated in parallel with the tiling arrays. Thus, our improved analysis approaches specifically designed for high-density tiling array data enabled us to reliably and sensitively identify many novel temporal replication patterns on human chromosomes

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using temperature-density, (T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials phi(r)>Phi/r^{4.9} when r \to \infty

On the Adsorption of Two-State Polymers

Monte Carlo(MC) simulations produce evidence that annealed copolymers incorporating two interconverting monomers, P and H, adsorb as homopolymers with an effective adsorption energy per monomer, $\epsilon_{eff}$, that depends on the PH equilibrium constants in the bulk and at the surface. The cross-over exponent, $\Phi,$ is unmodified. The MC results on the overall PH ratio, the PH ratio at the surface and in the bulk as well as the number of adsorbed monomers are in quantitative agreement with this hypothesis and the theoretically derived $\epsilon_{eff}$. The evidence suggests that the form of surface potential does not affect $\Phi$ but does influence the PH equilibrium.Comment: 22 pages, 10 figure