A mass,energy, vorticity,and potential enstrophy conserving lateral fluid–land boundary scheme for the shallow water equations

A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that conserves the domain-summed mass, energy, vorticity, and potential enstrophy in domains with arbitrarily shaped boundaries. The boundary scheme is derived from a previous scheme that conserves all four domain-summed quantities only in periodic domains without boundaries. It consists of a method for including land in the model along with evolution equations for the vorticity and extrapolation formulas for the depth at fluid–land boundaries. Proofs of mass, energy, vorticity, and potential enstrophy conservation are given. Numerical simulations are carried out demonstrating the conservation properties and accuracy of the boundary scheme for inviscid flows and comparing its performance with that of four alternative boundary schemes. The first of these alternatives extrapolates or finite-differences the velocity to obtain the vorticity at boundaries; the second enforces the free-slip boundary condition; the third enforces the super-slip condition; and the fourth enforces the no-slip condition. Comparisons of the conservation properties demonstrate that the new scheme is the only one of the five that conserves all four domain-summed quantities, and it is the only one that both prevents a spurious energy cascade to the smallest resolved scales and maintains the correct flow orientation with respect to an external forcing. Comparisons of the accuracy demonstrate that the new scheme generates vorticity fields that have smaller errors than those generated by any of the alternative schemes, and it generates depth and velocity fields that have errors about equal to those in the fields generated by the most accurate alternative scheme.     

Irregularity strength of digraphs

It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs. We consider generating irregular digraphs from arbitrary digraphs by adding multiple arcs. To this end, we define an irregular labeling of a digraph D to be an arc-labeling of the digraph such that the ordered pairs of the sums of the in-labels and out-labels at each vertex are all distinct. We define the strength of D to be the smallest of the maximum labels used across all irregular labelings. Similar definitions for graphs have been studied extensively and a different formulation of digraph irregularity was given in [H. Hackett, Irregularity strength of graphs and digraphs, Masters Thesis, University of Louisville, 1995]. Here we continue the study of irregular labelings of digraphs. We give a general lower bound on and determine exactly for tournaments, directed paths and cycles and the orientation of the path where all vertices have either in-degree 0 or out-degree 0. We also determine the irregularity strength of a union of directed cycles and a union of directed paths, the latter which requires a new result pertaining to finding circuits of given lengths containing prescribed vertices in the complete symmetric digraph with loops.     

Testing the conformational hypothesis of passive membrane permeability using synthetic cyclic peptide diastereomers

Little is known about the effect of conformation on passive membrane diffusion rates in small molecules. Evidence suggests that intramolecular hydrogen bonding may play a role by reducing the energetic cost of desolvating hydrogen bond donors, especially amide N-H groups. We set out to test this hypothesis by investigating the passive membrane diffusion characteristics of a series of cyclic peptide diastereomers based on the sequence cyclo[Leu-Leu-Leu-Leu-Pro-Tyr]. We identified two cyclic hexapeptide diastereomers based on this sequence, whose membrane diffusion rates differed by nearly two log units. Results of solution NMR studies and hydrogen/deuterium (H/D) exchange experiments showed that membrane diffusion rates correlated with the degree of intramolecular hydrogen bonding and H/D exchange rates. The most permeable diastereomer, cyclo[d-Leu-d-Leu-Leu-d-Leu-Pro-Tyr] (1), exhibited a passive membrane diffusion rate comparable to that of the orally available drug cyclosporine A.     

Solid-state bonding technique for template-stripped ultraflat gold substrates

A simple procedure using gold diffusion bonding for the preparation of template-stripped gold (TSG) surfaces is described. TSG surfaces are useful for surface studies because a very consistent flat gold surface with few defects can be easily prepared. We have developed a method of producing TSG surfaces that relies only on gold diffusion bonding rather than epoxies. The resulting substrates are free from concerns of solvent compatibility, heat stability, and impurities. Bonding of centimeter-sized substrates is performed at 300 degrees C for 2 h using a vise and aluminum foil.     

Defining the nucleotide binding sites of P2Y receptors using rhodopsin-based homology modeling

Ongoing efforts to model P2Y receptors for extracellular nucleotides, i.e., endogenous ADP, ATP, UDP, UTP, and UDP-glucose, were summarized and correlated for the eight known subtypes. The rhodopsin-based homology modeling of the P2Y receptors is supported by a growing body of site-directed mutagenesis data, mainly for P2Y₁ receptors. By comparing molecular models of the P2Y receptors, it was concluded that nucleotide binding could occur in the upper part of the helical bundle, with the ribose moiety accommodated between transmembrane domain (TM) 3 and TM7. The nucleobase was oriented towards TM1, TM2, and TM7, in the direction of the extracellular side of the receptor. The phosphate chain was oriented towards TM6, in the direction of the extracellular loops (ELs), and was coordinated by three critical cationic residues. In particular, in the P2Y₁, P2Y₂, P2Y₄, and P2Y₆ receptors the nucleotide ligands had very similar positions. ADP in the P2Y₁₂ receptor was located deeper inside the receptor in comparison to other subtypes, and the uridine moiety of UDP-glucose in the P2Y₁₄ receptor was located even deeper and shifted toward TM7. In general, these findings are in agreement with the proposed binding site of small molecules to other class A GPCRs.     

Rapid computation of intermolecular interactions in molecular and ionic clusters: self-consistent polarization plus symmetry-adapted perturbation theory

A method that we have recently introduced for rapid computation of intermolecular interaction energies is reformulated and subjected to further tests. The method employs monomer-based self-consistent field calculations with an electrostatic embedding designed to capture many-body polarization (the "XPol" procedure), augmented by pairwise symmetry-adapted perturbation theory (SAPT) to capture dispersion and exchange interactions along with any remaining induction effects. A rigorous derivation of the XPol+SAPT methodology is presented here, which demonstrates that the method is systematically improvable, and moreover introduces some additional intermolecular interactions as compared to the more heuristic derivation that was presented previously. Applications to various non-covalent complexes and clusters are presented, including geometry optimizations and one-dimensional potential energy scans. The performance of the XPol+SAPT methodology in its present form (based on second-order intermolecular perturbation theory and neglecting intramolecular electron correlation) is qualitatively acceptable across a wide variety of systems-and quantitatively quite good in certain cases-but the quality of the results is rather sensitive to the choice of one-particle basis set. Basis sets that work well for dispersion-bound systems offer less-than-optimal performance for clusters dominated by induction and electrostatic interactions, and vice versa. A compromise basis set is identified that affords good results for both induction and dispersion interactions, although this favorable performance ultimately relies on error cancellation, as in traditional low-order SAPT. Suggestions for future improvements to the methodology are discussed.     

A homochiral diamond framework constructed from Fe(III) and Mn(II) oxo-clusters supported by Sb(III) tartrate scaffolds

A homochiral diamond framework was obtained by using a secondary building unit (SBU) comprising an oxo-cluster containing 4Fe(III) and 3Mn(II) ions supported by Sb(3)O tartrate scaffolds. A fully protonated tetratopic cation, tetrakis(4-pyridyloxymethylene)methane (TPOM), acts as a template to arrange the clusters on a diamond lattice.     

Optimizing the energy status of skin cells during solar radiation.

Ionizing- and ultraviolet-radiation cause cell damage or death by directly altering DNA and protein structures and by production of reactive oxygen species (ROS) and reactive carbonyl species (RCS). These processes disrupt cellular energy metabolism at multiple levels. The formation of DNA strand breaks activates signaling pathways that consume NAD, which can lead to the depletion of cellular ATP. Poly(ADP)-ribose polymerase (PARP-1) is the enzyme responsible for much of the NAD degradation following DNA damage, although numerous other PARPs have been discovered recently that await functional characterization. Studies on mouse epidermis in vivo and on human cells in culture have shown that UV-B radiation provokes the transient degradation of NAD and the synthesis of ADP-ribose polymers by PARP-1. This enzyme functions as a component of a DNA damage surveillance network in eukaryotic cells to determine the fate of cells following genotoxic stress. Additionally, the activation of PARP-1 results in the activation of a nuclear proteasome that degrades damaged nuclear proteins including histones. Identifying approaches to optimize these responses while maintaining the energy status of cells is likely to be very important in minimizing the deleterious effects of solar radiation on skin.     

Global optima results for the Kauffman NK model

The Kauffman NK model has been used in theoretical biology, physics and business organizations to model complex systems with interacting components. Recent NK model results have focused on local optima. This paper analyzes global optima of the NK model. The resulting global optimization problem is transformed into a stochastic network model that is closely related to two well-studied problems in operations research. This leads to applicable strategies for explicit computation of bounds on the global optima particularly with K either small or close to N. A general lower bound, which is sharp for K = 0, is obtained for the expected value of the global optimum of the NK model. A detailed analysis is provided for the expectation and variance of the global optimum when K = N−1. The lower and upper bounds on the expectation obtained for this case show that there is a wide gap between the values of the local and the global optima. They also indicate that the complexity catastrophe that occurs with the local optima does not arise for the global optima.     

Analyzing the Complexity of Finding Good Neighborhood Functions for Local Search Algorithms

A drawback to using local search algorithms to address NP-hard discrete optimization problems is that many neighborhood functions have an exponential number of local optima that are not global optima (termed L-locals). A neighborhood function η is said to be stable if the number of L-locals is polynomial. A stable neighborhood function ensures that the number of L-locals does not grow too large as the instance size increases and results in improved performance for many local search algorithms. This paper studies the complexity of stable neighborhood functions for NP-hard discrete optimization problems by introducing neighborhood transformations. Neighborhood transformations between discrete optimization problems consist of a transformation of problem instances and a corresponding transformation of solutions that preserves the ordering imposed by the objective function values. In this paper, MAX Weighted Boolean SAT (MWBS), MAX Clause Weighted SAT (MCWS), and Zero-One Integer Programming (ZOIP) are shown to be NPO-complete with respect to neighborhood transformations. Therefore, if MWBS, MCWS, or ZOIP has a stable neighborhood function, then every problem in NPO has a stable neighborhood function. These results demonstrate the difficulty of finding effective neighborhood functions for NP-hard discrete optimization problems.This research is supported in part by the Air Force Office of Scientific Research (F49620-01-1-0007, FA9550-04-1-0110).