A second generation mesoscopic lipid bilayer model: connections to field-theory descriptions of membranes and nonlocal hydrodynamics

A new mesoscopic membrane model is developed in order to examine long-wavelength structural and dynamical membrane phenomena. Two different explicit mesoscopic solvent models are employed. The first mesoscopic solvent is denoted the big liquid oscillating blob system, which is parametrized to model water at a coarse-grained level and is motivated by a Langevin-like approach; the resulting membrane dynamics predict a solvent viscosity dependence consistent with the known viscosity of water. The second mesoscopic solvent is a Weeks-Chandler-Anderson model. Here, it is found that the correct mesoscopic hydrodynamic scaling of the membrane undulation dynamics is still preserved, although accelerated. When the behavior of the two membranes in close proximity to one another is examined, very little correlated motion is observed. However, the theoretically predicted scaling of the entropic undulation energy is confirmed, demonstrating that the entropic interaction between two membranes becomes increasingly repulsive with decreasing separation.     

Ultrafast laser studies of the photothermal properties of gold nanocages

Au nanocages were synthesized via a galvanic replacement reaction. The extinction peak of these hollow structured particles is shifted into the near-IR compared with the Ag nanocube templates. Energy transfer from the Au nanocages into the surrounding environment (water) as well as the coherently excited vibrational modes of the nanocages were studied by femtosecond pump-probe spectroscopy. The time scale for energy relaxation was found to increase with the size of the particles, with the relaxation time being independent of the laser intensity. The time scales for relaxation are comparable to those for solid spherical gold particles and are consistent with energy relaxation being controlled by heat dissipation in the solvent. The period of the coherently excited vibrational mode is proportional to the dimensions of the nanocages. Intensity-dependent measurements show that in solution the nanocages maintain their integrity up to lattice temperatures of 1100 +/- 100 K.     

Molecular simulation analysis and X-ray absorption measurement of Ca2+, K+ and Cl- ions in solution

This paper presents recent advances in the use of molecular simulations and extended X-ray absorption fine structure (EXAFS) spectroscopy, which enable us to understand solvated ions in solution. We report and discuss the EXAFS spectra and related properties governing solvation processes of different ions in water and methanol. Molecular dynamics (MD) trajectories are coupled to electron scattering simulations to generate the MD-EXAFS spectra, which are found to be in very good agreement with the corresponding experimental measurements. From these simulated spectra, the ion-oxygen distances for the first hydration shell are in agreement with experiment within 0.05-0.1 A. The ionic species studied range from monovalent to divalent, positive and negative: K+, Ca2+, and Cl-. This work demonstrates that the combination of MD-EXAFS and the corresponding experimental measurement provides a powerful tool in the analysis of the solvation structure of aqueous ionic solutions. We also investigate the value of electronic structure analysis of small aqueous clusters as a benchmark to the empirical potentials. In a novel computational approach, we determine the Debye-Waller factors for Ca2+, K+, and Cl- in water by combining the harmonic analysis of data obtained from electronic structure calculations on finite ion-water clusters, providing excellent agreement with the experimental values, and discuss how they compare with results from a harmonic classical statistical mechanical analysis of an empirical potential.     

22]Porphyrin-(3.1.1.3), a new vinylogous expanded porphyrin system

Acid-catalyzed condensation of a pyrrole bisacrylaldehyde with a tripyrrane, followed by oxidation with ferric chloride, gave a [22]porphyrin-(3.1.1.3). This stretched macrocycle shows a strong diamagnetic ring current by (1)H NMR spectroscopy and gives red-shifted porphyrin-like UV-vis spectra; coordination with palladium(II) induces an EZ isomerization to accommodate the metal cation while retaining highly diatropic characteristics. [structure: see text]     

Physical mechanism of the two-dimensional inverse energy cascade

We study the physical mechanisms of the two-dimensional inverse energy cascade using theory, numerics, and experiment. Kraichnan's prediction of a -5/3 spectrum with constant, negative energy flux is verified in our simulations of 2D Navier-Stokes equations. We observe a similar but shorter range of inverse cascade in laboratory experiments. Our theory predicts, and the data confirm, that inverse cascade results mainly from turbulent stress proportional to small-scale strain rotated by 45 degrees. This "skew-Newtonian" stress is explained by the elongation and thinning of small-scale vortices by large-scale strain which weakens their velocity and transfers their energy upscale.     

Holomorphic solutions to functional differential equations

The pantograph equation is perhaps one of the most heavily studied class of functional differential equations owing to its numerous applications in mathematical physics, biology, and problems arising in industry. This equation is characterized by a linear functional argument. Heard (1973) [10] considered a generalization of this equation that included a nonlinear functional argument. His work focussed on the asymptotic behaviour of solutions for a real variable x as x→∞. In this paper, we revisit Heard's equation, but study it in the complex plane. Using results from complex dynamics we show that any nonconstant solution that is holomorphic at the origin must have the unit circle as a natural boundary. We consider solutions that are holomorphic on the Julia set of the nonlinear argument. We show that the solutions are either constant or have a singularity at the origin. There is a special case of Heard's equation that includes only the derivative and the functional term. For this case we construct solutions to the equation and illustrate the general results using classical complex analysis.     

An application of Fourier transforms on finite Abelian groups to an enumeration arising from the Josephus problem

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We analyze an enumeration associated with the Josephus problem by applying a Fourier transform to a multivariate generating function. This yields a formula for the enumeration that reduces to a simple expression under a condition we call local prime abundance. Under this widely held condition, we prove (Corollary 3.4) that the proportion of Josephus permutations in the symmetric group Sn that map t to k (independent of the choice of t and k) is 1/n. Local prime abundance is intimately connected with a well-known result of S.S. Pillai, which we exploit for the purpose of determining when it holds and when it fails to hold. We pursue the first case where it fails, reducing an intractable DFT computation of the enumeration to a tractable one. A resulting computation shows that the enumeration is nontrivial for this case.

Video

For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=DnZi-Znuk-A.     

Online sum-paintability: The slow-coloring game

The slow-coloring game is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the uncolored vertices, scoring $\left|M\right|$ points. Painter then gives a color to a subset of $M$ that is independent in $G$. The game ends when all vertices are colored. Painter and Lister want to minimize and maximize the total score, respectively. The best score that each player can guarantee is the sum-color cost of $G$, written $\stackrel{?}{s}\left(G\right)$. The game is an online variant of online sum list coloring.We prove $\frac{\left|V\left(G\right)\right|}{2\alpha \left(G\right)}+\frac{1}{2}\le \frac{\stackrel{?}{s}\left(G\right)}{\left|V\left(G\right)\right|}\le max\left\{\frac{\left|V\left(H\right)\right|}{\alpha \left(H\right)}:H?G\right\}$, where $\alpha \left(G\right)$ is the independence number, and we study when equality holds in the bounds. We compute $\stackrel{?}{s}\left(G\right)$ for graphs with $\alpha \left(G\right)=2$. Among $n$-vertex trees, we prove that $\stackrel{?}{s}$ is minimized by the star and maximized by the path. We also study $\stackrel{?}{s}\left(K_{r,s}\right)$.     

The locus of Hodge classes in an admissible variation of mixed Hodge structure

We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.     

The structure of phosphate and borosilicate glasses and their structural evolution at high temperatures as studied with solid state NMR spectroscopy: Phase separation,crystallisation and dynamic species exchange

In this contribution we present an in-depth study of the network structure of different phosphate based and borosilicate glasses and its evolution at high temperatures. Employing a range of advanced solid state NMR methodologies, complemented by the results of XPS, the structural motifs on short and intermediate length scales are identified. For the phosphate based glasses, at temperatures above the glass transition temperature T_g, structural relaxation processes and the devitrification of the glasses were monitored in situ employing MAS NMR spectroscopy and X-ray diffraction. Dynamic species exchange involving rapid P–O–P and P–O–Al bond breaking and reforming was observed employing in situ ²⁷Al and ³¹P MAS NMR spectroscopy and could be linked to viscous flow. For the borosilicate glasses, an atomic scale investigation of the phase separation processes was possible in a combined effort of ex situ NMR studies on glass samples with different thermal histories and in situ NMR studies using high temperature MAS NMR spectroscopy including ¹¹B MAS, ²⁹Si MAS and in situ ²⁹Si{¹¹B} REAPDOR NMR spectroscopy.