Polymer-solvent co-crystallization during thermoreversible gelation in solutions of the helical polypeptide PBLG

Macromolecular aggregation during thermoreversible gelation in solutions of the helical polypeptide poly(γ-benzyl-L-glutamate) [PBLG] in benzyl alcohol [BA] were studied by small angle neutron and small angle X-ray scattering. Gelation is apparent as a large increase in the intensity scattered at low angles, signifying formation of a microfibrillar PBLG network. The aggregated phase in isotropic gels from semidilute solutions contains about 28% solvent. A periodic structure is observed when gelation is induced by rapid cooling to a low temperature, but not by slow cooling or gelation at a higher temperature. In gels from concentrated liquid crystal solutions, two crystalline structures are observed, depending on whether the solution is rapidly quenched and then annealed or slowly gelled at an elevated temperature. A phase diagram for the PBLG/BA system is presented and the observed microstructural transitions are rationalized in terms of a gelation mechanism involving a combination of liquid-liquid phase separation and crystallization in the form of polymer-solvent co-crystals.     

Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography

We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one and two space dimensions, and (ii) one-dimensional moving equilibrium states. Suitable energy stable numerical diffusion operators, based on energy and equilibrium variables, are designed to preserve these two types of steady states. Several numerical experiments illustrating the robustness of the energy preserving and energy stable well-balanced schemes are presented.     

Chain reactions, “impossible” reactions,and panenmentalist possibilities

Panenmentalist possibilities are individual pure possibilities existing independently of any mind, actual reality, and possible-world conception. These possibilities are a priori accessible to our intellect and imagination. In this paper, I attempt to shed some panenmentalist light on the discovery of chemical branched chain reactions and its implications on biology and cancer research. I also examine the case of the Belousov–Zhabotinsky reaction which, at first, was believed to be impossible. Finally, I proceed to examine through a panenmentalist lens Szilard’s discovery of the possibility of physical chain reactions and Mullis’s discovery of a polymerase chain reaction. All these major actual discoveries clearly depend on the discovery of the relevant panenmentalist possibilities and the ways in which they relate to one another.     

Three Novel Edge Detection Methods for Incomplete and Noisy Spectral Data

We propose three novel methods for recovering edges in piecewise smooth functions from their possibly incomplete and noisy spectral information. The proposed methods utilize three different approaches: #1. The randomly-based sparse Inverse Fast Fourier Transform (sIFT); #2. The Total Variation-based (TV) compressed sensing; and #3. The modified zero crossing. The different approaches share a common feature: edges are identified through separation of scales. To this end, we advocate here the use of concentration kernels (Tadmor, Acta Numer. 16:305–378, 2007), to convert the global spectral data into an approximate jump function which is localized in the immediate neighborhoods of the edges. Building on these concentration kernels, we show that the sIFT method, the TV-based compressed sensing and the zero crossing yield effective edge detectors, where finitely many jump discontinuities are accurately recovered. One- and two-dimensional numerical results are presented.     

Surface effects in non-uniform nanobeams: Continuum vs. atomistic modeling

Nanobeams are expected to be one of the key structural elements in nanotechnology. Contrary to macroscopic structures, surface effects can strongly influence the stress and deformation properties of nano-devices. In addition, at such small scales, material non-uniformity becomes significant and must be considered.In this work, a continuum model for nanobeams, including both surface effects and material heterogeneity is developed. The model treats the surfaces as separate material layers with finite thickness. The continuum solution is compared with atomistic simulations, from which the effective bulk and surface properties are computed independently. A special case of self-deflection due to surface non-uniformities, which is important for design of nanosensors, is studied. A comparison between continuum and atomistic solutions reveals differences, which originate from local transition effects in the neighborhood of strong non-uniformities. This discrepancy is addressed by defining an effective length, found by correlating the beam deflections from both methods.     

An improved local blow-up condition for Euler-Poisson equations with attractive forcing

We improve the recent result of Chae and Tadmor (2008) [10] proving a one-sided threshold condition which leads to a finite-time breakdown of the Euler-Poisson equations in arbitrary dimension n.     

Stress and heat flux for arbitrary multibody potentials: a unified framework

A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multibody potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the nonuniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the nonuniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the nonuniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multibody potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one.     

On the numerical radius and its applications

We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finite- and infinite- dimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems.     

A kinetic equation with kinetic entropy functions for scalar conservation laws

We construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws. In particular we prove that it is well-posed uniformly in — the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions — analogous to Boltzmann's microscopicH-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, we prove by both — BV compactness arguments in the multidimensional case and by compensated compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with 0 to the unique entropy solution of the corresponding conservation law.Research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665. Additional support for the second author was provided by U.S.-Israel BSF Grant No. 85-00346. Part of this research was carried out while the first author was visiting Tel-Aviv University     

Kinetic formulation of the isentropic gas dynamics andp-systems

We consider the 2×2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called thep-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new phenomenon occurs here, namely that the advection velocity is now a combination of the macroscopic and kinetic velocities. Various applications are given: we recover the invariant regions, deduce newL estimates using moments lemma and proveL –w* stability for 3.