Time and Space Fractional Diffusion in Finite Systems

Spatiotemporal nonlocal diffusion in a bounded system is addressed by considering fractional diffusion in a linear, composite system. By considering limiting conditions, solutions for combinations of Neumann and Dirichlet boundary conditions (either zero or nonzero) at the ends of a finite system are derived in terms of Mittag–Leffler functions by the Laplace transformation. Computational viability is demonstrated by inverting the solutions numerically and comparing resulting calculations with asymptotic solutions. Time and space fractional derivatives, defined by variables \(\alpha \) and \(\beta \), respectively, are employed in the Caputo sense; a single-sided, asymmetric space derivative is used. Inspection of the asymptotic solutions leads to insights on the structure of the solutions that may not be available otherwise; the resulting deductions are verified through the numerical inversions. For pure superdiffusion, characteristics of some of the solutions presented here are very similar to those of classical diffusion but combined effects for the corresponding situation result in power-law behaviors. Incidentally, to our knowledge, the pressure distribution for space fractional diffusion at long enough times in a finite system is derived based on first principles for the first time.     

Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.      

Gel sculpture: moldable, load-bearing and self-healing non-polymeric supramolecular gel derived from a simple organic salt

An easy access to a library of simple organic salts derived from tert-butoxycarbonyl (Boc)-protected L-amino acids and two secondary amines (dicyclohexyl- and dibenzyl amine) are synthesized following a supramolecular synthon rationale to generate a new series of low molecular weight gelators (LMWGs). Out of the 12 salts that we prepared, the nitrobenzene gel of dicyclohexylammonium Boc-glycinate (GLY.1) displayed remarkable load-bearing, moldable and self-healing properties. These remarkable properties displayed by GLY.1 and the inability to display such properties by its dibenzylammonium counterpart (GLY.2) were explained using microscopic and rheological data. Single crystal structures of eight salts displayed the presence of a 1D hydrogen-bonded network (HBN) that is believed to be important in gelation. Powder X-ray diffraction in combination with the single crystal X-ray structure of GLY.1 clearly established the presence of a 1D hydrogen-bonded network in the xerogel of the nitrobenzene gel of GLY.1. The fact that such remarkable properties arising from an easily accessible (salt formation) small molecule are due to supramolecular (non-covalent) interactions is quite intriguing and such easily synthesizable materials may be useful in stress-bearing and other applications.     

Shedding light on helical microtubules: real-time observations of microtubule self-assembly by light microscopy

Helical tubules are a fascinating and an intriguing class of self-assemblies. They occur frequently in biology and are believed to be intermediates in formation of gallstones. The pathway by which amphiphiles transform from an initial state of vesicles or micelles into such tubules has puzzled soft matter physicists, and it has raised important questions about the interplay between molecular chirality and self-assembly. Here, for the first time, we demonstrate direct, real-time observations by light microscopy of the pathway to helical microtubules from an initial solution of nanoscale vesicles. The tubules are formed in aqueous mixtures of the single-tailed diacetylenic surfactant, 10,12-pentacosadiynoic acid (PCDA), and a short-chain alcohol. The stepwise process involves nucleation of thin helical microribbons from the vesicle solution. These ribbons then thicken, rearrange, and fold into closed tubules. Subsequently, most tubules further rearrange into plate-like structures, and once again, we are able to visualize this process in real time. A notable aspect of the above system is that the precursors are achiral; yet, the tubules are formed from helical ribbons. Our study provides new insights into tubule formation that will be valuable in clarifying and refining theoretical models for these fascinating structures.     

Process optimization of vapor phase pyridine synthesis using response surface methodology

The vapor phase pyridine synthesis from acetaldehyde, formaldehyde and ammonia over HZSM-5 catalyst was studied. The process parameters like temperature, aldehyde ratio, and Si/Al ratio in HZSM-5 was investigated and the process conditions were optimized using surface response methodology (RSM) based on Box-Behnken design. The influence of process parameters investigated using analysis of variance (ANOVA), to identify the significant parameters. The optimum conditions for high yield of pyridine were identified to be a reaction temperature 400°C, aldehyde ratio 1: 1 and Si/Al ratio 106.7. A maximum of 55% yield of pyridine formed under the optimum experimental conditions. The proposed model equation using RSM has shown good agreement with the experimental data, with a correlation coefficient R ² = 0.99.     

Student Outcomes in a Local Systemic Change Project

The Local Systemic Change initiative of the National Science Foundation supports projects focusing primarily on teacher enhancement through extensive professional development and the use of standards‐based curriculum materials. The underlying rationale is that the effective use of such materials will ultimately result in enhanced student learning. However, the research base regarding the impact of these efforts on student learning is rather lean. This paper describes the results of a curriculum‐aligned assessment comprising selected items from the Third International Mathematics and Science Study. The assessment was administered to fifth graders involved in a Local Systemic Change project to address the following questions: How does the performance of students involved in the project compare nationally and internationally? and Does length of involvement in the project make a difference in student performance? Additional evidence to relate student outcomes to the project's systemic change efforts are provided.     

On stochastic games with additive reward and transition structure

In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player.For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.     

Two-particle correlations in 360 GeV/cp p interactions

Two particle correlations of hadrons produced in 360 GeV/cpp interactions are investigated in the transverse plane and in rapidity. The data were obtained at the European hybrid spectrometer equipped with a rapid cycling bubble chamber. The observed transverse and rapidity correlations are compared with the one string LUND-and a two string dual parton-model. These models predict in general stronger correlations in the transverse plane and much weaker correlations in rapidity than found in the data. The LUND-FRITIOF-and multichain dual parton models provide a better reproduction of the data, although the agreement is not yet satisfactory. Only the UA5 cluster model GENCL shows agreement with the data.     

A short convergent synthesis of the [3.2.1]dioxabicyclooctane subunit of sorangicin A via regioselective epoxide opening

In this paper, we disclose the synthesis of the dioxabicyclo[3.2.1]octane subunit of the potent antibiotic sorangicin A. The synthesis was achieved in a convergent manner in 8 steps. Regio- and stereoselective intermolecular epoxide opening, ring-closing metathesis and iodo-etherification are key steps. cis-2-Butene diol has been employed as a common staring material.