Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. B 75 (2007) 064107] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed.     

Forecast-driven model for prepositioning supplies in preparation for a foreseen hurricane

In this paper, we present a forecast-driven dynamic model for prepositioning relief items in preparation for a foreseen hurricane. Our model uses forecast advisories issued by the National Hurricane Center (NHC), which are issued every 6?h. Every time a new advisory is issued with updated information, our model determines the amount and location of units to be prepositioned and it also re-prepositions already prepositioned units. The model also determines the best time for starting the prepositioning activities. Our approach uses a combination of Decision Theory and stochastic programming. The outcomes of our model are presented in a way that could be easily understood by humanitarian practitioners who are ultimately the ones who would use and apply our model.     

Restricted set addition: The exceptional case of the Erd?s-Heilbronn conjecture

Let A≠B be nonempty subsets of the group of integers modulo a prime p. If p?|A|+|B|−2, then at least |A|+|B|−2 different residue classes can be represented as a+b, where a∈A, b∈B and a≠b. This result complements the solution of a problem of Erd?s and Heilbronn obtained by Alon, Nathanson, and Ruzsa.     

Novel 2-phosphabicyclo[2.2.2]oct-5-ene derivatives and their use in phosphinylations

The [4 + 2] cycloaddition of the double-bond isomers ( A and B ) of dihydrophosphinine oxide 1 afforded novel phosphabicyclo[2.2.2]oct-5-ene derivates ( 2–4 ), formation of which was justified by PM3 semiempirical calculations. The compounds of dimer type ( 2–4 ) were utilized in the UV light-mediated fragmentation-related phosphinylation of nucleophiles, especially in that of alcohols. To explore the role of structural modifications on the fragmentation ability, disulfide 5 , phosphabicyclooctane 7 obtained by the hydrogenation of 2 , and the adduct of dihydrophosphinine oxide 1 with benzoquinone ( 7 ) were also synthesized and tested in fragmentation. © 2004 Wiley Periodicals, Inc. Heteroatom Chem 15:97–106, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10221     

Formation of aryl dialkylphosphinates from dialkylphosphinous chlorides and arylmagnesium bromides under oxidative conditions

The reaction of dialkylphosphinous chlorides ( 1 ) with arylmagnesium bromides carried out in the air atmosphere was found to afford aryl‐dialkylphosphine oxides ( 2 ) and aryl dialkylphosphinates ( 3 ) in a comparable quantity. Formation of the latter product ( 3 ) is the first example that an aryl‐dialkylphosphine, formed as an intermediate, is autooxidized to the corresponding phosphinate. © 2001 John Wiley & Sons, Inc. Heteroatom Chem 12:38–41, 2001     

P-Substituted 3-phosphabicyclo [3.1.0] hexane 3-oxides from diastereoselective substitution at phosphorus

Preparation of P-amino-3-phosphabicyclo[3.1.0]-hexane 3-oxides either by addition of dichlorocarbene to the double bond of 1-amino-2,5-dihydro-1H-phosphole 1-oxides or by substitution of the P-chloro derivative of the bicyclic system was accomplished. Two different diastereomers are obtained by the two approaches; their ¹³C NMR spectra were interpreted on the basis of the P-ethoxy isomers, whose structures were confirmed by X-ray analysis. The P-hydroxy adduct was also prepared, and it was found that intermolecular O H … O hydrogen bonding connects the molecules together in the solid phase. This effect eliminates the possibility of diastereoisomerism, as was also observed in the case of P-hydroxy tetrahydrophosphinine oxides. Thermolysis of the P-hydroxy adduct is a better way to synthesize 1-hydroxy-1,2-dihydrophosphinine oxides than by hydrolysis of the phosphinic chlorides.