Sequential monitoring of a Bernoulli sequence when the pre-change parameter is unknown

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world situations: (1) the pre-change value of the Bernoulli parameter is known in advance, (2) computational efficiency is not paramount, and (3) enough observations occur between change points to allow asymptotic approximations to be used. We develop a novel change detection method based on Fisher’s exact test which does not make any of these assumptions. We show that our method can be implemented in a computationally efficient manner, and is hence suited to sequential monitoring where new observations are constantly being received over time. We assess our method’s performance empirically via using simulated data, and find that it is comparable to the optimal CUSUM scheme which assumes both pre- and post-change values of the parameter to be known.     

Towards the design of novel boron‐ and nitrogen‐substituted ammonia‐borane and bifunctional arene ruthenium catalysts for hydrogen storage

Electronic‐structure density functional theory calculations have been performed to construct the potential energy surface for H₂ release from ammonia‐borane, with a novel bifunctional cationic ruthenium catalyst based on the sterically bulky β‐diketiminato ligand (Schreiber et al., ACS Catal. 2012, 2, 2505). The focus is on identifying both a suitable substitution pattern for ammonia‐borane optimized for chemical hydrogen storage and allowing for low‐energy dehydrogenation. The interaction of ammonia‐borane, and related substituted ammonia‐boranes, with a bifunctional η⁶‐arene ruthenium catalyst and associated variants is investigated for dehydrogenation. Interestingly, in a number of cases, hydride‐proton transfer from the substituted ammonia‐borane to the catalyst undergoes a barrier‐less process in the gas phase, with rapid formation of hydrogenated catalyst in the gas phase. Amongst the catalysts considered, N,N‐difluoro ammonia‐borane and N‐phenyl ammonia‐borane systems resulted in negative activation energy barriers. However, these types of ammonia‐boranes are inherently thermodynamically unstable and undergo barrierless decay in the gas phase. Apart from N,N‐difluoro ammonia‐borane, the interaction between different types of catalyst and ammonia borane was modeled in the solvent phase, revealing free‐energy barriers slightly higher than those in the gas phase. Amongst the various potential candidate Ru‐complexes screened, few are found to differ in terms of efficiency for the dehydrogenation (rate‐limiting) step. To model dehydrogenation more accurately, a selection of explicit protic solvent molecules was considered, with the goal of lowering energy barriers for H‐H recombination. It was found that primary (1°), 2°, and 3° alcohols are the most suitable to enhance reaction rate. © 2014 Wiley Periodicals, Inc.     

The Copper Mediated Barbier Reactions of α,β-Unsaturated Ketones: Regioselective Conjugate and 1,2-Addition

The one-pot reaction of isophorone and other α, β,-unsaturated ketones with alkyl and aryl halides in the presence of magnesium and a copper salt (“Barbier” conditions) leads to the regiospecific formation of 1,4-addition products; the use of lithium leads to regioselective 1,2-addition.     

Nucleation kinetics of paracetamol–ethanol solutions from metastable zone widths

A study of the nucleation kinetics for a cooling crystallisation of paracetamol–ethanol solutions in a batch reactor is described in this paper. Metastable zone width (MSZW) experiments were conducted in order to estimate the nucleation kinetics of the system. Measured MSZWs can be affected by numerous process parameters, such as cooling rate, concentration, agitation rate, and working volume. Two theoretical approaches were employed to estimate the nucleation kinetics, the classical mass based approach of Nývlt, and a more recent approach by Kubota, which also considers number density. Both approaches were found to produce similar estimates for the nucleation rates of the paracetamol–ethanol solutions as a function of supersaturation for an assumed nucleus size of 10 μm. The theory of Kubota was found to predict satisfactory estimates for the induction time of the nucleation process from MSZW data. The induction time was observed to be independent of the solution temperature as suggested by Kubota’s theory. This is a novel finding and serves to validate the induction time theory of Kubota. In this investigation, MSZWs were observed to decrease with increased levels of agitation and found to be independent of working volume.     

Estimation of zeta potentials of titania nanoparticles by molecular simulation

Non-equilibrium molecular dynamics (NEMD) simulations have been performed for static electric fields for a range of positively charged spherical rutile-titania nanoparticles with radii of 1.5 to 2.9 nm for two different salt concentrations in water, in order to simulate electrophoresis directly. Using the observed limiting drag velocities, Helmholtz-Smoluchowski (HS) theory was used to estimate their ζ potentials. These estimates were compared to values from numerical solution of the non-linear Poisson-Boltzmann (PB) equation for representative configurations of the nanoparticles, in addition to idealised analytic and Debye-Hückel (DH) solutions about spherical particles of the same geometry and charge state, for the given salt concentrations. It was found that reasonable agreement was obtained between the various approaches, with the NEMD-HS results some 15%-15% smaller than the numerical PB results for more highly charged nanoparticles.     

In Situ Synchrotron X-ray Diffraction Studies of Hydrogen-Desorption Properties of 2LiBH4–Mg2FeH6 Composite

Adding a secondary complex metal hydride can either kinetically or thermodynamically facilitate dehydrogenation reactions. Adding Mg₂FeH₆ to LiBH₄ is energetically favoured, since FeB and MgB₂ are formed as stable intermediate compounds during dehydrogenation reactions. Such “hydride destabilisation” enhances H₂-release thermodynamics from H₂-storage materials. Samples of the LiBH₄ and Mg₂FeH₆ with a 2:1 molar ratio were mixed and decomposed under three different conditions (dynamic decomposition under vacuum, dynamic decomposition under a hydrogen atmosphere, and isothermal decomposition). In situ synchrotron X-ray diffraction results revealed the influence of decomposition conditions on the selected reaction path. Dynamic decomposition of Mg₂FeH₆–LiBH₄ under vacuum, or isothermal decomposition at low temperatures, was found to induce pure decomposition of LiBH₄, whilst mixed decomposition of LiBH₄ + Mg and formation of MgB₂ were achieved via high-temperature isothermal dehydrogenation.     

A parameter-uniform Schwarz method for a coupled system of reaction–diffusion equations

We consider an arbitrarily sized coupled system of one-dimensional reaction–diffusion problems that are singularly perturbed in nature. We describe an algorithm that uses a discrete Schwarz method on three overlapping subdomains, extending the method in [H. MacMullen, J.J.H. Miller, E. O’Riordan, G.I. Shishkin, A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers, J. Comput. Appl. Math. 130 (2001) 231–244] to a coupled system. On each subdomain we use a standard finite difference operator on a uniform mesh. We prove that when appropriate subdomains are used the method produces ε-uniform results. Furthermore we improve upon the analysis of the above-mentioned reference to show that, for small ε, just one iteration is required to achieve the expected accuracy.     

Global existence of time-dependent Yang-Mills-Higgs monopoles

We study the Cauchy problem for non-abelian Yang-Mills-Higgs theory in (3+1)-dimensional Minkowski spacetime. With suitable conditions on the background fields and a suitable choice of a Sobolev space for the subtracted gauge potentials and the Higgs field, we establish local existence. We then prove global existence by showing that an appropriate norm of the solutions cannot blow up in a finite time.     

Gravitational potentials: A constructive approach to general relativity

Recent investigations of the initial-value problem of general relativity have shown that the initial-value constraints can be formulated in all cases as a system of elliptic equations with well-defined physical and mathematical properties. The solutions of these equations can be regarded as generalized gravitational potentials. These potentials are interrelated and depend on their sources quasilinearly. They are particularly useful in analyzing asymptotically flat solutions of Einstein's equations. We have found from these results (1) a technique for constructing physically meaningful initial data in the integration of Einstein's equations, and (2) a method for characterization and analysis of the spacelike mass, momentum, angular momemtum, and multipole moments of gravitational fields.This essay received the third award from the Gravity Research Foundation for the year 1975. (Editor.)The research for this paper was partially supported by National Science Foundation grant GP43909 awarded to the University of North Carolina, Chapel Hill, North Carolina.     

Dynamical and energetic properties of hydrogen and hydrogen-tetrahydrofuran clathrate hydrates

Classical equilibrium molecular dynamics (MD) simulations have been performed to investigate the dynamical and energetic properties in hydrogen and mixed hydrogen-tetrahydrofuran sII hydrates at 30 and 200 K and 0.05 kbar, and also at intermediate temperatures, using SPC/E and TIP4P-2005 water models. The potential model is found to have a large impact on overall density, with the TIP4P-2005 systems being on average 1% more dense than their SPC/E counterparts, due to the greater guest-host interaction energy. For the lightly-filled mixed H(2)-THF system, in which there is single H(2) occupation of the small cage (1s1l), we find that the largest contribution to the interaction energy of both types of guest is the van der Waals component with the surrounding water molecules in the constituent cavities. For the more densely-filled mixed H(2)-THF system, in which there is double H(2) occupation in the small cage (2s1l), we find that there is no dominant component (i.e., van der Waals or Coulombic) in the H(2) interaction energy with the rest of the system, but for the THF molecules, the dominant contribution is again the van der Waals interaction with the surrounding cage-water molecules; again, the Coulombic component increases in importance with increasing temperature. The lightly-filled pure H(2) hydrate (1s4l) system exhibits a similar pattern vis-à-vis the H(2) interaction energy as for the lightly-filled mixed H(2)-THF system, and for the more densely-filled pure H(2) system (2s4l), there is no dominant component of interaction energy, due to the multiple occupancy of the cavities. By consideration of Kubic harmonics, there is some evidence of preferential alignment of the THF molecules, particularly at 200 K; this was found to arise at higher temperatures due to transient hydrogen bonding of the oxygen atom in THF molecules with the surrounding cage-water molecules.