On an effective solution of the optimal stopping problem for random walks

We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial associated with the maximum of the random walk. It is also shown that a value function of the optimal stopping problem on the finite interval {0, 1, . . . , T} converges with an exponential rate as T → ∞ to the limit under the assumption that jumps of the random walk are exponentially bounded

Structural effects in UO2_2 thin films irradiated with fission-energy Xe ions

Uranium dioxide thin films have been successfully grown on LSAT (Al$_{10}$La$_3$O$_{51}$Sr$_{14}$Ta$_7$) substrates by reactive magnetron sputtering. Irradiation by 92 MeV $^{129}$Xe$^{23+}$ ions to simulate fission damage that occurs within nuclear fuels caused microstructural and crystallographic changes. Initially flat and continuous thin films were produced by magnetron sputtering with a root mean square roughness of 0.35 nm determined by AFM. After irradiation, this roughness increased to 60-70 nm, with the films developing discrete microstructural features: small grains (~3 $\mu$m), along with larger circular (up to 40 $\mu$m) and linear formations with non-uniform composition according to the SEM, AFM and EDX results. The irradiation caused significant restructuring of the UO$_2$ films that was manifested in significant filmsubstrate mixing, observed through EDX analysis. Diffusion of Al from the substrate into the film in unirradiated samples was also observed.Engineering and Physical Sciences Research Council (Grant ID: EP/ I036400/1), Radioactive Waste Management Ltd (formerly the Radioactive Waste Management Directorate of the UK Nuclear Decommissioning Authority, contract NPO004411A-EPS02), Russian Foundation for Basic Research (projects 13-03-90916), CSAR, Grand Accelélérateur National d’Ions Lourds (GANIL) Caen France, French Network EMIR, CIMAP-CIRIL, M.V.Lomonosov Moscow State University Program of Development, CKP FMI IPCE RA

Quantifying the efficiency of hydroxyapatite mineralising peptides

We present a non-destructive analytical calibration tool to allow quantitative assessment of individual calcium phosphates such as hydroxyapatite (HAP) from mixtures including brushite. Many experimental approaches are used to evaluate the mineralising capabilities of biomolecules including peptides. However, it is difficult to quantitatively compare the efficacy of peptides in the promotion of mineralisation when inseparable mixtures of different minerals are produced. To address this challenge, a series of hydroxyapatite and brushite mixtures were produced as a percent/weight (0–100%) from pure components and multiple (N=10) XRD patterns were collected for each mixture. A linear relationship between the ratio of selected peak heights and the molar ratio was found. Using this method, the mineralising capabilities of three known hydroxyapatite binding peptides, CaP(S) STLPIPHEFSRE, CaP(V) VTKHLNQISQSY and CaP(H) SVSVGMKPSPRP, was compared. All three directed mineralisation towards hydroxyapatite in a peptide concentration dependent manner. CaP(V) was most effective at inducing hydroxyapatite formation at higher reagent levels (Ca2+ = 200mM), as also seen with peptide-silk chimeric materials, whereas CaP(S) was most effective when lower concentrations of calcium (20mM) and phosphate were used. The approach can be extended to investigate HAP mineralisation in the presence of any number of mineralisation promoters or inhibitors

Ion implantation in nanodiamonds: Size effect and energy dependence

Nanoparticles are ubiquitous in nature and are increasingly important for technology. They are subject to bombardment by ionizing radiation in a diverse range of environments. In particular, nanodiamonds represent a variety of nanoparticles of significant fundamental and applied interest. Here we present a combined experimental and computational study of the behaviour of nanodiamonds under irradiation by xenon ions. Unexpectedly, we observed a pronounced size effect on the radiation resistance of the nanodiamonds: particles larger than 8 nm behave similarly to macroscopic diamond (i.e. characterized by high radiation resistance) whereas smaller particles can be completely destroyed by a single impact from an ion in a defined energy range. This latter observation is explained by extreme heating of the nanodiamonds by the penetrating ion. The obtained results are not limited to nanodiamonds, making them of interest for several fields, putting constraints on processes for the controlled modification of nanodiamonds, on the survival of dust in astrophysical environments, and on the behaviour of actinides released from nuclear waste into the environment

Tuning the Reactivity of Nanoenergetic Gas Generators Based on Bismuth and Iodine oxidizers

There is a growing interest on novel energetic materials called Nanoenergetic Gas- Generators (NGGs) which are potential alternatives to traditional energetic materials including pyrotechnics, propellants, primers and solid rocket fuels. NGGs are formulations that utilize metal powders as a fuel and oxides or hydroxides as oxidizers that can rapidly release large amount of heat and gaseous products to generate shock waves. The heat and pressure discharge, impact sensitivity, long term stability and other critical properties depend on the particle size and shape, as well as assembling procedure and intermixing degree between the components. The extremely high energy density and the ability to tune the dynamic properties of the energetic system makes NGGs ideal candidates to dilute or replace traditional energetic materials for emerging applications. In terms of energy density, performance and controllability of dynamic properties, the energetic materials based on bismuth and iodine compounds are exceptional among the NGGs. The thermodynamic calculations and experimental study confirm that NGGs based on iodine and bismuth compounds mixed with aluminum nanoparticles are the most powerful formulations to date and can be used potentially in microthrusters technology with high thrust-to-weight ratio with controlled combustion and exhaust velocity for space applications. The resulting nano thermites generated significant value of pressure discharge up to 14.8 kPa m3/g. They can also be integrated with carbon nanotubes to form laminar composite yarns with high power actuation of up to 4700 W/kg, or be used in other emerging applications such as biocidal agents to effectively destroy harmful bacteria in seconds, with 22 mg/m2 minimal content over infected area

Drug dosing during pregnancy—opportunities for physiologically based pharmacokinetic models

Drugs can have harmful effects on the embryo or the fetus at any point during pregnancy. Not all the damaging effects of intrauterine exposure to drugs are obvious at birth, some may only manifest later in life. Thus, drugs should be prescribed in pregnancy only if the expected benefit to the mother is thought to be greater than the risk to the fetus. Dosing of drugs during pregnancy is often empirically determined and based upon evidence from studies of non-pregnant subjects, which may lead to suboptimal dosing, particularly during the third trimester. This review collates examples of drugs with known recommendations for dose adjustment during pregnancy, in addition to providing an example of the potential use of PBPK models in dose adjustment recommendation during pregnancy within the context of drug-drug interactions. For many drugs, such as antidepressants and antiretroviral drugs, dose adjustment has been recommended based on pharmacokinetic studies demonstrating a reduction in drug concentrations. However, there is relatively limited (and sometimes inconsistent) information regarding the clinical impact of these pharmacokinetic changes during pregnancy and the effect of subsequent dose adjustments. Examples of using pregnancy PBPK models to predict feto-maternal drug exposures and their applications to facilitate and guide dose assessment throughout gestation are discussed