Extreme value estimation for discretely sampled continuous processes

In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process. In practice, however, the processes are typically only observed at discrete points and one has to resort to interpolation to fill in the gaps. We discuss the influence of such an interpolation on estimators of marginal parameters as well as estimators of the exponent measure. In particular, natural conditions on the fineness of the observational scheme are developed which ensure that asymptotically the interpolated estimators behave in the same way as the estimators which use fully observed continuous processes.     

The dynamics of functioning investigating societal transitions with partial differential equations

In this article a mathematical framework is introduced and explored for the study of processes in societal transitions. A transition is conceptualised as a fundamental shift in the functioning of a societal system. The framework views functioning as a real-valued field defined upon a real variable. The initial status quo prior to a transition is captured in a field called the regime and the alternative that possibly takes over is represented in a field called a niche. Think for example of a transition in an energy supply system, where the regime could be centrally produced, fossil fuel based energy supply and a niche decentralised renewable energy production. The article then proceeds to translate theoretical notions on the interactions and dynamics of regimes and niches from transition literature into the language of this framework. This is subsequently elaborated in some simple models and studied analytically or by means of computer simulation.

An incremental mean first passage analysis for a quasistatic model of polymer translocation through a nanopore

For the translocation of a polymer through a nanopore, a quasistatic assumption for the dynamics yields a tractable form for the entropic barrier. Although this is a much simplified model, interesting features such as robust scaling emerge from its application. To explore these details, we present a method of mapping the translocation process as an incremental mean first passage problem. In this approach, the quantity of interest is the average first time t(0) at which the polymer achieves a displacement of Δs in the translocation coordinate s. Constructing scenarios with different initial conditions and boundary conditions, analytic and exact numerical approaches are used to resolve the dynamics of translocation in detail and generate new insight into the nature of the entropic barrier.     

LLE data for the ionic liquid 3-methyl-N-butyl pyridinium dicyanamide with several aromatic and aliphatic hydrocarbons

(Liquid + liquid) equilibrium data for ternary systems of several aromatic and aliphatic hydrocarbons with the ionic liquid 3-methyl-N-butylpyridinium dicyanamide were determined at T = 303.15 K and 328.15 K and atmospheric pressure. As aromatics benzene, cumene and p-xylene have been chosen, as paraffins n-hexane and n-nonane were used. The experimental data were regressed and could be adequately correlated with the NRTL model. A logical order in the extraction capacity of 3-methyl-N-butylpyridinium dicyanamide for the different aromatics is obtained: benzene > p-xylene > cumene.     

Variable time lag and backward ejection in full-dimensional analysis of strong-field double ionization

Ensembles of 400,000 two-electron trajectories in three space dimensions are used with Newtonian equations of motion to track atomic double ionization under very strong laser fields. We report a variable time lag between e-e collision and double ionization, and find that the time lag plays a key role in the emergence directions of the electrons. These are precursors to production of electron momentum distributions showing substantial new agreement with experimental data.     

Direct measurement of energetic electrons coupling to an imploding low-adiabat inertial confinement fusion capsule

We have imaged hard x-ray (>100 keV) bremsstrahlung emission from energetic electrons slowing in a plastic ablator shell during indirectly driven implosions at the National Ignition Facility. We measure 570 J in electrons with E>100 keV impinging on the fusion capsule under ignition drive conditions. This translates into an acceptable increase in the adiabat α, defined as the ratio of total deuterium-tritium fuel pressure to Fermi pressure, of 3.5%. The hard x-ray observables are consistent with detailed radiative-hydrodynamics simulations, including the sourcing and transport of these high energy electrons.     

Temperature effects on 13C n.m.r. chemical shifts of normal alkanes and some line r and branched 1-alkenes

¹³C n.m.r. chemical shifts of a number of 1,1-disubstituted ethylenes are presented. Moreover, effects of changing temperatures on the ¹³C n.m.r. chemical shifts of some of these compounds as well as of three normal alkanes are given. These variations in chemical shifts are attributed to varying amounts of sterically induced shifts in the different conformational equilibria. In addition to the well-known 1,4 interaction between two alkyl groups shielding effects on the carbon atoms of the connecting bonds are also proposed. No definite explanation of this effect is presented at this time. It is further shown that no simple correlations exist between ¹³C n.m.r. chemical shifts and calculated total charge densities at this level. Instead, the experimental results in 1-alkenes are rationalized by assuming a linear dependence of the ¹³C n.m.r. chemical shifts of C-1 and C-2 via rehybridizations on changes in bond angles for small skeletal deformations caused by steric interactions. These changes in geometries, as well as conformational energies in three 1-alkenes, were calculated by means of VFF calculations. Finally. upfield shifts for both C-2 and C-4 are proposed for those conformations of 1-alkenes in which the C-3? C-4 group interacts with the p_z-orbital of C-2.     

On the observation closest to the origin

Out of n i.i.d. random vectors in $\text{R}$^d let X¹_n be the one closest to the origin. We show that X¹_n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation. The result is then applied to a problem of density estimation.     

Deactivation with silazanes in chromatography,mechanism of the reaction and practical consequences in capillary GC and RP-HPLC: A29Si CP-MAS NMR study

The reaction of Cab-O-Sil, a highly dispersed vitreous quartz, with hexamethyldisilazane (HMDS) was studied in the temperature range 380–500°C, using ²⁹Si solid state NMR and other techniques. Such studies are of importance in view of deactivation procedures of fused silica at high temperatures in capillary GC. The commonly accepted reaction equation: predominates only below ca. 400°C. Above ca. 400°C the intermediate cleavage product Me₃SiNH₂ reacts with surface silanol groups to form ?SioSiMe₂NH₂ + CH₄. At higher temperatures these groups may ultimately form (?SiO)₃SiNH₂ groups (analogously to the formation of bi-and tridentate linkages starting from ?SiOSiMe₃ groups), but (?SiO)₃SiNH₂ groups are also directly formed at lower temperatures, simultaneously with the ?SiOSiMe₃ groups, probably by reaction with siloxane bridges: . The reactions of the trimethylsilylamine part of HMDS with Cab-O-Sil were confirmed by an independent series of silylations using N,N-dimethyltrimethylsilylamine instead of HDMS. The presence of amino groups as ?SiNH₂ was confirmed by FT-IR. This may be one of the reasons why very high temperature silylation with disilazanes does not provide a satisfactory deactivation of fused silica GC columns: the active ?SiOH groups are “replaced” by active ?SiNH₂ groups. However, such a material may be of interest in LC. Silylation with silazanes at ca. 350°C in humid atmosphere and/or after extensive hydroxylation (leaching) of the surface should yield sufficiently deactivated surfaces with a rather well defined surface structure.