Shock waves in colliding nuclei

We consider the circumstances under which nuclear matter at high densities can be produced in heavy ion collisions. We argue that lab energies of a few hundred MeV per nucleon will be suitable : the matter velocity will exceed the speed of isentropic compression waves, while the nuclear matter has sufficient stopping power to generate a shock front. From the hydrodynamic conservation laws we show that there is a maximum attainable compression ratio ν_∞, determined by the thermal properties of the high-density matter. In an independent-fermion model, ν_∞ = 4, but it can be much larger if the phase of the system changes, for example by excitation of nucleon isobars, production of π-mesons, or the scalar-field condensation conjectured by Lee and Wick. We discuss the propagation of the shock front and subsequent decompression of the dense, hot matter.     

A probabilistically attained set of polynomials that generate stirling numbers of the second kind

Using probabilistic arguments, we derive a sequence of polynomials in one variable which generate the Stirling numbers of the second kind. Specifically, S^m_c=(c!/m!)P_c-m(c), where S^m_c is the desired Stirling number and P_c-m(·) is the polynomial of degree c-m.     

Nanoscale Structuring of Surfaces by Using Atomic Layer Deposition

Controlled structuring of surfaces is interesting for a wide variety of areas, including microelectronic device fabrication, optical devices, bio(sensing), (electro‐, photo)catalysis, batteries, solar cells, fuel cells, and sorption. A unique feature of atomic layer deposition (ALD) is the possibility to form conformal uniform coatings on arbitrarily shaped materials with controlled atomic‐scale thickness. In this Minireview, we discuss the potential of ALD for the nanoscale structuring of surfaces, highlighting its versatile application to structuring both planar substrates and powder materials. Recent progress in the application of ALD to porous substrates has even made the nanoscale structuring of high‐surface‐area materials now feasible, thereby enabling novel applications, such as those in the fields of catalysis and alternative energy.     

Controlled excitations of the Belousov-Zhabotinsky reaction: Experimental procedures

The purpose of this research was to explore the unstirred, ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction as an experimental model for the response of excitable media to small perturbations (slightly larger than the threshold for excitations). Following Showalter et al. (Showalter, K.; Noyes, R. M.; Turner, H. J.Am. Chem. Soc. 1979, 101, 7463-69), we used a positively biased silver electrode to release silver ions into a BZ reaction mixture, removing bromide ions and causing an excitation if sufficient bromide was removed. We found (1) a scaling region in which the delay before activation increased linearly as the size of the perturbation decreased, qualitatively consistent with but not fully explained by the Oregonator of Field et al. (Field, R. J.; K?r?s, E.; Noyes, R. M. J. Am. Chem. Soc. 1972, 94, 8649-64); (2) evidence for a 10 s oligomerization time scale; and (3) that activations were always delayed until after the end of a pulse of current, with the delay essentially constant for sufficiently long pulses, an effect not seen in simple ODE models but consistent with the anomalously large current apparently required for activation (Showalter, K.; Noyes, R. M. J. Am. Chem. Soc. 1976, 98, 3730-31) and explainable by bromide transport. Overall, the BZ system appeared to be well-suited as an experimental prototype, despite its complexity.     

Erdalkalien

Ohne Zusammenfassung     

Stickstoffbestimmung

Ohne Zusammenfassung     

Discounting axioms imply risk neutrality

Although most applications of discounting occur in risky settings, the best-known axiomatic justifications are deterministic. This paper provides an axiomatic rationale for discounting in a stochastic framework. Consider a representation of time and risk preferences with a binary relation on a real vector space of vector-valued discrete-time stochastic processes on a probability space. Four axioms imply that there are unique discount factors such that preferences among stochastic processes correspond to preferences among present value random vectors. The familiar axioms are weak ordering, continuity and nontriviality. The fourth axiom, decomposition, is non-standard and key. These axioms and the converse of decomposition are assumed in previous axiomatic justifications for discounting with nonlinear intraperiod utility functions in deterministic frameworks. Thus, the results here provide the weakest known sufficient conditions for discounting in deterministic or stochastic settings. In addition to the four axioms, if there exists a von Neumann-Morgenstern utility function corresponding to the binary relation, then that function is risk neutral (i.e., affine). In this sense, discounting axioms imply risk neutrality.