Hydrogen bonded rings,chains and lassos: the case of t-butyl alcohol clusters

Infrared OH stretching spectra of hydrogen bonded 2-methyl-propan-2-01 (t-butyl alcohol) clusters are investigated by ragout-jet FTIR spectroscopy. A spectral difference technique is used to discriminate approximately between neighbouring cluster sizes. Dimers, trimers and cyclic tetramers can be detected along with larger clusters, which exhibit a surprisingly structured vibrational fingerprint. Comparison is made to the spectra of related alcohols and to energetic and harmonic vibrational predictions from electronic structure calculations. The experimentally observed 32% increase in OH stretching wavenumber shift from methanol dimer to t-butyl alcohol dimer is reproduced at the HF/3-21G level (+ 33%). It is also qualitatively correct at the MP2/6-31 +G* level (+ l5%), whereas it has the wrong sign at the B3LYP/6-31+ G* level (5%) and is negligible at the HF/6-31+ G* level, disregarding anharmonic effects. The cyclic tetramer of t-butyl alcohol is found to be particularly stable due to a favourable updown alternation of the bulky t-butyl groups. Beyond the t-butyl alcohol tetramer, lasso structures are found to be energetically competitive with simple ring structures. A many-body decomposition shows that this is due to a reduced cooperativity in the sterically hindered pentamer ring. The resulting thermodynamic and kinetic relevance of cyclic tetramers is discussed.     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

On stability radii of infinite-dimensional time-varying discrete--time systems

This note introduces a stability radius for discrete–timelinear time–varying systems on Banach spaces under structuredtime–varying perturbations of multiple–output feedbacktype. Additive perturbations are considered which can be representedas a series of infinitely many perturbation terms. We derivecounterparts to some results established for time–varyingdifferentiable systems in [5, 7] and apply the results to periodicsystems.     

o-Terphenyl: flips of the end rings in the crystal phase

We demonstrate by selective saturation deuteron NMR experiments on a crystal of selectively deuterated o-terphenyl (OTP) that both end rings I and II attached to the central ring undergo thermally activated flip motions. In crystals of OTP, the end rings I and II are not symmetry related, their dynamics can be different and, in fact, is different, although mutual steric hindrance of the rings suggests a strong correlation. We measured the rates k _I and k _II of the flips of both end rings I and II as a function of temperature. We find that, independent of the temperature, k _I exceeds k _II by roughly a factor of 100. This result excludes correlated flips of rings I and II in the sense that a flip of one ring necessarily entails a flip of the other. The activation energies E_aI and E_aII of the two flip processes turn out to be equal (80.5 kJ mol^?1) within experimental errors. This is taken as a hint that the flips are, after all, related to each other. A mechanism is proposed of how this is possible under the constraint k _I » k _II.     

Determining Knotsw and Links by Cyclic Branched Coverings

It is well known that different knots or links in the 3-sphere can have homeomorphic n-fold cyclic branched coverings. We consider the following problem: for which values of nis a knot of link determined by itsn-fold cyclic branched covering? We consider the class of hyperbolic resp.2π/n-hyperbolic links. The isometry or symmetry groups of such links are finite, and their n-fold branched coverings are hyperbolic 3-manifolds. Our main result states that if ndoes not divide the order of the finite symmetry group of such a link, then the link is determined by its n-fold branched covering. In a sense, the result is best possible; the key argument of its proof is algebraic using some basic result about finite p-groups. The main result applies, for example, to the cyclic branched coverings of the 2-bridge links; in particular, it gives a classification of the maximally symmetricD₆-manifolds which are exactly the 3-fold branched coverings of the 2-bridge links.     

Deuterium—carbon multiple-quantum NMR in liquid crystals: polarization transfer and off-magic-angle spinning

The polarization transfer dynamics in a recently introduced deuterium—carbon NMR correlation method is studied, both theoretically and experimentally. The technique, which exploits heteronuclear multiple-quantum coherences, is useful for measuring and assigning ²H quad-rupolar couplings in ordered media. It is also shown that the experiment is suitable for implementation under off-magic-angle spinning conditions. The approach is demonstrated on a perdeuterated liquid crystal.     

Fairness Norms Can Explain the Emergence of Specific Cooperation Norms in the Battle of the Prisoner's Dilemma

Cooperation norms often emerge in situations, where the long term collective benefits help to overcome short run individual interests, for instance in repeated Prisoner's Dilemma (PD) situations. Often, however, there are different paths to cooperation, benefiting different kinds of actors to different degrees. This leads to payoff asymmetries even in the state of cooperation, and consequently can give rise to normative conflicts about which norms should be in place. This norm coordination problem will be modeled as a Battle of the Sexes game (BoS) with different degrees of asymmetry in payoffs. I combine the PD and the BoS to the 3 × 3 Battle of the Prisoner's Dilemma (BOPD) with several asymmetric cooperative and 1 noncooperative equilibria. Game theoretical and “behavioral” predictions are derived about the kind of norms that are likely to emerge under different shadows of the future and degrees of asymmetry and tested in a lab experiment. The experimental data show that game theory fairly well predicts the basic main effects of the experimental manipulations but “behavioral” predictions perform better in describing the equilibrium selection process of emerging norms.     

13C NMR of tunnelling methyl groups

The dipolar interactions between the protons and the central ¹³C nucleus of a ¹³CH₃ group are used to study rotational tunnelling and incoherent dynamics of such groups in molecular solids. Single-crystal ¹³C NMR spectra are derived for arbitrary values of the tunnel frequency ν_t. Similarities to ESR and ²H NMR are pointed out. The method is applied to three different materials. In the hydroquinone/acetonitrile clathrate, the unique features in the ¹³C NMR spectra which arise from tunnelling with a tunnel frequency that is much larger than the dipolar coupling between the methyl protons and the ¹³C nucleus are demonstrated, and the effects of incoherent dynamics are studied. The broadening of the ¹³C resonances is related to the width of the quasi-elastic line in neutron scattering. Selective magnetization transfer experiments for studying slow incoherent dynamics are proposed. For the strongly hindered methyl groups of L-alanine, an upper limit for ν_t is derived from the ¹³C NMR spectrum. In aspirin? (acetylsalicylic acid), incoherent reorientations dominate the spectra down to the lowest temperatures studied; their rate apparently increases with decreasing temperature below 25 K.