Super‐ and Ferroelastic Organic Semiconductors for Ultraflexible Single‐Crystal Electronics

Like silicon, single crystals of organic semiconductors are pursued to attain intrinsic charge transport properties. However, they are intolerant to mechanical deformation, impeding their application in flexible electronic devices. Such contradictory properties, namely exceptional molecular ordering and mechanical flexibility, are unified in this work. We found that bis(triisopropylsilylethynyl)pentacene (TIPS‐P) crystals can undergo mechanically induced structural transitions to exhibit superelasticity and ferroelasticity. These properties arise from cooperative and correlated molecular displacements and rotations in response to mechanical stress. By utilizing a bending‐induced ferroelastic transition of TIPS‐P, flexible single‐crystal electronic devices were obtained that can tolerate strains (?) of more than 13 % while maintaining the charge carrier mobility of unstrained crystals (μ>0.7 μ₀). Our work will pave the way for high‐performance ultraflexible single‐crystal organic electronics for sensors, memories, and robotic applications.     

High-field MRS studies in brain slices

We are applying multi-nuclear high-field (500 MHz) MR spectroscopy of metabolising whole tissue preparations of the mammalian brain to studies on individual components of convulsions, which include prolonged depolarization, metabolic deprivation, and the effects of excitotoxins. The responses of glial cells and neurones can be partially distinguished by following labelling patterns of metabolic intermediates from ¹³C-labelled glucose or acetate (which enters only glial cells). This approach clearly confirmed our earlier indications that the metabolic response to depolarization (40 mM extracellular K⁺) occurs essentially in glial cells. Some evidence for metabolic shuttling between glia and neurones was obtained from the changes in C3/C4 ratios of glutamate and glutamine, and the C2/C3 of GABA. Mechanisms for metabolic support of neurones by glia may be of importance in neuronal protection under such metabolic stress as occurs in epilepsy. Changes in free intracellular divalent cations ([Ca²⁺]_i and [Zn²⁺]_i) were monitored using the ¹⁹F-MRS indicator, 5FBAPTA. Large increases in [Ca²⁺]_i and decreases in PCr were produced by excitotoxins (glutamate and NMDA), depolarization or ischaemia, but intracellular Zn²⁺ appeared only after exposure to the excitotoxins. The NMDA receptor blocker, MK801, removed all of the responses to NMDA, but only prevented the appearance of Zn²⁺ observed with glutamate. These results indicate that the damage caused to neurones by such insults as convulsions is not due simply to the presence of excessive excitotoxic glutamate.     

Isotopy Stable Dynamics Relative to Compact Invariant Sets

Let f be an orientation-preserving homeomorphism of a compactorientable manifold. Sufficient conditions are given for thepersistence of a collection of periodic points under isotopyof f relative to a compact invariant set A. Two main applicationsare described. In the first, A is the closure of a single discreteorbit of f, and f has a Smale horseshoe, all of whose periodicorbits persist; in the second, A is a minimal invariant Cantorset obtained as the limit of a sequence of nested periodic orbits,all of which are shown to persist under isotopy relative toA. 1991 Mathematics Subject Classification: 58F20, 58F15.     

Molecular structure and mass spectrum of dicarbonylbis(tetraphenylcyclobutadiene)molybdenum

The crystal structure on dicarbonylbis(tetraphenylcyclobutadiene)molybdenum has been determined from three-dimensional X-ray data collected by counter methods. The structure consists of monomeric units with each Mo atom bonded to two carbonyl and two Ph₄C₄ groups. Excluding phenyl substituents, the local symmetry about Mo is very nearly C_2υ. Both cyclobutadiene (CBD) groups are asymmetrically bonded to Mo, and the spread in Mo—C(CBD) distances (2.26 to 2.38 Å;) is significantly larger than that found with other structures containing substituted cyclobutadiene groups. The carbonyl groups show several short intramolecular C?C contacts with the cyclobutadiene C atoms (2.68 to 3.03 Å;) and with each other (2.63 Å;). They appear to be wedged between the Ph₄C₄ groups and to be responsible for the asymmetric bonding of the cyclobutadiene groups. The mass spectrum, which shows the characteristic fragmentation pattern of cyclobutadienemetal complexes, suggests a relatively high thermal stability for the title compound. Crystallographic data are as follows: space group P2₁/n; unit cell a 20.15(2), b 18.82(3), c 11.03(1) Å;, β 91.59(6)°; V 4181 Å;³; d_calc for Z = 4 is 1.380 and d_obs is 1.365(7) g/cm³. A total of 1659 reflections with F² ≥ 2σ were used to refine the structure to final values of R_F = 0.063 and R_wF = 0.041.     

The role of isomorphism in synthetic analysis. Pruning the search tree by finding disjoint isomorphic substructures

Isomorphism is an equivalence relation that is less stringent than identity (equality), and it is useful for synthetic analysis, since it allows one to find reflexive routes for targets even when they do not have an element of symmetry.     

The effect of the stability of mixed finite element approximations on the accuracy and rate of convergence of solution when solving incompressible flow problems

The stability of two different mixed finite element methods for incompressible flow problems are theoretically analysed. The effect of the stability of the mixed approximation on the accuracy and the rate of convergence of solution is assessed for two non-trivial problems. The numerical results presented indicate that if the stability of the mixed approximation is not guaranteed then both pressure and velocity solutions are markedly less accurate. In one of the cases considered the ultimate convergence of both the pressure and the velocity solutions is seriously in doubt.     

Pruning theory and Thurston’s classification of surface homeomorphisms

Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading– both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy. Received February 20, 2000 / final version received February 26, 2001?Published online May 29, 2001     

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.