Periodic points for onto cellular automata

Let φ be a one-dimensional surjective cellular automaton map. We prove that if φ is a closing map, then the configurations which are both spatially and temporally periodic are dense. (If φ is not a closing map, then we do not know whether the temporally periodic configurations must be dense.) The results are special cases of results for shifts of finite type, and the proofs use symbolic dynamical techniques.     

3D Dynamic analysis of soil–tool interaction using the finite element method

Previous experimental and finite element studies have shown the influence of both soil initial conditions and blade operating conditions on cutting forces. However, most of these finite element analyses (FEA) are limited to small blade displacements to reduce element distortion which can cause solution convergence problems. In this study a dynamic three-dimensional FEA of soil–tool interaction was carried out based on predefined failure surfaces to investigate the effect of cutting speed and angle on cutting forces over large blade displacements. Sandy soil was considered in this study and modeled using the hypoplastic constitutive model implemented in the commercial FEA package, ABAQUS. Results reveal the validity of the concept of predefined failure surfaces in simulating soil–tool interaction and the significant effect of cutting acceleration on cutting forces.     

Coherent optical control of the spin of a single hole in an InAs/GaAs quantum dot

We demonstrate coherent optical control of a single hole spin confined to an InAs/GaAs quantum dot. A superposition of hole-spin states is created by fast (10-100?ps) dissociation of a spin-polarized electron-hole pair. Full control of the hole spin is achieved by combining coherent rotations about two axes: Larmor precession of the hole spin about an external Voigt geometry magnetic field, and rotation about the optical axis due to the geometric phase shift induced by a picosecond laser pulse resonant with the hole-trion transition.     

The group theoretical approach to nuclear quadrupole resonance

The phenomenon of nuclear quadrupole resonance is presented from the grouptheoretical point of view. This approach allows one to discuss the splitting of the nuclear spin states without prior wave-mechanical calculation. Nuclear quadrupole moments are also compared with moecular quadrupole moments and the differences discussed. Finally the selection rules are deduced.     

Excitation dynamics of Rydberg states in C<Subscript>60</Subscript>

The electron and nuclear dynamics of C₆₀ fullerenes irradiated with femtosecond laser pulses are investigated with photoelectron and photoion spectroscopy. The focus of this work is the detailed exploration of the population mechanism of Rydberg levels within the excitation process of neutral C₆₀. The effect of excitation wavelength, intensity, chirp, and polarization on the kinetic energy distribution of photoelectrons in single-pulse experiments gives first insight into the underlying processes. In combination with time-resolved two-color pump-probe spectroscopy depending on either pump, or probe pulse intensity, a more complete picture of the interaction can be drawn. The results point towards a very interesting but nevertheless complex behavior including four steps: (i) non-adiabatic multielectron excitation of the HOMO (h_u) → LUMO+1 (t_1g) transition; (ii) thermalization within the hot electron cloud on a time scale below 100 fs, followed by a coupling of energy to vibrational modes of the molecule via doorway state(s); (iii) population of electronically excited Rydberg states by multiphoton absorption, and (iv) single photon ionization from the excited Rydberg states. This excitation process results in a characteristic sequence of photoelectron lines in the photoemission spectra. The comparison of the experimental results with recent theoretical work gives convincing evidence that non-adiabatic multielectron dynamics (NMED) plays a key role for the understanding of the response of C₆₀ to short-pulse laser radiation.     

A new synthesis of difluoromethanesulfonamides--a novel pharmacophore for carbonic anhydrase inhibition

Preparation of the key intermediate carboxydifluoromethanesulfonamide provides direct synthetic access to a wide range of novel difluoromethanesulfonamides, including the acetazolamide analogue (2-ethanoylamino-1,3,4-thiadiazol-5-yl)-difluoromethanesulfonamide. Their water solubility and stability, ether partition coefficient, pK(a) and submicromolar dissociation constants for human carbonic anhydrase isozyme II (HCA II) make them promising candidates for topical glaucoma therapy.     

Trends in exchange coupling for trimethylenemethane-type Bis(semiquinone) biradicals and correlation of magnetic exchange with mixed valency for cross-conjugated systems

A magnetostructural correlation (conformational electron spin exchange modulation) within an isostructural series of biradical complexes is presented. X-ray crystal structures, variable-temperature electron paramagnetic resonance spectroscopy, zero-field splitting parameters, and variable-temperature magnetic susceptibility measurements were used to evaluate molecular conformation and electron spin exchange coupling in this series of molecules. Our combined results indicate that the ferromagnetic portion of the exchange couplings occurs via the cross-conjugated pi-systems, while the antiferromagnetic portion occurs through space and is equivalent to incipient bond formation. Thus, molecular conformation controls the relative amounts of ferro- and antiferromagnetic contributions to exchange coupling. In fact, the exchange parameter correlates with average semiquinone ring torsion angles via a Karplus-Conroy-type relation. Because of the natural connection between electron spin exchange coupling and electronic coupling related to electron transfer, we also correlate the exchange parameters in the biradical complexes to mixed valency in the corresponding quinone-semiquinone radical anions. Our results suggest that delocalization in the cross-conjugated, mixed-valent radical anions is proportional to the ferromagnetic contribution to the exchange coupling in the biradical oxidation states.     

From clusters to ionic complexes: structurally characterized thallium titanium double alkoxides

A series of sterically varied titanium alkoxides [[Ti(OR)(4)](n)(), n = 4, OR = OCH(2)CH(3) (OEt); n = 1, OCH(CH(3))(2) (OPr(i)); n = 2, OCH(2)C(CH(3))(3) (ONep); n = 1, OC(6)H(3)(CH(3))(2)-2,6 (DMP)] were reacted with a series of thallium alkoxides [[Tl(OR)](x) (x = 4, OR = OEt, ONep; n = infinity, DMP)]. The resultant products of the [Tl(mu(3)-OEt)](4)-modified [Ti(OR)(4)](n)() (OR = OEt, OPr(i), ONep) were found by X-ray analysis to be Tl(4)Ti(2)(mu-O)(mu(3)-OEt)(8)(OEt)(2) (1), Tl(4)Ti(2)(mu-O)(mu(3)-OPr(i))(5)(mu(3)-OEt)(3)(OEt)(2) (2), and TlTi(2)(mu(3)-OEt)(2)(mu-OEt)(mu-ONep)(2)(ONep)(4) (3), respectively. The reaction of [Tl(mu(3)-OEt)](4), 12HOEt, and 4[Ti(mu-ONep)ONep)(3)](2) to generate 3 in a higher yield resulted in the isolation of TlTi(2)(mu(3)-OEt)(mu(3)-ONep)(mu-OEt)(mu-ONep)(2)(ONep)(4) (4). Compounds 1 and 2 possess an octahedral (Oh) arrangement of two Ti and four Tl metal atoms around a mu-O central oxide atom (the Tl-O distance is too long to be considered a bond). For both compounds, each Ti atom adopts a distorted Oh geometry with one terminal OEt ligand. The Tl atoms are formally 4-coordinated, adopting a distorted pyramidal geometry using four mu(3)-OR (OR = OEt or OPr(i)) ligands to complete their coordination sphere. The Tl atoms reside approximately 1.4 A below the basal plane of oxygens. In contrast to these structures, both 3 and 4 utilize ONep ligands and display reduced oligomerization yielding trinuclear complexes without oxo formation. The two Ti cations are Oh, and the single Tl cation is in a formal distorted pyramidal (PYD) arrangement. If the lone pair of the Tl cations are considered in the geometry, each Tl adopts a square base pyramidal geometry. Two terminal ONep ligands are bound to each Ti with the remainder of the molecule consisting of mu(3)- and mu-ONep ligands. The reaction of [Tl(mu(3)-ONep)](4) with two equivalents of [Ti(mu-ONep)(ONep)(3)](2) also led to the isolation of the homoleptic trinuclear complex TlTi(2)(mu(3)-ONep)(2)(mu-ONep)(3)(ONep)(4) (5) which is analogous in structure to the mixed ligand species of 3 and 4. Each Ti is Oh coordinated with six ONep ligands, and the single Tl is PYD bound by ONep ligands. A further increase in the steric bulk of the pendant ligands, using [Tl(mu-DMP)](infinity) and [Ti(mu-ONep)(ONep)(3)](2), resulted in a further decrease in the nuclearity yielding the dinuclear species TlTi(mu-DMP)(mu-ONep)(DMP)(ONep)(2) (6). For 6, the two metals are bound by a mu-ONep and a mu-DMP ligand. The Tl metal center was solved in a bent geometry while the Ti adopted a distorted trigonal bipyramidal (TBP) geometry using three ONep and two DMP ligands to fill its coordination sphere. Further increasing the steric bulk of the ancillary ligands using Ti(DMP)(4) and [Tl(mu-DMP)](infinity) led to the formation of [Tl(+)][(-)(eta(2-3)-DMP)Ti(DMP)(4)] (7). The Ti metal center is in a TBP geometry, and the "naked" Tl cation resides unencumbered by solvent molecules but was found to have a strong pi-interaction with four DMP ligands of neighboring Ti(DMP)(5)(-) anions. For this novel set of compounds, (205)Tl NMR spectroscopy was used to investigate the solution behavior of these compounds. Multiple (205)Tl resonances were observed for the solution spectra of the crystalline material of 1-6, and a broad singlet was observed for 7. The large number of minor resonances noted for these compounds was attributed to sensitivity of the Tl cation based on small variations due to ligand rearrangement. However, the major resonance noted in the (205)Tl NMR solution spectra of 1-7 are in agreement with their respective solid-state structures.