Staggered ladder spectra

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd- and even-parity states. The ladders are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation corresponds, in the limit of weak damping, to a generalized Ornstein-Uhlenbeck process where the random force depends upon position as well as time. The process describes damped stochastic acceleration, and exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.     

Perturbation Theory for a Stochastic Process with Ornstein-Uhlenbeck Noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.     

A pulsed, optically-pumped rubidium laser at high pump intensity

A rubidium laser operating at 795 nm is optically pumped by a pulsed titanium sapphire laser to investigate the dynamics of Diode Pumped Alkali Lasers (DPALs). Linear scaling of output intensity for longitudinal excitation at intensities of 1.3-43 kW/cm² and as much as 32 times threshold is observed. The slope efficiency depends directly on the number of absorbed photons for alkali concentrations of 0.8-2.0 × 10¹³ atoms/cm³ with no evidence for second order kinetics. The effective absorption cross section is reduced in part by the broad spectral width of the pump source relative to the pressure broadened lineshape. Spin orbit relaxation between the pumped and upper laser levels is sufficiently fast at 550 Torr of methane to prevent bottlenecking at all but the highest intensities. Comparison of laser characteristics with a quasi-two level analytic model suggests performance near the ideal steady-state limit, with the exception of modest mode matching.     

Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ～±10^?4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L¹ optimisation method. A lower bound estimate for the noise on the GND density determination is ～±10¹² m^?2 for a 200-nm step size, and near the indent densities as high as 10¹⁵ m^?2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ～±10¹⁴m^?2 for the GND density.     

Two polymorphs of 20‐desmethyl‐β‐carotene

Two polymorphs of 20‐desmethyl‐β‐carotene (systematic name: 20‐nor‐β,β‐carotene), C₃₉H₅₄, in monoclinic and triclinic space groups, were formed in the same vial by recrystallization from pyridine and water. Each polymorph crystallizes with the complete molecule as the asymmetric unit, and the two polymorphs show differing patterns of disorder. The β end rings of both polymorphs have the 6‐s‐cis conformation, and are twisted out of the plane of the polyene chain by angles of −53.2 (8) and 47.3 (8)° for the monoclinic polymorph, and −43.6 (3) and 56.1 (3)° for the triclinic polymorph. The cyclohexene end groups are in the half‐chair conformation, but the triclinic polymorph shows disorder of one ring. Overlay of the molecules shows that they differ in the degree of nonplanarity of the polyene chains and the angles of twist of the end rings. The packing arrangements of the two polymorphs are quite different, with the monoclinic polymorph showing short intermolecular contacts of the disordered methyl groups with adjacent polyene chain atoms, and the triclinic polymorph showing π–π stacking interactions of the almost parallel polyene chains. The determination of the crystal structures of the two title polymorphs of 20‐desmethyl‐β‐carotene allows information to be gained regarding the structural effects on the polyene chain, as well as on the end groups, versus that of the parent compound β‐carotene. The absence of the methyl group is known to have an impact on various functions of the title compound.     

Substrate specificity of the acyl transferase domains of EpoC from the epothilone polyketide synthase

The production of epothilone mixtures is a direct consequence of the substrate tolerance of the module 3 acyltransferase (AT) domain of the epothilone polyketide synthase (PKS) which utilises both malonyl- and methylmalonyl-CoA extender units. Particular amino acid motifs in the active site of AT domains influence substrate selection for methylmalonyl-CoA (YASH) or malonyl-CoA (HAFH). This motif appears in hybrid form (HASH) in epoAT3 and may represent the molecular basis for the relaxed specificity of the domain. To investigate this possibility the AT domains from modules 2 and 3 of the epothilone PKS were examined in the heterologous DEBS1-TE model PKS. Substitution of AT1 of DEBS1-TE by epoAT2 and epoAT3 both resulted in functional PKSs, although lower yields of total products were observed when compared to DEBS1-TE (2% and 11.5% respectively). As expected, epoAT3 was significantly more promiscuous in keeping with its nature during epothilone biosynthesis. When the mixed motif (HASH) of epoAT3 within the hybrid PKS was mutated to HAFH (indicative of malonyl-CoA selection) it resulted in a non-productive PKS. When this mixed motif was converted to YASH (indicative of methylmalonyl-CoA selection) the selectivity of the hybrid PKS for methylmalonyl-CoA showed no statistically significant increase, and was associated with a loss of productivity.     

Interfacial interactions in polymer-layered silicate nanocomposites

Interactions between sodium montmorillonite (Na-MMT) and a variety of probes, some of which are intended to model components of a polyurethane system, have been studied. Particular attention was given to the effect of preadsorbed water on the adsorption behavior of the probes. Flow microcalorimetry (FMC), diffuse reflectance Fourier transform infrared spectroscopy (DRIFTS), and wide-angle X-ray scattering (WAXS) were used to monitor the adsorption process. The probe set included alcohols, amines, ethers, poly(propylene glycol) monobutyl ethers (PPG), and 4-ethylphenyl isocyanate (4-EPI). FMC revealed that the preadsorbed water molecules on undried Na-MMT hindered the adsorption of alcohol and ether probes, but had little effect on the adsorption of amines. Drying of Na-MMT to less than 0.3% w/w H2O led to an increase in heat of adsorption and generally greater retention of the probes. PPG showed strong interaction with Na-MMT due to multipoint adsorption. With dried Na-MMT, WAXS revealed that PPG of molecular weight (MW) 1000 was partly intercalated into the gallery while lower molecular weight PPG (MW 340) did not intercalate the Na-MMT. DRIFTS spectra of 4-EPI adsorbed on undried Na-MMT revealed urea linkages, indicating formation of N,N'-bis(4-ethylphenyl) urea. In contrast, with dried Na-MMT the 4-EPI formed a urethane linkage with hydroxyl groups present at the edges of the silicate platelets.     

Time-dependent photoionization of azulene: competition between ionization and relaxation in highly excited states

Pump-probe photoionization has been used to map the relaxation processes taking place from highly vibrationally excited levels of the S(2) state of azulene, populated directly or via internal conversion from the S(4) state. Photoelectron spectra obtained by 1+2(') two-color time-resolved photoelectron imaging are invariant (apart from in intensity) to the pump-probe time delay and to the pump wavelength. This reveals a photoionization process which is driven by an unstable electronic state (e.g., doubly excited state) lying below the ionization potential. This state is postulated to be populated by a probe transition from S(2) and to rapidly relax via an Auger-like process onto highly vibrationally excited Rydberg states. This accounts for the time invariance of the photoelectron spectrum. The intensity of the photoelectron spectrum is proportional to the population in S(2). An exponential energy gap law is used to describe the internal conversion rate from S(2) to S(0). The vibronic coupling strength is found to be larger than 60+/-5 microeV.     

Phase modulation using different orientations of a chiral nematic in liquid crystal over silicon devices

Modulation of the intensity of light by high quality reflective micro-displays is predominantly carried out by liquid crystal over silicon (LCoS) spatial light modulator (SLM) technology for applications such as pico-projectors. Wider use of these devices, in applications such as computer-generated holography and optical correlation, is limited by their phase modulation ability and illumination polarisation state dependence. These devices rely on planar or twisted nematic liquid crystals to modulate the light, but due to their viscoelastic properties they are inherently slow. Research into the use of the polymer stabilised blue phase has already shown that it can offer high speed phase modulation. However, other chiral nematic orientations are yet to be compared in LCoS devices. In this article, we demonstrate that polymer-stabilised chiral nematic liquid crystal electro-optical effects can offer phase modulation in silicon backplane devices. The uniform standing helix and focal conic textures are shown to be independent of the input light polarisation state and the uniform lying helix is shown to be polarisation dependent. These optical responses are then compared with that of the blue phase to identify a suitable orientation for further development in LCoS technology in order to find a high-speed, full phase modulating material.