Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Rigid tetracatenar liquid crystals derived from 1,10-phenanthroline

Tetracatenar liquid crystals were obtained by substituting the 1,10-phenanthroline central core unit at the 3- and 8-positions by extended, rigid acetylene moieties, equipped at the termini with two alkoxy chains of various lengths (n = 6, 8, 10, 12, 14). The liquid crystals exhibit a rich mesomorphism including smectic C, cubic, hexagonal and rectangular columnar phases, depending on the alkoxy chain length. The corresponding rhenium(I) complexes containing the bulky [ReBr(CO)₃] fragment are not liquid-crystalline. The ligands and rhenium(I) complexes were investigated by scanning tunneling microscopy (STM). Both the ligands and the rhenium(I) complexes can be self-assembled into monolayers at the TCB–graphite and octanoic acid–graphite interfaces. The ligands and rhenium(I) complexes are luminescent.

1-butyl-3-methylimidazolium 3,5-dinitro-1,2,4-triazolate: a novel ionic liquid containing a rigid, planar energetic anion

The novel ionic liquid, 1-butyl-3-methylimidazolium 3,5-dinitro-1,2,4-triazolate has been synthesized and exhibits an unexpectedly low melting point (35 degreesC) considering the size and shape of the rigid, planar anion; analogous tetraalkylammonium salts (methyl, ethyl and n-butyl) have also been prepared and the tetraethylammonium example was characterized by single crystal X-ray diffraction.

Conventional 3D staging PET/CT in CT simulation for lung cancer: impact of rigid and deformable target volume alignments for radiotherapy treatment planning

Objective: Positron emission tomography (PET)/CT scans can improve target definition in radiotherapy for non-small cell lung cancer (NSCLC). As staging PET/CT scans are increasingly available, we evaluated different methods for co-registration of staging PET/CT data to radiotherapy simulation (RTP) scans.

Methods: 10 patients underwent staging PET/CT followed by RTP PET/CT. On both scans, gross tumour volumes (GTVs) were delineated using CT (GTVCT) and PET display settings. Four PET-based contours (manual delineation, two threshold methods and a source-to-background ratio method) were delineated. The CT component of the staging scan was co-registered using both rigid and deformable techniques to the CT component of RTP PET/CT. Subsequently rigid registration and deformation warps were used to transfer PET and CT contours from the staging scan to the RTP scan. Dice’s similarity coefficient (DSC) was used to assess the registration accuracy of staging-based GTVs following both registration methods with the GTVs delineated on the RTP PET/CT scan.

Results: When the GTVCT delineated on the staging scan after both rigid registration and deformation was compared with the GTVCT on the RTP scan, a significant improvement in overlap (registration) using deformation was observed (mean DSC 0.66 for rigid registration and 0.82 for deformable registration, p50.008). A similar comparison for PET contours revealed no significant improvement in overlap with the use of deformable registration.

Conclusions: No consistent improvements in similarity measures were observed when deformable registration was used for transferring PET-based contours from a staging PET/CT. This suggests that currently the use of rigid registration remains the most appropriate method for RTP in NSCLC.

Novel pyridyl-stabilised rigid-rod organometallic polymers and their monomeric precursors

Reaction of trans-[Pt(NC5H4CHBu2n)(2)Cl-2] 1 with an excess of HC=CR (R = Ph, C6H4Me, C6H4NO2) affords the monomeric complex trans-[Pt(NC5H4CHBu2n)(2)(C=CR)(2)] (R = Ph 2a, C6H4Me 2b, C6H4NO2 2c), the trans arrangement of the alkynyl ligands being confirmed from spectroscopic data and by an X-ray analysis of 2c;when 1 is treated with 1 equiv, of HC=CC6H2(Me)(2)C=CH the polymer [Pt(NC5H4CHBu2n)(2)C=CC6H2Me2C=C](n) is formed, which is soluble in a range of organic solvents.

Vortex-induced vibrations of a rigid cylinder on elastic supports with endstops. Part 1: Experimental Results

This paper describes an experimental investigation into the effect of restricting the vortex-induced vibrations of a spring-mounted rigid cylinder by means of stiff mechanical endstops. Cases of both asymmetric and symmetric restraint are investigated. Results show that limiting the amplitude of the vibrations strongly affects the dynamics of the cylinder, particularly when the offset is small. Fluid-structure interaction is profoundly affected, and the well-known modes of vortex shedding observed with a linear elastic system are modified or absent. There is no evidence of lock-in, and the dominant impact frequency corresponds to a constant Strouhal number of 0.18. The presence of an endstop on one side of the motion can lead to large increases in displacements in the opposite direction. Attention is also given to the nature of the developing chaotic motion, and to impact velocities, which in single-sided impacts approach the maximum velocity of a cylinder with linear compliance undergoing VIV at lock-in. With symmetrical endstops, impact velocities were about one-half of this. Lift coefficients are computed from an analysis of the cylinder’s motion between impacts.

Serviceability design of a cold-formed steel portal frame having semi-rigid joints

Details are given of a cold-formed steel portal framing system that uses simple bolted moment-connections for both the eaves and apex joints. However, such joints function as semi-rigid and, as a result, the design of the proposed system will be dominated by serviceability requirements. While serviceability is a mandatory design requirement, actual deflection limits for portal frames are not prescribed in many of the national standards. In this paper, a review of the design constraints that have an effect on deflection limits is discussed, and rational values appropriate for use with cold-formed steel portal frames are recommended. Adopting these deflection limits, it is shown through a design example how a cold-formed steel portal frame having semi-rigid eaves and apex joints can be a feasible alternative to rigid-jointed frames in appropriate circumstances.