Simple expressions for the long walk distance

The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently small positive parameter. The walk distances are graph-geodetic, moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter $t$ approaches its limiting values. In this paper, simple expressions for the long walk distance are obtained. They involve the generalized inverse, minors, and inverses of submatrices of the symmetric irreducible singular M-matrix ${\cal L}=\rho I-A,$ where $\rho$ is the Perron root of $A.$Comment: 7 pages. Accepted for publication in Linear Algebra and Its Application

Linear stability analysis of resonant periodic motions in the restricted three-body problem

The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$, $0\leq \mu \leq 1/2$, that circle each other with period equal to $2\pi$. When $\mu=0$, the problem admits orbits for the massless particle that are ellipses of eccentricity $e$ with the primary of mass 1 located at one of the focii. If the period is a rational multiple of $2\pi$, denoted $2\pi p/q$, some of these orbits perturb to periodic motions for $\mu > 0$. For typical values of $e$ and $p/q$, two resonant periodic motions are obtained for $\mu > 0$. We show that the characteristic multipliers of both these motions are given by expressions of the form $1\pm\sqrt{C(e,p,q)\mu}+O(\mu)$ in the limit $\mu\to 0$. The coefficient $C(e,p,q)$ is analytic in $e$ at $e=0$ and C(e,p,q)=O(e^{\abs{p-q}}). The coefficients in front of e^{\abs{p-q}}, obtained when $C(e,p,q)$ is expanded in powers of $e$ for the two resonant periodic motions, sum to zero. Typically, if one of the two resonant periodic motions is of elliptic type the other is of hyperbolic type. We give similar results for retrograde periodic motions and discuss periodic motions that nearly collide with the primary of mass $1-\mu$

The Local Velocity Anomaly

There is a velocity discontinuity at about 7 Mpc between the galaxies of the Local Sheet that are moving together with low internal velocity dispersion and the adjacent structures. The Local Sheet bounds the Local Void. The Local Sheet is determined to have a peculiar velocity of 260 km/s away from the center of the void. In order for this large velocity to be generated by an absence of gravity, the Local Void must be at least 45 Mpc in diameter and be very empty.Comment: Invited review, "Galaxies in the Local Volume", Sydney, 8-13 July, 2007. eds. B. Koribalski & H. Jerjen, Astrophys. & Space Sci. Proceed. 10 pages with 7 figure

Liquid Crystal-Solid Interface Structure at the Antiferroelectric-Ferroelectric Phase Transition

Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented

Three-Dimensional Self-Navigated T2 Mapping for the Detection of Acute Cellular Rejection After Orthotopic Heart Transplantation.

T2 mapping is a magnetic resonance imaging technique measuring T2 relaxation time, which increases with the myocardial tissue water content. Myocardial edema is a component of acute cellular rejection (ACR) after heart transplantation. This pilot study compares in heart transplantation recipients a novel high resolution 3-dimensional (3D) T2-mapping technique with standard 2-dimensional (2D) T2-mapping for ACR detection. Consecutive asymptomatic patients (n = 26) underwent both 3D T2 mapping and reference 2D T2 mapping magnetic resonance imaging on the day of endomyocardial biopsy (EMB). 3D T2 maps were obtained at an isotropic spatial resolution of 1.72 mm (voxel volume 5.1 mm(3)). 2D and 3D maps were matched anatomically, and maximum segmental T2 values were compared blinded to EMB results. In addition, all 3D T2 maps were rendered as 3D images and inspected for foci of T2 elevation. T2 values of segments from 2D and reformatted 3D T2 maps agreed (p > 0.5). The highest 2D segmental T2 values were 49.9 ± 4.0 ms (no ACR = 0R, n = 18), 48.9 ± 0.8 ms (mild ACR = 1R, n = 3), and 65.0 ms (moderate ACR = 2R). Rendered 3D T2 maps of cases with 1R showed foci with significantly elevated T2 signal (T2 = 58.2 ± 3.6 ms); 5 cases (28%) in the 0R group showed foci with increased T2 values (>2 SD above adjacent tissue) that were not visible on the 2D T2 maps. This pilot study in a small cohort suggests equivalency of standard segmental analysis between 3D and 2D T2-mapping. 3D T2 mapping provides a spatial resolution that permits detection of foci with elevated T2 in patients with mild ACR

Tilt order parameters, polarity and inversion phenomena in smectic liquid crystals

The order parameters for the phenomenological description of the smectic-{\it A} to smectic-{\it C} phase transition are formulated on the basis of molecular symmetry and structure. It is shown that, unless the long molecular axis is an axis of two-fold or higher rotational symmetry, the ordering of the molecules in the smectic-{\it C} phase gives rise to more than one tilt order parameter and to one or more polar order parameters. The latter describe the indigenous polarity of the smectic-{\it C} phase, which is not related to molecular chirality but underlies the appearance of spontaneous polarisation in chiral smectics. A phenomenological theory of the phase transition is formulated by means of a Landau expansion in two tilt order parameters (primary and secondary) and an indigenous polarity order parameter. The coupling among these order parameters determines the possibility of sign inversions in the temperature dependence of the spontaneous polarisation and of the helical pitch observed experimentally for some chiral smectic-{\it $C^{\ast}$} materials. The molecular interpretation of the inversion phenomena is examined in the light of the new formulation.Comment: 12 pages, 5 figures, RevTe

Phase transition between synchronous and asynchronous updating algorithms

We update a one-dimensional chain of Ising spins of length $L$ with algorithms which are parameterized by the probability $p$ for a certain site to get updated in one time step. The result of the update event itself is determined by the energy change due to the local change in the configuration. In this way we interpolate between the Metropolis algorithm at zero temperature for $p$ of the order of 1/L and for large $L$, and a synchronous deterministic updating procedure for $p=1$. As function of $p$ we observe a phase transition between the stationary states to which the algorithm drives the system. These are non-absorbing stationary states with antiferromagnetic domains for $p>p_c$, and absorbing states with ferromagnetic domains for $p\leq p_c$. This means that above this transition the stationary states have lost any remnants to the ferromagnetic Ising interaction. A measurement of the critical exponents shows that this transition belongs to the universality class of parity conservation.Comment: 5 pages, 3 figure

A Simple Model of Liquid-liquid Phase Transitions

In recent years, a second fluid-fluid phase transition has been reported in several materials at pressures far above the usual liquid-gas phase transition. In this paper, we introduce a new model of this behavior based on the Lennard-Jones interaction with a modification to mimic the different kinds of short-range orientational order in complex materials. We have done Monte Carlo studies of this model that clearly demonstrate the existence of a second first-order fluid-fluid phase transition between high- and low-density liquid phases

The Importance of Time Congruity in the Organisation.

In 1991 Kaufman, Lane, and Lindquist proposed that time congruity in terms of an individual's time preferences and the time use methods of an organisation would lead to satisfactory performance and enhancement of quality of work and general life. The research reported here presents a study which uses commensurate person and job measures of time personality in an organisational setting to assess the effects of time congruity on one aspect of work life, job-related affective well-being. Results show that time personality and time congruity were found to have direct effects on well-being and the influence of time congruity was found to be mediated through time personality, thus contributing to the person–job (P–J) fit literature which suggests that direct effects are often more important than indirect effects. The study also provides some practical examples of ways to address some of the previously cited methodological issues in P–J fit research

Photonic band structure of highly deformable, self-assembling systems

We calculate the photonic band structure at normal incidence of highly deformable, self-assembling systems - cholesteric elastomers subjected to external stress. Cholesterics display brilliant reflection and lasing owing to gaps in their photonic band structure. The band structure of cholesteric elastomers varies sensitively with strain, showing new gaps opening up and shifting in frequency. A novel prediction of a total band gap is made, and is expected to occur in the vicinity of the previously observed de Vries bandgap, which is only for one polarisation