Energy-Momentum Complex in M\o ller's Tetrad Theory of Gravitation

M\o ller's Tetrad Theory of Gravitation is examined with regard to the energy-momentum complex. The energy-momentum complex as well as the superpotential associated with M\o ller's theory are derived. M\o ller's field equations are solved in the case of spherical symmetry. Two different solutions, giving rise to the same metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.Comment: LaTeX2e with AMS-LaTeX 1.2, 13 page

Multimodal optical characterisation of collagen photodegradation by femtosecond infrared laser ablation.

Collagen is a structural component of the human body, as a connective tissue it can become altered as a result of pathophysiological conditions. Although the collagen degradation mechanism is not fully understood, it plays an important role in ageing, disease progression and applications in therapeutic laser treatments. To fully understand the mechanism of collagen alteration, in our study photo-disruptive effects were induced in collagen I matrix by point-irradiation with a femtosecond Ti-sapphire laser under controlled laser ablation settings. This was followed by multi-modal imaging of the irradiated and surrounding areas to analyse the degradation mechanism. Our multi-modal methodology was based on second harmonic generation (SHG), scanning electron microscope (SEM), autofluorescence (AF) average intensities and the average fluorescence lifetime. This allowed us to quantitatively characterise the degraded area into four distinct zones: (1) depolymerised zone in the laser focal spot as indicated by the loss of SHG signal, (2) enhanced crosslinking zone in the inner boundary of the laser induced cavity as represented by the high fluorescence ring, (3) reduced crosslinking zone formed the outer boundary of the cavity as marked by the increased SHG signal and (4) native collagen. These identified distinct zones were in good agreement with the expected photochemical changes shown using Raman spectroscopy. In addition, imaging using polarisation-resolved SHG (p-SHG) revealed both a high degree of fibre re-orientation and a SHG change in tensor ratios around the irradiation spot. Our multi-modal optical imaging approach can provide a new methodology for defining distinct zones that can be used in a clinical setting to determine suitable thresholds for applying safe laser treatments without affecting the surrounding tissues. Furthermore this technique can be extended to address challenges observed in collagen based tissue engineering and used as a minimally invasive diagnostic tool to characterise diseased and non-diseased collagen rich tissues

The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior

We have numerically investigated the effect of the delay times $\tau_f$ and $\tau_s$ of a mixture of fast and slow vehicles on the fundamental diagram of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time $\tau_s$ the current profile displays qualitatively five different forms depending on $\tau_f$, $\tau_s$ and the fractions $d_f$ and $d_s$ of the fast and slow cars respectively. The velocity (current) exhibits first order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to the jamming one respectively accompanied by the existence of a local minimal current. Furthermore, there exist a critical value of $\tau_f$ above which the metastability and hysteresis appear. The spatial-temporal traffic patterns present more complex structur

Wetting of an Ising system with perfect and corrugated surfaces in a transverse field

Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established.Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established

A Monte Carlo Study of the Order-Disorder Layering Transitions in the Blume-Capel Model

The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated.The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated