Three Dimensional Quantum Gravity Coupled to Ising Matter

We establish the phase diagram of three--dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two spin phases with a first order transition between them.Comment: 12 page

Secondary Crystallization of Isotactic Polystyrene

When isotactic polystyrene (i-PS) is crystallized from the melt or from the glassy state at rather large supercooling an additional melting peak appears on the curve during scanning in a differential calorimeter. The overall rate of crystallization deduced from the total peak areas as a function of crystallization time did not fit the Avrami equation well. When we omit the area of the additional melting peak in the kinetic analysis a much better fit is obtained. We also observed that no lamellar thickening occurs during isothermal crystallization. In view of the low degree of crystallinity of i-PS these results lead to the idea that a secondary crystallization process takes place within the amorphous parts of the spherulites resulting in this additional melting peak on the DSC curve. The large supercooling needed and the increase in peak area with increasing molecular weight make us suppose that intercrystalline links are probably responsible for the additional melting peak of bulk-crystallized i-PS. Electron microscopic studies of surface replicas of i-PS support this view.

A simulation study on the interactive effects of radiation and plant density on growth of cut chrysanthemum

In the present study, we used a photosynthesis-driven crop growth model to determine acceptable plant densities for cut chrysanthemum throughout the year at different intensities of supplementary light. Dry matter partitioning between leaves, stems, and flowers was simulated as a function of crop developmental stage. Leaf area index was simulated as leaf dry mass multiplied by specific leaf area, the latter being a function of season. Climatic data (hourly global radiation, greenhouse temperature, and CO2 concentration) and initial organ dry mass were model inputs. Assimilation lights were switched on and off based on time and ambient global radiation intensity. Simulated plant fresh mass with supplementary light (49 µmol m-2 s-1) for 52 cultivations (weekly plantings, reference plant densities, and length of the long and short day period) was used as reference plant fresh mass. For four other supplementary light intensities (31, 67, 85, and 104 µmol m-2 s-1), dry matter production was simulated with the reference plant density and length of the long and short day period for each planting week and plant fresh mass was calculated. The acceptable plant density was then calculated as the ratio between plant fresh mass and reference plant fresh mass multiplied by the reference density. Under low natural light intensities, plant density could be increased substantially (>30%) at increased supplementary light intensities, while maintaining the desired plant mass. Simulated light use efficiency (g additional dry mass ¿ MJ-1 additional supplementary light) was higher in winter (4.7) than in summer (3.5), whereas it hardly differed between the supplementary light intensities. This type of simulations can be used to support decisions on the acceptable level of plant density at different intensities of supplementary lighting or lighting strategies and on optimum supplementary light intensities

The equivalent medium for the elastic scattering by many small rigid bodies and applications

We deal with the elastic scattering by a large number $M$ of rigid bodies, $D_m:=\epsilon B_m+z_m$, of arbitrary shapes with $0<\textcolor{black}{\epsilon}<<1$ and with constant Lam\'e coefficients $\lambda$ and $\mu$. We show that, when these rigid bodies are distributed arbitrarily (not necessarily periodically) in a bounded region $\Omega$ of $\mathbb{R}^3$ where their number is $M:=M(\textcolor{black}{\epsilon}):=O(\textcolor{black}{\epsilon}^{-1})$ and the minimum distance between them is $d:=d(\textcolor{black}{\epsilon})\approx \textcolor{black}{\epsilon}^{t}$ with $t$ in some appropriate range, as $\textcolor{black}{\epsilon} \rightarrow 0$, the generated far-field patterns approximate the far-field patterns generated by an equivalent medium given by $\omega^2\rho I_3-(K+1)\mathbf{C}_0$ where $\rho$ is the density of the background medium (with $I_3$ as the unit matrix) and $(K+1)\mathbf{C}_0$ is the shifting (and possibly variable) coefficient. This shifting coefficient is described by the two coefficients $K$ and $\mathbf{C}_0$ (which have supports in $\overline{\Omega}$) modeling the local distribution of the small bodies and their geometries, respectively. In particular, if the distributed bodies have a uniform spherical shape then the equivalent medium is isotropic while for general shapes it might be anisotropic (i.e. $\mathbf{C}_0$ might be a matrix). In addition, if the background density $\rho$ is variable in $\Omega$ and $\rho =1$ in $\mathbb{R}^3\setminus{\overline{\Omega}}$, then if we remove from $\Omega$ appropriately distributed small bodies then the equivalent medium will be equal to $\omega^2 I_3$ in $\mathbb{R}^3$, i.e. the obstacle $\Omega$ characterized by $\rho$ is approximately cloaked at the given and fixed frequency $\omega$.Comment: 27pages, 2 figure