HYDROSTATIC LIMIT FOR THE SYMMETRIC EXCLUSION PROCESS WITH LONG JUMPS: SUPER-DIFFUSIVE CASE

Hydrostatic behavior for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities are derived. The jump rate is described by a transition probability $p$ which is proportional to $\vert \cdot\vert ^{-(\gamma +1)}$ for $1<\gamma<2$ (super-diffusive case). The reservoirs add or remove particles with rate proportional to $ \kappa>0$.

Wave Emission From Bottom Vibrations in Subsurface Open-channel Shear Flow

The linearized water-wave radiation problem for a 2D oscillating bottom source in an inviscid shear flow with a free surface is investigated analytically. The fluid depth is constant. The velocity of the basic flow varies linearly with depth (uniform vorticity), with zero surface velocity. The far-field surface waves radiated out from the 2D source are calculated, based on Euler’s equation of motion with the application of radiation conditions. There are always two waves, one emitted in the upstream direction and the other in the downstream direction. The energy fluxes of these two waves are calculated. The hydrostatic limit of zero wave number is related to the theory of undular bores.

Comparison of Simulated Precipitation over East Asia in Two Regional Models with Hydrostatic and Nonhydrostatic Dynamical Cores

This study examines the characteristics of a nonhydrostatic dynamical core compared to a corresponding hydrostatic dynamical core in the Regional Model Program (RMP) of the Global/Regional Integrated Model system (GRIMs), a spectral model for regional forecasts, focusing on simulated precipitation over Korea. This kind of comparison is also executed in the Weather Research and Forecasting (WRF) finite-difference model with the same physics package used in the RMP. Overall, it is found that the nonhydrostatic dynamical core experiment accurately reproduces the heavy rainfall near Seoul, South Korea, on a 3-km grid, relative to the results from the hydrostatic dynamical core in both models. However, the characteristics of nonhydrostatic effects on the simulated precipitation differ between the RMP and WRF Model. The RMP with the nonhydrostatic dynamical core improves the local maximum, which is exaggerated in the hydrostatic simulation. The hydrostatic simulation of the WRF Model displaces the major precipitation area toward the mountainous region along the east coast of the peninsula, which is shifted into the observed area in the nonhydrostatic simulation. In the simulation of a summer monsoonal rainfall, these nonhydrostatic effects are negligible in the RMP, but the simulated monsoonal rainfall is still influenced by the dynamical core in the WRF Model even at a 27-km grid spacing. One of the reasons for the smaller dynamical core effect in the RMP seems to be the relatively strong horizontal diffusion, resulting in a smaller grid size of the hydrostatic limit.

Anisotropic compressibility of the coordination polymer emim[Mn(btc)]

The effect of pressure on the crystal structure of a coordination polymer, emim[MnII(btc)] (emim = 1-ethyl,3-methyl imidazolium cation, btc = 1,3,5-benzene-tricarboxylate), was investigated with single-crystal X-ray diffraction. At 4.3 GPa the unit-cell volume had decreased by 14% compared with ambient conditions. The unit-cell contraction is highly anisotropic, with thea- andb-axes decreasing by 5.5 and 9.5%, respectively, and thec-axis compressing a mere 0.25% up to 1.7 GPa followed by a 0.2% expansion between 1.7 and 4.3 GPa. The 0.2% increase in length of thec-axis in this interval happens above the quasi-hydrostatic limit of the pressure-transmitting medium and therefore it might be a consequence of strain gradients. Under ambient conditions, two MnO6units are connected by two carboxylate ligands to form dimeric units. On increasing pressure, a non-bonded O atom from a bridging carboxylate group approaches the Mn atom, with the Mn—O distance decreasing from 2.866 (1) Å at 0.3 GPa to 2.482 (6) Å at 4.3 GPa, increasing the coordination environment of the Mn ion from six- to seven-coordinated.

The ecstasy and the agony; compression studies of 3,4-methylenedioxymethamphetamine (MDMA)

MDMA (3,4-methylenedioxymethamphetamine) is a Class A substance that is usually found in a tableted form. It is only observed in one orthorhombic polymorph under ambient conditions. It shows slight positional disorder around the methlyenedioxy ring which persists during compression up to 6.66 GPa. The crystal quality deteriorates above 6.66 GPa where the hydrostatic limit of the pressure-transmitting medium is exceeded. The structure undergoes anisotropic compression with thea-axis compressing the greatest (12%cf.4 and 10% for theb- andc-axes, respectively). This is due to the pattern of the hydrogen bonding which acts like a spring and allows the compression along this direction.

High-pressure phase transitions in the rare-earth orthoferrite LaFeO3

Sequential Rietveld refinements were applied on high-pressure synchrotron powder X-ray diffraction measurements of lanthanum ferrite (LaFeO3) revealing two phase transitions on the room-temperature isotherm up to a pressure of 48 GPa. The first structural phase transition of second order occurs at a pressure of 21.1 GPa, changing the space group fromPbnmtoIbmm. The second transition, involving a isostructural first-order phase transition, occurs at approximately 38 GPa, indicating a high-spin to low-spin transition of the Fe3+ion. Following the behavior of the volume up to the hydrostatic limit of methanol–ethanol it was possible to use inverted equations of state (EoS) to determine a bulk modulus ofB0= 172 GPa and a corresponding pressure derivative ofB′0= 4.3. In addition, the linearized version of the inverted EoS were used to determine the corresponding moduli and pressure derivatives for each lattice direction.