On the global well-posedness for the Boussinesq system with horizontal dissipation

In this paper, we investigate the Cauchy problem for the tridimensional Boussinesq equations with horizontal dissipation. Under the assumption that the initial data is an axisymmetric without swirl, we prove the global well-posedness for this system. In the absence of vertical dissipation, there is no smoothing effect on the vertical derivatives. To make up this shortcoming, we first establish a magic relationship between $\frac{u^{r}}{r}$ and $\frac{\omega_\theta}{r}$ by taking full advantage of the structure of the axisymmetric fluid without swirl and some tricks in harmonic analysis. This together with the structure of the coupling of \eqref{eq1.1} entails the desired regularity.Comment: 32page

Two-Dimensional Electronic Spectroscopy of Chlorophyll a: Solvent Dependent Spectral Evolution

The interaction of the monomeric chlorophyll Q-band electronic transition with solvents of differing physical-chemical properties is investigated through two-dimensional electronic spectroscopy (2DES). Chlorophyll constitutes the key chromophore molecule in light harvesting complexes. It is well-known that the surrounding protein in the light harvesting complex fine-tunes chlorophyll electronic transitions to optimize energy transfer. Therefore, an understanding of the influence of the environment on the monomeric chlorophyll electronic transitions is important. The Q-band 2DES is inhomogeneous at early times, particularly in hydrogen bonding polar solvents, but also in nonpolar solvents like cyclohexane. Interestingly this inhomogeneity persists for long times, even up to the nanosecond time scale in some solvents. The reshaping of the 2DES occurs over multiple time scales and was assigned mainly to spectral diffusion. At early times the reshaping is Gaussian-like, hinting at a strong solvent reorganization effect. The temporal evolution of the 2DES response was analyzed in terms of a Brownian oscillator model. The spectral densities underpinning the Brownian oscillator fitting were recovered for the different solvents. The absorption spectra and Stokes shift were also properly described by this model. The extent and nature of inhomogeneous broadening was a strong function of solvent, being larger in H-bonding and viscous media and smaller in nonpolar solvents. The fastest spectral reshaping components were assigned to solvent dynamics, modified by interactions with the solute

Effects of rTMS of pre-supplementary motor area on fronto basal ganglia network activity during stop-signal task

Stop-signal task (SST) has been a key paradigm for probing human brain mechanisms underlying response inhibition, and the inhibition observed in SST is now considered to largely depend on a fronto basal ganglia network consisting mainly of right inferior frontal cortex, pre-supplementary motor area (pre-SMA), and basal ganglia, including subthalamic nucleus, striatum (STR), and globus pallidus pars interna (GPi). However, causal relationships between these frontal regions and basal ganglia are not fully understood in humans. Here, we partly examined these causal links by measuring human fMRI activity during SST before and after excitatory/inhibitory repetitive transcranial magnetic stimulation (rTMS) of pre-SMA. We first confirmed that the behavioral performance of SST was improved by excitatory rTMS and impaired by inhibitory rTMS. Afterward, we found that these behavioral changes were well predicted by rTMS-induced modulation of brain activity in pre-SMA, STR, and GPi during SST. Moreover, by examining the effects of the rTMS on resting-state functional connectivity between these three regions, we showed that the magnetic stimulation of pre-SMA significantly affected intrinsic connectivity between pre-SMA and STR, and between STR and GPi. Furthermore, the magnitudes of changes in resting-state connectivity were also correlated with the behavioral changes seen in SST. These results suggest a causal relationship between pre-SMA and GPi via STR during response inhibition, and add direct evidence that the fronto basal ganglia network for response inhibition consists of multiple top-down regulation pathways in humans

Water Dynamics at Protein Interfaces: Ultrafast Optical Kerr Effect Study

The behavior of water molecules surrounding a protein can have an important bearing on its structure and function. Consequently, a great deal of attention has been focused on changes in the relaxation dynamics of water when it is located at the protein surface. Here we use the ultrafast optical Kerr effect to study the H-bond structure and dynamics of aqueous solutions of proteins. Measurements are made for three proteins as a function of concentration. We find that the water dynamics in the first solvation layer of the proteins are slowed by up to a factor of 8 in comparison to those in bulk water. The most marked slowdown was observed for the most hydrophilic protein studied, bovine serum albumin, whereas the most hydrophobic protein, trypsin, had a slightly smaller effect. The terahertz Raman spectra of these protein solutions resemble those of pure water up to 5 wt % of protein, above which a new feature appears at 80 cm–1, which is assigned to a bending of the protein amide chain

A model for selection of eyespots on butterfly wings

The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell

COMPARISON OF SOLUTION ALGORITHM FOR FLOW AROUND A SQUARE CYLINDER

ABSTRACT Numerical accuracy, numerical stability and calculation time are all important factors in the computational fluid dynamics. In this study, we compare two solution algorithms, the Simplified Marker and Cell (SMAC) method in the MAC-type methods and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm in the SIMPLE-type algorithms, with respect to flow around a square cylinder in constant density and unsteady-state calculations using a staggered grid to investigate the numerical accuracy, the numerical stability and the computational time. For the flow around a square cylinder, the SMAC and SIMPLE solutions are in excellent agreement at the Strouhal number, drag and lift coefficients. However, SMAC is more unstable than SIMLE with a large Courant number. The computational time of the SMAC is shorter than that of the SIMPLE with a small Courant number

Effect of operating conditions on fluid flow over a high speed rotary bell-cup atomizer

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.Using the volume of fluid (VOF) method, we analyze two-dimensional fluid flow over high-speed rotary bell-cup atomizers. The fluid behavior is analyzed and the liquid film thickness is quantitatively evaluated. The atomizer is flat in shape and has a paint supply hole. The bell rotational speed obtained is 15,000, 25,000, and 35,000 rpm; and the liquid flow rate obtained is 150, 300, 450, and 600 mL/min. The liquid used in this experiment is assumed to be water and the gas is assumed to be air. The results show that the liquid flows through the bell-cup surface toward the edge and forms a liquid film. At the measuring point, the film is initially thick but it then decreases to a practically constant value. The increase in the bell rotational speed causes the film thickness to decrease. Furthermore, the increase in the rotational speed causes the film thickness to become constant, whereas the increase in the liquid flow rate causes the film thickness to increase. These results show that the rotational speed and flow rate strongly affect the thickness of the filmdc201

Transport properties of copper phthalocyanine based organic electronic devices

Ambipolar charge carrier transport in Copper phthalocyanine (CuPc) is studied experimentally in field-effect transistors and metal-insulator-semiconductor diodes at various temperatures. The electronic structure and the transport properties of CuPc attached to leads are calculated using density functional theory and scattering theory at the non-equilibrium Green's function level. We discuss, in particular, the electronic structure of CuPc molecules attached to gold chains in different geometries to mimic the different experimental setups. The combined experimental and theoretical analysis explains the dependence of the mobilityand the transmission coefficient on the charge carrier type (electrons or holes) and on the contact geometry. We demonstrate the correspondence between our experimental results on thick films and our theoretical studies of single molecule contacts. Preliminary results for fluorinated CuPc are discussed.Comment: 18 pages, 16 figures; to be published in Eur. Phys. J. Special Topic