Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.Comment: 32 page

Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence takes place in the topology induced by a weighted variation norm and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

Good practices for a literature survey are not followed by authors while preparing scientific manuscripts

The number of citations received by authors in scientific journals has become a major parameter to assess individual researchers and the journals themselves through the impact factor. A fair assessment therefore requires that the criteria for selecting references in a given manuscript should be unbiased with respect to the authors or the journals cited. In this paper, we advocate that authors should follow two mandatory principles to select papers (later reflected in the list of references) while studying the literature for a given research: i) consider similarity of content with the topics investigated, lest very related work should be reproduced or ignored; ii) perform a systematic search over the network of citations including seminal or very related papers. We use formalisms of complex networks for two datasets of papers from the arXiv repository to show that neither of these two criteria is fulfilled in practice

Kinetic Analysis of Substrate Utilization by Native and TNAP-, NPP1-, or PHOSPHO1-Deficient Matrix Vesicles

During the process of endochondral bone formation, chondrocytes and osteoblasts mineralize their extracellular matrix by promoting the formation of hydroxyapatite seed crystals in the sheltered interior of membrane-limited matrix vesicles (MVs). Here, we have studied phosphosubstrate catalysis by osteoblast-derived MVs at physiologic pH, analyzing the hydrolysis of ATP, ADP, and PPi by isolated wild-type (WT) as well as TNAP-, NPP1- and PHOSPHO1-deficient MVs. Comparison of the catalytic efficiencies identified ATP as the main substrate hydrolyzed by WT MVs. The lack of TNAP had the most pronounced effect on the hydrolysis of all physiologic substrates. The lack of PHOSPHO1 affected ATP hydrolysis via a secondary reduction in the levels of TNAP in PHOSPHO1-deficient MVs. The lack of NPP1 did not significantly affect the kinetic parameters of hydrolysis when compared with WT MVs for any of the substrates. We conclude that TNAP is the enzyme that hydrolyzes both ATP and PPi in the MV compartment. NPP1 does not have a major role in PPi generation from ATP at the level of MVs, in contrast to its accepted role on the surface of the osteoblasts and chondrocytes, but rather acts as a phosphatase in the absence of TNAP. © 2010 American Society for Bone and Mineral Research

Empirical investigation to explore potential gains from the amalgamation of Phase Changing Materials (PCMs) and wood shavings

The reduction of gained heat, heat peak shifting and the mitigation of air temperature fluctuations are some desirable properties that are sought after in any thermal insulation system. It cannot be overstated that these factors, in addition to others, govern the performance of such systems thus their effect on indoor ambient conditions. The effect of such systems extends also to Heating, Ventilation and Air-conditioning (HVAC) systems that are set up to operate optimally in certain conditions. Where literature shows that PCMs and natural materials such as wood-shavings can provide efficient passive insulation for buildings, it is evident that such approaches utilise methods that are of a degree of intricacy which requires specialist knowledge and complex techniques, such as micro-encapsulation for instance. With technical and economic aspects in mind, an amalgam of PCM and wood-shavings has been created for the purpose of being utilised as a feasible thermal insulation. The amalgamation was performed in the simplest of methods, through submerging the wood shavings in PCM. An experimental procedure was devised to test the thermal performance of the amalgam and compare this to the performance of the same un-amalgamated materials. Comparative analysis revealed that no significant thermal gains would be expected from such amalgamation. However, significant reduction in the total weight of the insulation system would be achieved that, in this case, shown to be up to 20.94%. Thus, further reducing possible strains on structural elements due to the application of insulation on buildings. This can be especially beneficial in vernacular architectural approaches where considerably large amounts and thicknesses of insulations are used. In addition, cost reduction could be attained as wood shavings are significantly cheaper compared to the cost of PCMs