A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page

Downwind Odor Predictions from Four Swine Finishing Barns Using CALPUFF

A collaborative research effort by several institutions is investigating odor emissions from swine production facilities, and the impacts of those emissions on farm neighbours. Trained human receptors were used to measure the downwind odor concentrations from four tunnel ventilated swine barns near Story City, Iowa. Twenty-six measurement events were conducted between June and November 2004 and modeled using a specially coded short time-step version of CALPUFF to predict short time step durations. Source emission measurements and extensive meteorological data were collected along with ambient olfactometry analysis using the Nasal Ranger™ device (St. Croix Sensory, St. Paul MN). Approximately 64% of measured odor generally falls within the range of modeled values. Analysis of measured odor concentration and corresponding meteorology indicate that maximum ambient odor impacts occur with lower ambient temperature during non-turbulent conditions. Analysis of the data set did not yield a strong relationship directly (R2=0.33), but a regression analysis indicated that the modified CALPUFF model yielded a slope or scaling factor of 0.99, indicating overall a good relationship between model and observed. However, when the data is tested with the Spearman’s rank correlation coefficient an rs of 0.17 was calculated, indicating a poor rank correlation and was not significant (p=0.05). Statistical analysis is inconclusive as to whether the results have bias, but indicate large error in the results. Given that there were no scaling or peak to mean ratio adjustments to the model predictions, the results are very promising for predicting odors using CALPUFF

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity

Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor fields) belong -- together with Majorana spinor fields -- to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class-(5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three respectively corresponding to flagpole, flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that in particular the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration.Comment: 11 pages, RevTeX, accepted for publication in Int.J.Geom.Meth.Mod.Phys. (2009

Water footprints of cities indicators for sustainable consumption and production

Water footprints have been proposed as sustainabilityindicators, relating the consumption of goods likefood to the amount of water necessary for their productionand the impacts of that water use in the source regions. Wefurther developed the existing water footprint methodology,by globally resolving virtual water flows from production toconsumption regions for major food crops at 5 arcmin spatialresolution. We distinguished domestic and internationalflows, and assessed local impacts of export production. Applyingthis method to three exemplary cities, Berlin, Delhiand Lagos, we find major differences in amounts, composition,and origin of green and blue virtual water imports,due to differences in diets, trade integration and crop waterproductivities in the source regions. While almost all ofDelhi’s and Lagos’ virtual water imports are of domestic origin,Berlin on average imports from more than 4000 km distance,in particular soy (livestock feed), coffee and cocoa.While 42% of Delhi’s virtual water imports are blue waterbased, the fractions for Berlin and Lagos are 2 and 0.5 %, respectively,roughly equal to the water volumes abstracted inthese two cities for domestic water use. Some of the externalsource regions of Berlin’s virtual water imports appear tobe critically water scarce and/or food insecure. However, forderiving recommendations on sustainable consumption andtrade, further analysis of context-specific costs and benefitsassociated with export production will be required

Motor skill learning-induced functional plasticity in the primary somatosensory cortex: A comparison between young and older adults

While in young adults (YAs) the underlying neural mechanisms of motor learning are well-studied, studies on the involvement of the somatosensory system during motor skill learning in older adults (OAs) remain sparse. Therefore, the aim of the present study was to investigate motor learning-induced neuroplasticity in the primary somatosensory cortex (S1) in YAs and OAs. Somatosensory evoked potentials (SEPs) were used to quantify somatosensory activation prior and immediately after motor skill learning in 20 right-handed healthy YAs (age range: 19–35 years) and OAs (age range: 57–76 years). Participants underwent a single session of a 30-min co-contraction task of the abductor pollicis brevis (APB) and deltoid muscle. To assess the effect of motor learning, muscle onset asynchrony (MOA) between the onsets of the contractions of both muscles was measured using electromyography monitoring. In both groups, MOA shortened significantly during motor learning, with YAs showing bigger reductions. No changes were found in SEP amplitudes after motor learning in both groups. However, a correlation analysis revealed an association between baseline SEP amplitudes of the N20/P25 and N30 SEP component and the motor learning slope in YAs such that higher amplitudes are related to higher learning. Hence, the present findings suggest that SEP amplitudes might serve as a predictor of individual motor learning success, at least in YAs. Additionally, our results suggest that OAs are still capable of learning complex motor tasks, showing the importance of motor training in higher age to remain an active part of our society as a prevention for care dependency