Abstract:
Point-of-care diagnostic testing using PCR requires a device that is fast, economical, and practical. Sub-minute amplification has been demonstrated using high concentrations of primers and polymerase in glass capillaries, but its platform is limited to research use. A system using heated copper blocks to clamp a microfluidic flow-through PCR card fabricated from thin film polycarbonate was modeled, fabricated, and tested. Models show that fluid flowing through a thin-film device clamped between temperature-controlled copper blocks equilibrates to a temperature change in 250 milliseconds. A 2-step, 35 cycle PCR with 1.06 second cycles specifically amplified a 69-base pair fragment from a 450-base pair synthetic DNA template of random sequence with the same performance as the glass capillary system. This system demonstrates the feasibility of <1 minute PCR in an inexpensive, disposable sample container.

Abstract:
The history of water management in the Fertile Crescentis closely related to the religion. This is most clear in ancientEgyptin pharaonic time. The class of priests serving under the pharaoh had also many other administrative duties, they had good skill in science, collected hydrological and astronomical data and used it to levy taxes and predict the floods that irrigated the arable land. The special hydrological features of the riverNilemake it rather predictable in behavior compared to other major rivers of the region. In this social position the priests had great influence and could use it to stop the pharaoh Ikhnaton in his attempt to establish a monotheistic religion by ousting Amon-Ra and replacing him with Aton. Social life was very colorful at pharaohs’ court and the various arts and festivals flourished. The most remarkable of these was the Opet festival where pharaoh himself was the leading figure together with the statues of the gods. The festival was to last 10 days and during that time the riverNilewas to change color from grayish to reddish and thereby mark the beginning of the life-giving flood and bear witness to the good relations between the king and the divine powers. This kind of event, an annual prayer by the king to the gods for good harvest was well known in many societies, but it shows the remarkable skills of the Amon-Ra priest that they were ready to predict the onset of theNileflood within ten days and get away with it.

Abstract:
Los rumiantes alimentados con forrajes de elevado contenido de proteína rápidamente degradable en el rumen o suplementados con nitrógeno no proteínico, absorben cantidades sustanciales de amonio en el rumen y muy poca glucosa en el intestino, en circunstancias que requieren mantener una adecuada capacidad ureagénica y gluconeogénesis para sostener su eficiencia productiva. En esta condición se eleva la producción de amonio ruminal, el cual se absorbe y posteriormente se metaboliza por el hígado en urea. Las elevadas concentraciones de amonio en el rumen pueden sobrepasar la capacidad hepática de sintetizar urea, lo que provoca una sobrecarga en el ciclo de la urea y demanda una excesiva cantidad de -cetoglutarato y oxalacetato para la formación de glutamato y aspartato, metabolitos que también son requeridos en el ciclo de Krebs y en la vía gluconeogénica, alterando con ello la capacidad gluconeogénica del organismo. El trabajo recopila y analiza las interrelaciones entre la ureagénesis y gluconeogénesis hepática en rumiantes en condiciones de pastoreo con forrajes de elevado contenido de proteínas.

Abstract:
Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in an exterior domain in three dimensions numerically. The main point is that the necessity to truncate for numerical purposes the exterior domain to a finite sub-domain leads to the problem of finding so called "artificial boundary conditions" to replace the conditions at infinity. To solve this problem we provide a vector filed that describes the leading asymptotic behavior of the solution at large distances. This vector field depends explicitly on drag and lift which are determined in a self-consistent way as part of the solution process. When compared with other numerical schemes the size of the computational domain that is needed to obtain the hydrodynamic forces with a given precision is drastically reduced, which in turn leads to an overall gain in computational efficiency of typically several orders of magnitude.

Abstract:
We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in terms of an asymptotic expansion at large distances from the boundary. The expansion is universal in the sense that it only depends on the source term through some multiplicative constants. This expansion is identical to the one for the problem of an exterior flow around a small body moving at constant velocity parallel to the boundary, and can be used as an artificial boundary condition on the edges of truncated domains for numerical simulations.

Abstract:
New explicit solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{2}\setminus\left\{ \boldsymbol{0}\right\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scale-invariant solutions. While the Hamel solutions are parameterized by a discrete parameter $n$, the flux $\Phi$ and an angle $\theta_{0}$, the new solutions generalize the Hamel solutions by introducing an additional parameter $a$ which produces a rotation. The new solutions decay like $\left|\boldsymbol{x}\right|^{-1}$ as the Hamel solutions, and exhibit spiral behavior. The new variety of asymptotes induced by the existence of these solutions further emphasizes the difficulties faced when trying to establish the asymptotic behavior of the Navier-Stokes equations in a two-dimensional exterior domain or in the whole plane.

Abstract:
Let w be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane -\infty1, with zero Dirichlet boundary conditions at y=1 and at infinity, and with a small force term of compact support. Then, |xyw(x,y)| is uniformly bounded in the half-plane. The proof is given in a specially adapted functional framework and complements previous work.

Abstract:
We discuss artificial boundary conditions for stationary Navier-Stokes flows past bodies in the half-plane, for a range of low Reynolds numbers. When truncating the half-plane to a finite domain for numerical purposes, artificial boundaries appear. We present an explicit Dirichlet condition for the velocity at these boundaries in terms of an asymptotic expansion for the solution to the problem. We show a substantial increase in accuracy of the computed values for drag and lift when compared with results for traditional boundary conditions. We also analyze the qualitative behavior of the solutions in terms of the streamlines of the flow. The new boundary conditions are universal in the sense that they depend on a given body only through one constant, which can be determined in a feed-back loop as part of the solution process.

Abstract:
We investigate analytically and numerically the existence of stationary solutions converging to zero at infinity for the incompressible Navier-Stokes equations in a two-dimensional exterior domain. More precisely, we find the asymptotic behaviour for such solutions in the case where the net force on the boundary of the domain is non-zero. In contrast to the three dimensional case, where the asymptotic behaviour is given by a scale invariant solution, the asymptote in the two-dimensional case is not scale invariant and has a wake. We provide an asymptotic expansion for the velocity field at infinity, which shows that, within a wake of width $|\boldsymbol{x}|^{2/3}$, the velocity decays like $|\boldsymbol{x}|^{-1/3}$, whereas outside the wake, it decays like $|\boldsymbol{x}|^{-2/3}$. We check numerically that this behaviour is accurate at least up to second order and demonstrate how to use this information to significantly improve the numerical simulations. Finally, in order to check the compatibility of the present results with rigorous results for the case of zero net force, we consider a family of boundary conditions on the body which interpolate between the non-zero and the zero net force case.

Abstract:
We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall.