Physical properties of some McVittie metrics

A class of McVittie's new nonquadratic solutions is investigated in some detail with regard to its physical properties. It is found that decreasing pressure and density are not compatible with center regularity for these perfect fluid spheres. It is further seen that for gaseous spheres (i.e., the density drops to zero at the outer boundary of the sphere together with the pressurep) oscillatory motions arenot possible. For these gaseous models the pressure and the density are both positive inside the outer surface, and their respective gradients are negative. For the outer gaseous shells models are constructed where for a certain time interval the pressure is increasing for contracting models. Without any restriction with respect to time, for these shell models it found that the density is increasing for contracting models, and the adiabatic speed of sound is less than the speed of light. It is also found that the trace of the energy-momentum tensor is positive, the total mass is negative, and for collapsing shells the rate of change of circumference as measured by an observer riding on the shell is an increasing function of time. However, all these models have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate.     

Cellulase retention and sugar removal by membrane ultrafiltration during lignocellulosic biomass hydrolysis

Technologies suitable for the separation and reuse of cellulase enzymes during the enzymatic saccharification of pretreated corn stover are investigated to examine the economic and technical viability of processes that promote cellulase reuse while removing inhibitory reaction products such as glucose and cellobiose. The simplest and most suitable separation is a filter with relatively large pores on the order of 20–25 mm that retains residual corn stover solids while passing reaction products such as glucose and cellobiose to form a sugar stream for a variety of end uses. Such a simple separation is effective because cellulase remains bound to the residual solids. Ultrafiltration using 50-kDa polyethersulfone membranes to recover cellulase enzymes in solution was shown not to enhance further the saccharification rate or overall conversion. Instead, it appears that the necessary cellulase enzymes, including β-glucosidase, are tightly bound to the substrate; when fresh corn stover is contacted with highly washed residual solids, without the addition of fresh enzymes, glucose is generated at a high rate. When filtration was applied multiple times, the concentration of inhibitory reaction products such as glucose and cellobiose was reduced from 70 to 10 g/L. However, an enhanced saccharification performance was not observed, most likely because the concentration of the inhibitory products remained too high. Further reduction in the product concentration was not investigated, because it would make the reaction unnecessarily complex and result in a product stream that is much too dilute to be useful. Finally, an economic analysis shows that reuse of cellulase can reduce glucose production costs, especially when the enzyme price is high. The most economic performance is shown to occur when the cellulase enzyme is reused and a small amount of fresh enzyme is added after each separation step to replace lost or deactivated enzyme.     

Nonstatic gas spheres in general relativity

A model for a time-dependent relativistic gas sphere is given. Both pressurep and density are positive inside the outer boundary of the sphere, and they both drop to zero at the boundary itself. Their respective gradients are negative. For expanding models the pressure and the density are decreasing, and for contracting models the pressure and the density are increasing. The adiabatic sound speed is thus real, and for the layers close to the surface of the sphere it is found that the adiabatic sound speed is less than the speed of light. For these layers the condition>3p is also fulfilled. However, the area 4R ² for a sphere of constantr is not an increasing function of comoving radial coordinater.     

On kth-order embeddings of K3 surfaces and Enriques surfaces

We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or on an Enriques surface S to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big line bundle on a K3 surface S to be birationally k-very ample and birationally k-spanned (our definition), and relate these concepts to the Clifford index and gonality of smooth curves in |L| and the existence of a particular type of rank 2 bundles on S. Received: 28 March 2000 / Revised version: 20 October 2000     

X-ray emission from clusters of galaxies and cosmological parameters

Clusters of galaxies are excellent probes of cosmic structure and evolution. X-ray studies of clusters provide some of their key parameters, viz., temperature of the hot intra-cluster gas, its metallicity, X-ray luminosity and surface brightness giving mass distribution and mass-flow rate in the case of cooling flows. X-ray measurements for a large sample of clusters have lead to estimates of the total gravitating mass in them, which can be compared to the virial masses derived from dynamical considerations and gravitational lensing in some of them. X-ray derived total masses are consistent with masses obtained from the other methods after the effects due to the presence of cooling flows are taken into account in the analyses. Estimated virial masses, lack of evolution in X-ray properties, and detection of several very hot clusters at high redshifts indicate a Universe with a low value (≤ 0.3) for the Ω parameter.     

Severi varieties on blow-ups of the symmetric square of an elliptic curve

We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces.     

A comment on an exact solution with a stiff equation of state

Recently, an analytical stellar model with a stiff equation of state and density distribution= _c (1-r ²/r _o ² ) was presented. We show that such a solution cannot exist.     

Regular exact models for a nonstatic gas sphere in general relativity

Some new exact models for an expanding or a contracting gaseous sphere (i.e., the density is to vanish at the outer boundary together with the pressurep) are given. The physical properties of the models are investigated, and it is found that both the pressure and the density are positive inside the outer boundary of the sphere, and their respective gradients are negative. The density is increasing for contracting spheres, and it is decreasing for expanding spheres. It is also shown that this is the case for the pressure at any moment for the layers close to the boundary of the spheres. For these layers it is further shown that the adiabatic speed of sound is less than the speed of light, and the trace of the energy-momentum tensor is positive. The rate of change of the circumference as measured by an observer riding on the boundary of the sphere is increasing for expanding spheres and it is decreasing for collapsing spheres. We also find that the physical radius is an increasing function of comoving radial coordinate. The mass function is further shown to be positive.