Problems on electrorheological fluid flows

We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field strength, and on the angle between the vectors of velocity and electric field. We study general problems on the flow of such fluids at nonhomogeneous mixed boundary conditions, wherein values of velocities and surface forces are given on different parts of the boundary. We consider the cases where the viscosity function is continuous and singular, equal to infinity, when the second invariant of the rate of strain tensor is equal to zero. In the second case the problem is reduced to a variational inequality. By using the methods of a fixed point, monotonicity, and compactness, we prove existence results for the problems under consideration. Some efficient methods for numerical solution of the problems are examined.Comment: Presented to the journal "Discrete and Continuous Dynamical Systems, Series

Adaptive multilevel methods for obstacle problems

The authors consider the discretization of obstacle problems for second-order elliptic differential operators by piecewise linear finite elements. Assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies, the linear problems are solved iteratively by preconditioned conjugate gradient iterations. The proposed preconditioners are treated theoretically as abstract additive Schwarz methods and are implemented as truncated hierarchical basis preconditioners. To allow for local mesh refinement semilocal and local a posteriors error estimates are derived, providing lower and upper estimates for the discretization error. The theoretical results are illustrated by numerical computations

A Super-Integrable Discretization of the Calogero Model

A time-discretization that preserves the super-integrability of the Calogero model is obtained by application of the integrable time-discretization of the harmonic oscillator to the projection method for the Calogero model with continuous time. In particular, the difference equations of motion, which provide an explicit scheme for time-integration, are explicitly presented for the two-body case. Numerical results exhibit that the scheme conserves all the$(=3)$ conserved quantities of the (two-body) Calogero model with a precision of the machine epsilon times the number of iterations.Comment: 22 pages, 5 figures. Added references. Corrected typo

Adaptive multilevel-methods for obstacle problems in three space dimensions

We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub-problems are solved iteratively by preconditioned cg-iterations. We propose a variant of the BPX preconditioner and prove an O(j) estimate for the resulting condition number To allow for local mesh refinement we derive semi-local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations

Effect of Level of Barley in Finishing Diets of Swine Performance and Carcass Characteristics

Barley continues to be a feed ingredient available to swine producers in South Dakota, that can be used as a substitute for corn. In experiments reported in the 1984 South Dakota Swine Day Proceedings we reported that pigs fed barley diets gained slower during the grower period (60 to 125 lbs) but not during the finisher period (125 to 220 lb). This experiment was designed to evaluate various levels of barley, 0 to 100% of the grain, in diets fed to pigs from an average of 80 to 220 lb market weight

Comparison of Required Energy Intake of Gilts and Sows to Obtain Recommended Gestation Gains

Three trials utilizing 104 crossbred sows and gilts were conducted to evaluate energy needs to provide_ predetermined gestation gains for gilts and sows. In trial l» gilts required similar energy levels (6918 kcal ME) to gain .9 lb/day as bred sows required (7008 kcal ME) to gain .5 lb/day during gestation. Open sows and gilts consumed much more energy but were unable to gain at the predetermined levels. In trial 2, 8 month old gilts required more energy than mature sows (5898 vs 5028 kcal ME) and 11 month old gilts consumed more than either other group to gain at an intermediate level. In trial 3, a daily difference in energy consumption of approximately 800 kcal of ME existed between gilts and sows fed to predetermined gestation gains. If the results of the last two trials are averaged, a difference in energy consumption of 840 kcal of ME/day is found between gilts fed to gain .9 lb/day and sows fed to gain .5 lb/day. This difference is approximately .6 lb of additional gestation feed needed per day for the bred gilt if gestation gain is used as a criteria of evaluation

Influence of Gestation Energy on Large White x Landrace Sow Productivity

Production remains extremely important in our swine industry today. In the past 5-10 years, there has been an increase in the usage of white breeds in swine herds. The white or mother breeds are noted for their increased productivity; however, a question has stirred as to the feeding regime of these productive females. This question is important as feed costs are the major portion of operating expenses for the hog producers. Little controlled research has been conducted in the United States to establish the caloric intake requirement of the white sows during gestation. The National Research Council (NRC, 1979) lists the energy requirement of the bred sow and gilt as 6.1 Meal of. digestible energy (DE) or 5.8 Meal of metabolizable energy (ME) daily. This recommendation is largely based on research with traditional 3-way crossbred sows. Great Britain swine researchers in the 1960\u27s and United States researchers Frobish and workers (1966) were the last to evaluate the effect of gestation energy on strictly white sows. To help answer the current concerns of white sow nutrition, this research project was designed to study the influence of gestation energy on Large White x Landrace sow productivity

Comparison of Sow and Gilt Performance as Affected by Gestation Energy Intake

Gestation energy needs of sows include maintenance as well as tissue growth associated with pregnancy and fetal development. Gilts have the additional demands of body tissue growth but less maintenance needs because of smaller body size. Differences in total daily energy needs between sows and gilts have not been resolved. Results of three trials conducted to compare energy needs for specific gestation gains for sows and gilts were reported last year (Swine 84-10). These results suggested the need for approximately 870 Kcal of additional metabolizable energy (ME) (.6 lb of feed) for gilts with the desired gains of .5 lb/day for sows and .9 lb/day for gilts. The trial reported herein was designed to evaluate comparative performance of sows and gilts fed a wide range of ME levels