Vibrationally averaged interatomic distances

Equations are presented for the avereage internuclear distance r(g) and r(a) in terms of elements of the L matrix and the L tensor. These are an alternative to the equations presented by Kuchitsu and Morino.

Short Communication: effects of 2-hydroxy-4-(methylthio) butanoic acid isopropyl ester on milk production and composition of lactating Holstein dairy cows

Sixteen multiparous Holstein cows were used to determine the effects of 2-hydroxy-4-(methylthio) butanoic acid isopropyl ester (HMBi: 0 vs. 1.26 g/kg of total ration dry matter (DM) and dietary crude protein (CP) concentration [14.7% (low) vs. 16.9% (standard), DM basis] on milk yield and composition using a replicated 4 x 4 Latin square design experiment with 4-wk periods. Cows were fed ad libitum a total mixed ration with a 1: 1 forage-to-concentrate ratio (DM basis), and diets provided an estimated 6.71 and 1.86% lysine and methionine, respectively, in metabolizable protein for the low-protein diet and 6.74 and 1.82% in the standard protein diet. Dry matter intake, milk yield, and composition were measured during wk 4 of each period. There were no effects on DM intake, which averaged 24.7 kg/d. There was an interaction between dietary CP and HMBi for milk yield and 3.5% fat-corrected milk (FCM). Feeding HMBi decreased milk and FCM yield when fed with the low-CP diet but did not affect milk or FCM yield when fed with the standard CP diet. Feeding HMBi increased milk protein concentration regardless of diet CP concentration and increased milk protein yield when added to the standard CP diet but not the low-CP diet. The positive effect of HMBi on milk protein yield was only observed at the standard level of dietary CP, suggesting other factors limited the response to HMBi when dietary protein supply was restricted.

Plasma concentrations of gut peptides in dairy cattle increase after calving

Effects of transition from late gestation to early lactation on plasma concentrations of glucose-dependent insulinotropic polypeptide (GIP), glucagon-like peptide 1-(7-36) amide (GLP-1), and cholecystokinin (CCK) have not been reported in cattle. The objective of the present study was to measure plasma concentrations of GLP-1, GIP, CCK, insulin, glucose, and nonesterified fatty acids in blood plasma obtained from the coccygeal vein of 32 Holstein cows at an average of 11 d before, and 5, 12, and 19 d after calving. Feed dry matter intake (DMI) averaged 14.4, 17.7, and 19.9 kg/d on d 5, 12, and 19 of lactation, respectively, as milk yield increased (30.6, 36.6, and 39.7 kg/d, respectively). Plasma concentrations of insulin and glucose were lower postpartum than prepartum, but did not differ among samples collected after calving. In contrast, plasma concentration of gut peptides increased linearly after calving, perhaps as a consequence of increased feed intake and nutrient absorption; however, the increases in plasma concentrations of GIP and GLP-1 as lactation progressed were not associated with increased DMI per se, and likely reflect the endocrine and metabolic adaptations of lactogenesis. In contrast, increased concentration of CCK was related both to increasing days in milk and DMI. By 19 d postpartum, concentrations of GLP-1, GIP, and CCK increased by 2.3-, 1.8-, and 2.8-fold, respectively, compared with values at 11 d before calving. Although these peptides have direct and indirect effects that reduce appetite and DMI in other species (including increased insulin secretion), these may be glucose- or insulin-dependent functions, and insulin and glucose concentrations were reduced in early lactation.

On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

A geometric approach to generalized Stokes conjectures

We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Experimental analysis of the Reynolds flocking model

The classic Reynolds flocking model is formally analysed, with results presented and discussed. Flocking behaviour was investigated through the development of two measurements of flocking, flock area and polarisation, with a view to applying the findings to robotic applications. Experiments varying the flocking simulation parameters individually and simultaneously provide new insight into the control of flock behaviour.

The effect of adding stinging nettle (Urtica dioica) haylage to a total mixed ration on performance and rumen function of lactating dairy cows

In vitro studies found that inclusion of dried stinging nettle (Urtica dioica) at 100 mg/g dry matter (DM) increased the pH of a rumen fluid inoculated fermentation buffer by 30% and the effect was persistent for 7 days. Our objective was to evaluate the effects of adding stinging nettle haylage to a total mixed ration on feed intake, eating and rumination activity, rumen pH, milk yield, and milk composition of lactating dairy cows. Six lactating Holstein-Friesian cows were used in a replicated 3 × 3 Latin Square design experiment with 3 treatments and 3 week periods. Treatments were a control (C) high-starch (311 g/kg DM) total mixed ration diet and two treatment diets containing 50 (N5) and 100 (N10) g nettle haylage (DM/kg) as a replacement for ryegrass silage (Lolium perenne). There was an increase (linear, P < 0.010) in the proportion of large particles and a reduction in medium (linear, P = 0.045) and fine particles (linear, P = 0.026) in the diet offered with increasing nettle inclusion. A numerical decrease (linear, P = 0.106) in DM intake (DMI) was observed as nettle inclusion in the diet increased. Milk yield averaged 20.3 kg/day and was not affected by diet. There was a decrease (quadratic, P = 0.01) in the time animals spent ruminating as nettle inclusion in the diet increased, in spite of an increase in the number of boli produced daily for the N5 diet (quadratic, P = 0.031). Animals fed the N10 diet spent less time with a rumen pH below 5.5 (P < 0.05) than cows fed the N5 diet. Averaged over an 8.5 h sampling period, there were no changes in the concentration or proportions of acetate or propionate in the rumen, but feeding nettle haylage reduced the concentrations of n-butyrate (quadratic, P < 0.001), i-butyrate (linear, P < 0.009) and n-caproate (linear, P < 0.003). Milk and fat and protein corrected milk yield were not affected when nettles replaced ryegrass silage in the diet of lactating dairy cows, despite a numerical reduction in feed intake. Rumination activity was reduced by the addition of nettle haylage to the diet, which may reflect differences in fibre structure between the nettle haylage and ryegrass silage fed. Changes observed in rumen pH suggest potential benefits of feeding nettle haylage for reducing rumen acidosis. However, the extent to which these effects were due to the fermentability and structure of the nettle haylage compared to the ryegrass silage fed, or a bioactive component of the nettles, is not certain