scholarly journals Bowen–York model solution redux

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Emel Altas ◽  
Bayram Tekin
Keyword(s):  
Energy Content ◽  
Analytical Form ◽  
Initial Energy ◽  
Model Solution ◽  
Linear Momentum ◽  
Hamiltonian Constraint ◽  
Initial Value ◽  
Relativistic Case ◽  
Stationary Part ◽  
Dynamical Time

AbstractInitial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the “model” solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

scholarly journals Magnetically driven jets and winds from weakly magnetized accretion discs

2019 ◽  
Vol 490 (3) ◽  
pp. 3112-3133 ◽  
Author(s):  
J Jacquemin-Ide ◽  
J Ferreira ◽  
G Lesur
Keyword(s):  
Numerical Simulations ◽  
Energy Content ◽  
Initial Energy ◽  
Accretion Discs ◽  
Analytical Models ◽  
Magnetorotational Instability ◽  
New Class ◽  
Analytical Criterion ◽  
First Time

Abstract Semi-analytical models of disc outflows have successfully described magnetically driven, self-confined super-Alfvénic jets from near-Keplerian accretion discs. These jet-emitting discs (JEDs) are possible for high levels of disc magnetization μ defined as μ = 2/β, where beta is the usual plasma parameter. In near-equipartition JEDs, accretion is supersonic and jets carry away most of the disc angular momentum. However, these solutions prove difficult to compare with cutting-edge numerical simulations, for the reason that numerical simulations show wind-like outflows but in the domain of small magnetization. In this work, we present for the first time self-similar isothermal solutions for accretion–ejection structures at small magnetization levels. We elucidate the role of magnetorotational instability-like (MRI) structures in the acceleration processes that drive this new class of solutions. The disc magnetization μ is the main control parameter: Massive outflows driven by the pressure of the toroidal magnetic field are obtained up to μ ∼ 10−2, while more tenuous centrifugally driven outflows are obtained at larger μ values. The generalized parameter space and the astrophysical consequences are discussed. We believe that these new solutions could be a stepping stone in understanding the way astrophysical discs drive either winds or jets. Defining jets as self-confined outflows and winds as uncollimated outflows, we propose a simple analytical criterion based on the initial energy content of the outflow, to discriminate jets from winds. We show that jet solution is achieved at all magnetization levels, while winds could be obtained only in weakly magnetized discs that feature heating.

The utilization of the dietary energy of pangola and setaria by young growing beef cattle

1982 ◽  
Vol 98 (2) ◽  
pp. 395-404 ◽  
Author(s):  
G. D. Tudor ◽  
D. J. Minson
Keyword(s):  
Protein Content ◽  
Dry Matter ◽  
Production Systems ◽  
Energy Content ◽  
Live Weight ◽  
Initial Energy ◽  
Metabolizable Energy ◽  
Net Energy ◽  
Lower Efficiency ◽  
Tropical Grasses

SUMMARYThe net energy values for growth and fattening of two artificially dried tropical grasses-, pangola (Digitaria decumbens) and setaria (S. sphacelata var. sericea cv. Nandi), of similar estimated metabolizable energy content (8·07 and 7·96 MJ/kg D.M.) were determined with cattle using a slaughter technique. Growing cattle with a mean initial weight of 175 kg were given equal quantities of dry matter of the two grasses at each of three planes of nutrition above maintenance for a period of 152 days.The initial energy, fat and protein content of the total body of the 24 test animals was estimated from regressions relating fasted live weight to theśe components, derived from 12 similar cattle slaughtered at the beginning of the feeding period. The final energy, fat and protein content of the test animals was determined directly by chemical analysis. The metabolizable energy (ME) content of the grasses was estimated from the level of digestible energy (DE) determined with eight cattle, assuming that ME = 0·815 DE.The cattle fed pangola gained more live weight, empty-body weight, fat, protein and energy than animals fed similar quantities of setaria. The net energy value for growth and fattening (NEf) was determined using regressions relating energy retention to the quantity of dry matter eaten. NEf in MJ/kg dry matter was 2·27 for pangola and 1·31 for setaria.Efficiency of utilization of ME for growth and fattening (kf) was.27·7% for pangola and 16·9% for setaria. These values for tropical grasses are lower than any values reported for temperate pasture species. Thus the lower efficiency of utilization of ME may cause the lower production of cattle which graze tropical grasses.It was concluded that as the kf values of different tropical grasses are not constant, kf values should be measured on a wider range of tropical grasses so that this factor can be taken into account when evaluating grasses in animal production systems.

scholarly journals On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hatice Taskesen ◽  
Necat Polat ◽  
Abdulkadir Ertaş
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Type Equation ◽  
Global Solutions ◽  
Initial Energy ◽  
Potential Well ◽  
Global Weak Solutions ◽  
Power Type ◽  
Initial Value ◽  
The Cauchy Problem

We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.

York’s Solution to the Initial-Value Problem

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Hamiltonian Constraint ◽  
Conformal Transformations ◽  
Initial Value ◽  
Spatial Metrics ◽  
Conformal Method ◽  
Conformal Equivalence

In this chapter I briefly review York’s method (or the conformal method) for solving the initial value problem of (GR). This method, developed initially by Lichnerowicz and then generalized by Choquet-Bruhat and York, allows to find solutions of the constraints of (GR) (in particular the Hamiltonian, or refoliation constraint) by scanning the conformal equivalence class of spatial metrics for a solution of the Hamiltonian constraint, exploiting the fact that, in a particular foliation (CMC), the transverse nature of the momentum field is preserved under conformal transformations. This method allows to transform the initial value problem into an elliptic problem for the solution for which good existence and uniqueness theorems are available. Moreover this method allows to identify the reduced phase space of (GR) with the cotangent bundle to conformal superspace (the space of conformal 3-geometries), when the CMC foliation is valid. SD essentially amounts to taking this phase space as fundamental and renouncing the spacetime description when the CMC foliation is not available.

scholarly journals Energy and protein nutrition of early-weaned pigs. 1. effect of energy intake and energy: protein on growth, efficiency and nitrogen utilization of pigs between 8–32 d

1980 ◽  
Vol 43 (2) ◽  
pp. 289-304 ◽  
Author(s):  
K. J. McCracken ◽  
S. M. Eddie ◽  
W. G. Stevenson
Keyword(s):  
Least Squares Method ◽  
Energy Content ◽  
Skim Milk ◽  
Nitrogen Retention ◽  
Growth Efficiency ◽  
Initial Energy ◽  
Feed Conversion ◽  
Response Curves ◽  
Protein Levels ◽  
Rate Of Increase

1. The effect of energy and protein intake on the growth, food efficiency and nitrogen retention of artificially-reared pigs was studied over three 8 d periods between 8–32 d of age in an experiment employing a 5×3×2 factorial design. The factors were initial energy: N value (I; 250, 355, 460, 565 or 670 kJ/g N), rate of increase of 1 at 8 d intervals (0, 12.5 or 25%) and plane of nutrition (three times daily to appetite or 75% of this intake).2. The range of energy: N values was obtained by formulating five diets based on dried skim milk, lactose and casein and feeding appropriate combinations of two diets. The diets, which were pelleted, contained 100 g maize oil/kg and the gross energy content was approximately 20 MJ/kg.3. N digestibility was high at all three age intervals, reaching 0.99 on the diet containing the highest dietary crude protein (N × 6.25) level. Metabolic faecal N excretion was found to be 1.1 g/kg dry matter (DM) intake.4. Growth rate, feed conversion ratio (kg food intake/kg wt gain; FCR), N retention (NR) and the proportion of digested N retained (NR:apparent digested N (ADN)) were significantly (P < 0.001) affected by I values at all age intervals and the responses were quadratic. Response curves were calculated by the least squares method and optimum values of I determined for each of the criteria.A constant energy:N value of approximately 400 kJ/g N was indicated by growth, FCR and NR optima but the NR:ADN value fell from 0.77 for the 8–16 d period to 0.60 for the 24–32 d period at this I value. It is concluded that a suitable compromise would be an I value of 470 kJ/g N increasing by 10%/week.5. There was a significant interaction between plane of nutrition and I values on FCR between 16–24 d (P < 0.001) and 8–32 d (P < 0.01) indicating that FCR was better at high protein levels and worse at low protein levels when the diets were fed on the lower plane of nutrition.

scholarly journals Explaining the low luminosity of Uranus: a self-consistent thermal and structural evolution

2020 ◽  
Vol 633 ◽  
pp. A50 ◽  
Author(s):  
Allona Vazan ◽  
Ravit Helled
Keyword(s):  
Energy Content ◽  
Structural Evolution ◽  
Initial Energy ◽  
Planetary Science ◽  
Composition Gradient ◽  
Internal Cooling ◽  
Composition Distribution ◽  
Convective Mixing ◽  
Deep Interior ◽  
Composition Gradients

The low luminosity of Uranus is a long-standing challenge in planetary science. Simple adiabatic models are inconsistent with the measured luminosity, which indicates that Uranus is non-adiabatic because it has thermal boundary layers and/or conductive regions. A gradual composition distribution acts as a thermal boundary to suppress convection and slow down the internal cooling. Here we investigate whether composition gradients in the deep interior of Uranus can explain its low luminosity, the required composition gradient, and whether it is stable for convective mixing on a timescale of some billion years. We varied the primordial composition distribution and the initial energy budget of the planet, and chose the models that fit the currently measured properties (radius, luminosity, and moment of inertia) of Uranus. We present several alternative non-adiabatic internal structures that fit the Uranus measurements. We found that convective mixing is limited to the interior of Uranus, and a composition gradient is stable and sufficient to explain its current luminosity. As a result, the interior of Uranus might still be very hot, in spite of its low luminosity. The stable composition gradient also indicates that the current internal structure of Uranus is similar to its primordial structure. Moreover, we suggest that the initial energy content of Uranus cannot be greater than 20% of its formation (accretion) energy. We also find that an interior with a mixture of ice and rock, rather than separated ice and rock shells, is consistent with measurements, suggesting that Uranus might not be “differentiated”. Our models can explain the luminosity of Uranus, and they are also consistent with its metal-rich atmosphere and with the predictions for the location where its magnetic field is generated.

scholarly journals SPIN FLUIDS IN BIANCHI-I f(R)-COSMOLOGY WITH TORSION

2012 ◽  
Vol 09 (07) ◽  
pp. 1250054 ◽  
Author(s):  
STEFANO VIGNOLO ◽  
LUCA FABBRI
Keyword(s):  
Conservation Laws ◽  
Initial Value Problem ◽  
Bianchi Type ◽  
Hamiltonian Constraint ◽  
Type I ◽  
Field Equations ◽  
Initial Value ◽  
Bianchi I ◽  
Jordan And Einstein Frames ◽  
General Conservation

We study Weyssenhoff spin fluids in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity; the resulting field equations are derived and discussed in both Jordan and Einstein frames, clarifying the role played by the spin and the non-linearity of the gravitational Lagrangian f(R) in generating the torsional dynamical contributions. The general conservation laws holding for f(R)-gravity with torsion are employed to provide the conditions needed to ensure the preservation of the Hamiltonian constraint and the consequent correct formulation of the associated initial value problem. Examples are eventually given.

On the influence of specimen thickness in TEM images of super-conducting vortices

1996 ◽  
Vol 54 ◽  
pp. 724-725
Author(s):  
J. Bonevich ◽  
D. Capacci ◽  
G. Pozzi ◽  
K. Harada ◽  
H. Kasai ◽  
...  
Keyword(s):  
Flux Line ◽  
Analytical Form ◽  
Realistic Model ◽  
Electron Holography ◽  
Specimen Thickness ◽  
Flux Tubes ◽  
Analytical Expression ◽  
Flux Lines ◽  
Normal Core ◽  
Two Parameters

The successful observation of superconducting flux lines (fluxons) in thin specimens both in conventional and high Tc superconductors by means of Lorentz and electron holography methods has presented several problems concerning the interpretation of the experimental results. The first approach has been to model the fluxon as a bundle of flux tubes perpendicular to the specimen surface (for which the electron optical phase shift has been found in analytical form) with a magnetic flux distribution given by the London model, which corresponds to a flux line having an infinitely small normal core. In addition to being described by an analytical expression, this model has the advantage that a single parameter, the London penetration depth, completely characterizes the superconducting fluxon. The obtained results have shown that the most relevant features of the experimental data are well interpreted by this model. However, Clem has proposed another more realistic model for the fluxon core that removes the unphysical limitation of the infinitely small normal core and has the advantage of being described by an analytical expression depending on two parameters (the coherence length and the London depth).

Demonstrating Nutrient Cost Gradients: A Brooklyn Case Study

2014 ◽  
Vol 84 (5-6) ◽  
pp. 244-251 ◽  
Author(s):  
Robert J. Karp ◽  
Gary Wong ◽  
Marguerite Orsi
Keyword(s):  
Low Income ◽  
Energy Content ◽  
Food Selection ◽  
The United States ◽  
United States Department ◽  
Micronutrient Deficiencies ◽  
Caloric Density ◽  
Low Income Families ◽  
The Cost ◽  
The Impact

Abstract. Introduction: Foods dense in micronutrients are generally more expensive than those with higher energy content. These cost-differentials may put low-income families at risk of diminished micronutrient intake. Objectives: We sought to determine differences in the cost for iron, folate, and choline in foods available for purchase in a low-income community when assessed for energy content and serving size. Methods: Sixty-nine foods listed in the menu plans provided by the United States Department of Agriculture (USDA) for low-income families were considered, in 10 domains. The cost and micronutrient content for-energy and per-serving of these foods were determined for the three micronutrients. Exact Kruskal-Wallis tests were used for comparisons of energy costs; Spearman rho tests for comparisons of micronutrient content. Ninety families were interviewed in a pediatric clinic to assess the impact of food cost on food selection. Results: Significant differences between domains were shown for energy density with both cost-for-energy (p < 0.001) and cost-per-serving (p < 0.05) comparisons. All three micronutrient contents were significantly correlated with cost-for-energy (p < 0.01). Both iron and choline contents were significantly correlated with cost-per-serving (p < 0.05). Of the 90 families, 38 (42 %) worried about food costs; 40 (44 %) had chosen foods of high caloric density in response to that fear, and 29 of 40 families experiencing both worry and making such food selection. Conclusion: Adjustments to USDA meal plans using cost-for-energy analysis showed differentials for both energy and micronutrients. These differentials were reduced using cost-per-serving analysis, but were not eliminated. A substantial proportion of low-income families are vulnerable to micronutrient deficiencies.

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