Geometric Integrability of the Camassa-Holm Equation. II

It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.

Effects of increasing levels of pea hulls in the diet on productive performance, development of the gastrointestinal tract, and nutrient retention of broilers from one to eighteeen days of age

The effects of inclusion of pea hulls (PH) in the diet on growth performance, development of the gastrointestinal tract and nutrient retention were studied in broilers from 1 to 18d of age. There were a control diet based on low fibre ingredients (69.3 total dietary fibre (16.1g crude fibre/kg)) and three additional diets that resulted from the dilution of the basal diet with 25, 50 and 75g PH/kg (81.2, 93.2, and 105.1g total dietary fibre/kg diet, respectively). Each treatment was replicated six times and the experimental unit was a cage with 12 chicks. Growth performance, development of the gastrointestinal tract and the coefficients of total tract apparent retention (CTTAR) of nutrients were recorded at 6, 12 and 18d of age. In addition, jejunal morphology was measured at 12 and 18d and the coefficients of apparent ileal digestibility (CAID) of nutrients at 18d of age. Pea hulls inclusion affected all the parameters studied. The inclusion of 25 and 50g PH/kg diet improved growth performance as compared to the control diet. The relative weight (g/kg body weight) of proventriculus (P≤0.01), gizzard (P≤0.001) and ceca (P≤0.05) increased linearly as the level of PH in the diet increased. The inclusion of PH affected quadratically (P≤0.01) villus height:crypt depth ratio with the highest value shown at 25g PH/kg. In general, the CTTAR and CAID of nutrients increased linearly and quadratically (P≤0.05) with increasing levels of PH, showing maximum values with PH level between 25 and 50g/kg diet. We conclude that the size of the digestive organs increases with increasing levels of PH in the diet. In general, the best performance and nutrient digestibility values were observed with levels of PH within the range of 25 and 50g/kg. Therefore, young broilers have a requirement for a minimum amount of dietary fibre. When pea hulls are used as a source of fibre, the level of total dietary fibre required for optimal performance is within the range of 81.2–93.2g/kg diet (25.6–35.0g crude fibre/kg diet). An excess of total dietary fibre (above 93.2g/kg diet) might reduce nutrient digestibility and growth performance to values similar to those observed with the control diet.

Equation of state for hot dense matter using a relativistic screened hydrogenic model

The study of matter under conditions of high density, pressure, and temperature is a valuable subject for inertial confinement fusion (ICF), astrophysical phenomena, high-power laser interaction with matter, etc. In all these cases, matter is heated and compressed by strong shocks to high pressures and temperatures, becomes partially or completely ionized via thermal or pressure ionization, and is in the form of dense plasma. The thermodynamics and the hydrodynamics of hot dense plasmas cannot be predicted without the knowledge of the equation of state (EOS) that describes how a material reacts to pressure and how much energy is involved. Therefore, the equation of state often takes the form of pressure and energy as functions of density and temperature. Furthermore, EOS data must be obtained in a timely manner in order to be useful as input in hydrodynamic codes. By this reason, the use of fast, robust and reasonably accurate atomic models, is necessary for computing the EOS of a material.

Equation of State and Opacities for Warm Dense Matter.

We will present recent developments in the calculation of opacity and equation of state tables suitable for including in the radiation hydrodynamic code ARWEN [1] to study processes like ICF or X-ray secondary sources. For these calculations we use the code BiG BART to compute opacities in LTE conditions, with self-consistent data generated with the Flexible Atomic Code (FAC) [2]. Non-LTE effects are approximately taken into account by means of the improved RADIOM model [3], which makes use of existing LTE data tables. We use the screened-hydrogenic model [4] to derive the Equation of State using the population and energy of the levels avaliable from the atomic data

Effect of wheat inclusion and xylanase supplementation of the diet on intestinal enzyme activity, nutrient retention and performance in laying hen from 25 to 47 wks of age

A trial was conducted to examine the effects of increasing levels of wheat in the diet and xylanase (ES) supplementation on nitrogen and ether extract retention, pH of the GIT, productive performance from 25 to 47 wks of age, and enzyme activity at the small intestine level. The basal diets (from 25 to 33 wks and from 33 to 47 wks) consisted of soybean meal and corn, and the wheat was introduced in the experimental diets at expenses of corn, primarily.

New reynolds equation for line contact based on the carreau model modification by bair

This paper presents a new form of the one-dimensional Reynolds equation for lubricants whose rheological behaviour follows a modified Carreau rheological model proposed by Bair. The results of the shear stress and flow rate obtained through a new Reynolds–Carreau equation are shown and compared with the results obtained by other researchers.

A non-perturbative renormalization group study of the stochastic NavierStokes equation

We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4−2 ɛ of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ɛ=2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ɛ dependence of the scaling dimension of the eddy diffusivity at ɛ=3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

Effect of ion flux on helium retention in helium-irradiated tungsten

Helium retention in irradiated tungsten leads to swelling, pore formation, sample exfoliation and embrittlement with deleterious consequences in many applications. In particular, the use of tungsten in future nuclear fusion plants is proposed due to its good refractory properties. However, serious concerns about tungsten survivability stems from the fact that it must withstand severe irradiation conditions. In magnetic fusion as well as in inertial fusion (particularly with direct drive targets), tungsten components will be exposed to low and high energy ion (helium) irradiation, respectively. A common feature is that the most detrimental situations will take place in pulsed mode, i.e., high flux irradiation. There is increasing evidence on a correlation between a high helium flux and an enhancement of detrimental effects on tungsten. Nevertheless, the nature of these effects is not well understood due to the subtleties imposed by the exact temperature profile evolution, ion energy, pulse duration, existence of impurities and simultaneous irradiation with other species. Physically based Kinetic Monte Carlo is the technique of choice to simulate the evolution of radiation-induced damage inside solids in large temporal and space scales. We have used the recently developed code MMonCa (Modular Monte Carlo simulator), presented in this conference for the first time, to study He retention (and in general defect evolution) in tungsten samples irradiated with high intensity helium pulses. The code simulates the interactions among a large variety of defects and impurities (He and C) during the irradiation stage and the subsequent annealing steps. In addition, it allows us to vary the sample temperature to follow the severe thermo-mechanical effects of the pulses. In this work we will describe the helium kinetics for different irradiation conditions. A competition is established between fast helium cluster migration and trapping at large defects, being the temperature a determinant factor. In fact, high temperatures (induced by the pulses) are responsible for large vacancy cluster formation and subsequent additional trapping with respect to low flux irradiation.

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive k2, are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Extension of the characteristic equation to absorption chillers with adiabatic absorbers

Various researchers have developed models of conventional H2O–LiBr absorption machines with the aim of predicting their performance. In this paper, the methodology of characteristic equations developed by Hellmann et al. (1998) is applied. This model is able to represent the capacity of single effect absorption chillers and heat pumps by means of simple algebraic equations. An extended characteristic equation based on a characteristic temperature difference has been obtained, considering the facility features. As a result, it is concluded that for adiabatic absorbers a subcooling temperature must be specified. The effect of evaporator overflow has been characterized. Its influence on cooling capacity has been included in the extended characteristic equation. Taking into account the particular design and operation features, a good agreement between experimental performance data and those obtained through the extended characteristic equation has been achieved at off-design operation. This allows its use for simulation and control purposes.

Effect of ion flux on helium retention in helium-irradiated tungsten

Helium retention in irradiated tungsten leads to swelling, pore formation, sample exfoliation and embrittlement with deleterious consequences in many applications. In particular, the use of tungsten in future nuclear fusion plants is proposed due to its good refractory properties. However, serious concerns about tungsten survivability stems from the fact that it must withstand severe irradiation conditions. In magnetic fusion as well as in inertial fusion (particularly with direct drive targets), tungsten components will be exposed to low and high energy ion irradiation (helium), respectively. A common feature is that the most detrimental situations will take place in pulsed mode, i.e., high flux irradiation. There is increasing evidence of a correlation between a high helium flux and an enhancement of detrimental effects on tungsten. Nevertheless, the nature of these effects is not well understood due to the subtleties imposed by the exact temperature profile evolution, ion energy, pulse duration, existence of impurities and simultaneous irradiation with other species. Object Kinetic Monte Carlo is the technique of choice to simulate the evolution of radiation-induced damage inside solids in large temporal and space scales. We have used the recently developed code MMonCa (Modular Monte Carlo simulator), presented at COSIRES 2012 for the first time, to study He retention (and in general defect evolution) in tungsten samples irradiated with high intensity helium pulses. The code simulates the interactions among a large variety of defects and during the irradiation stage and the subsequent annealing steps. The results show that the pulsed mode leads to significantly higher He retention at temperatures higher than 700 K. In this paper we discuss the process of He retention in terms of trap evolution. In addition, we discuss the implications of these findings for inertial fusion.

Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range

In recent years, the technology for measuring the diameter and height of standing trees has improved significantly. These enhancements allow estimation of the volume of standing trees using stem taper equations, which traditionally have been constructed with data from felled trees, in an accurate and economically feasible way. A nondestructive method was evaluated with data from 38 pines and was validated with data from another 38 pines, both in the Northern Iberian Range (Spain). The electronic dendrometer Criterion RD1000 (Laser Technology Inc.) and the laser hypsometer TruPulse (Laser Technology Inc.) were used due to their accuracy and interoperability. The methodology was valid (unbiased and precise) measuring from a distance similar to the height of the tree. In this distance, statistical criteria and plots based on the residuals showed no clear advantage in volume estimation with models fitted with data from destructive methods against models fitted with data from the proposed non-destructive technique. This methodology can be considered useful for individual volume estimation and for developing taper equations.

Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrodinger equation

The effective mass Schrodinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band which are similar to those originated in quantum wires and quantum wells coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.