Double Zero Research Articles

Non-relativistic metrics with extremal limits

We present solutions of type IIB supergravity with z = 2 Schrodinger asymptotics that admit an extremal limit, i.e. the black hole horizon has a double zero. These solutions are obtained as TsT transformations of the charged planar black hole in AdS 5 × S 5. Unlike the uncharged solution, the Ramond-Ramond two-form is turned on. We study the thermodynamic properties of these new solutions, and we show that the ratio of shear viscosity to entropy density is 1/4π even in the extremal limit. We also consider the TsT-transformed soliton and show that, for a special radius of the compact circle, there is a confinement-deconfinement phase transition at zero temperature between the soliton and black hole phases. © SISSA 2009.

Some Aspects of Radio Wave Propagation in Double Zero Metamaterials Having the Real Parts of Epsilon and Mu Equal to Zero

Recently, various uncommon materials such as metamaterials have been the subject of intensive research. In this paper, we introduce a new class of materials called double zero materials (DZR) having the real parts of both its epsilon and mu equal to zero and investigate the electromagnetic wave propagation in them, particularly the propagation constant k and intrinsic impedance η. We investigate the reflection and transmission coefficients from multilayer structures made of DZR material located in various media. It is shown that the DZR constants namely k and η and also the reflection and transmission coefficients from the multilayer structures are all real quantities. Several numerical examples are provided for both dispersive and nondispersive DZR materials.

Egg performance, egg quality, and nutrient utilization in laying hens fed diets with different levels of rapeseed expeller cake

The aim of this study was to evaluate the effect of different levels of rapeseed expeller cake (RC) in the diet of laying hens on egg performance, egg quality, retention and excretion of nitrogen, calcium and phosphorus, and metabolizability of energy. The experiment was carried out with 72 Bovans Brown hens, from 28 to 53 weeks of age. Experimental treatment consisted of four isonitrogenous and isocaloric corn-soybean diets (as calculated: 17% crude protein, 11.6 MJ/kg metabolizable energy, 0.81% lysine, 0.36% methionine, 3.60% calcium and 0.37% available phosphorus), containing 0, 4, 6 or 8% RC. The RC used was produced from double zero rapeseed and contained 29.3% crude protein, 17.4% crude fat, 10.8% crude fibre, 0.63% calcium, 0.97% phosphorus, 1.91% lysine and 0.84% methionine. During the experimental period, the dietary level of RC had no significant effects on egg performance and egg quality parameters. Boiled eggs from hens fed a diet with 8% RC were characterized by an inferior flavour to those from other groups. There were no treatment effects on nitrogen balance or metabolizability of energy, though the highest dietary level of RC negatively affected retention and excretion of calcium and phosphorus.;

Stability and bifurcation for a flexible beam under a large linear motion with a combination parametric resonance

Stability and bifurcation behaviors for a model of a flexible beam undergoing a large linear motion with a combination parametric resonance are studied by means of a combination of analytical and numerical methods. Three types of critical points for the bifurcation equations near the combination resonance in the presence of internal resonance are considered, which are characterized by a double zero and two negative eigenvalues, a double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues in nonresonant case, respectively. The stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters. Especially, for the third case, the explicit expressions of the critical bifurcation curves leading to incipient and secondary bifurcations are obtained with the aid of normal form theory. Bifurcations leading to Hopf bifurcations and 2-D tori and their stability conditions are also investigated. Some new dynamical behaviors are presented for this system. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic ones.

Transverse intersection of invariant manifolds in perturbed multi-symplectic systems

A multi-symplectic system is a PDE with a Hamiltonian structure in both temporal and spatial variables. This article considers spatially periodic perturbations of symmetric multi-symplectic systems. Due to their structure, unperturbed multi-symplectic systems often have families of solitary waves or front solutions, which together with the additional symmetries lead to large invariant manifolds. Periodic perturbations break the translational symmetry in space and might break some of the other symmetries as well. In this article, periodic perturbations of a translation invariant PDE with a one-dimensional symmetry group are considered. It is assumed that the unperturbed PDE has a three-dimensional invariant manifold associated with a solitary wave or front connection of multi-symplectic relative equilibria. Using the momentum associated with the symmetry group, sufficient conditions for the persistence of invariant manifolds and their transversal intersection are derived. In the equivariant case, invariance of the momentum under the perturbation gives the persistence of the full three-dimensional manifold. In this case, there is also a weaker condition for the persistence of a two-dimensional submanifold with a selected value of the momentum. In the non-equivariant case, the condition leads to the persistence of a one-dimensional submanifold with a seleceted value of the momentum and a selected action of the symmetry group. These results are applicable to general Hamiltonian systems with double zero eigenvalue in the linearization due to continuous symmetry. The conditions are illustrated on the example of the defocussing non-linear Schrödinger equations with perturbations which illustrate the three cases. The perturbations are: an equivariant Hamiltonian perturbation which keeps the momentum level sets invariant; an equivariant damped, driven perturbation; and a perturbation which breaks the rotational symmetry.

Development and characterisation of a Brassica carinata inbred line incorporating genes for low glucosinolate content from B. juncea

The presence of high levels of sinigrin in the seeds represents a serious constraint for the commercial utilisation of Ethiopian mustard (Brassica carinata A. Braun) meal. The objective of this research was the introgression of genes for low glucosinolate content from B. juncea into B. carinata. BC1F1 seed from crosses between double zero B. juncea line Heera and B. carinata line N2-142 was produced. Simultaneous selection for B. carinata phenotype and low glucosinolate content was conducted from BC1F2 to BC1F4 plant generations. Forty-three BC1F4 derived lines were selected and subject to a detailed phenotypic and molecular evaluation to identify lines with low glucosinolate content and genetic proximity to B. carinata. Sixteen phenotypic traits and 80 SSR markers were used. Eight BC1F4 derived lines were very close to N2-142 both at the phenotypic and molecular level. Three of them, with average glucosinolate contents from 52 to 61 micromoles g−1, compared to 35 micromoles g−1 for Heera and 86 micromoles g−1 for N2-142, were selected and evaluated in two additional environments, resulting in average glucosinolate contents from 43 to 56 micromoles g−1, compared to 29 micromoles g−1 for Heera and 84 micromoles g−1 for N2-142. The best line (BCH-1773), with a glucosinolate profile made up of sinigrin (>95%) and a chromosome number of 2n = 34, was further evaluated in two environments (field and pots in open-air conditions). Average glucosinolate contents over the four environments included in this research were 42, 31 and 74 micromoles g−1 for BCH-1773, Heera and N2-142, respectively. These are the lowest stable levels of glucosinolates reported so far in B. carinata.

The effect of feeding untreated rapeseed and iodine supplement on egg quality

The objective of the experiment was to evaluate the effect of the feeding of 80 g/kg (R8) and 100 g/kg (R10) of untreated rapeseed (RS) on egg quality including sensory quality in comparison with a control diet without rapeseed (R0). The addition of iodine (I) was also evaluated (1 mg/kg (R10) vs. 3 mg/kg (R10+I)). “Double zero” RS was used. The contents of energy and crude protein were almost the same in the diets. Laying hybrid ISABROWN was used in the experiment. The quality of eggs was analyzed 11 times every 28 days, from 19 to 64 weeks of age. 30 eggs per each group were always analyzed. Boiled eggs were assessed twice around the peak of egg production. Egg weight decreased (<I>P</I> < 0.001) with the increased level of RS (62.9 g, 61.8 g and 60.7 g, respectively). A reduction in egg weight in R8 and R10 diets resulted in the lower weight of albumen and eggshells. The addition of I to R10 diet increased (<I>P</I> < 0.001) egg weight (62.1 g vs. 60.7 g). The yolk proportion in egg weight was the highest (26.0%, <I>P</I> < 0.001) and the albumen weight ratio was the lowest (64.2%, <I>P</I> < 0.001) in group R8. Iodine supplementation improved (<I>P</I> < 0.001) yolk weight (15.7 g vs. 15.3 g). The proportion of RS in the diet did not affect the eggshell strength. An increase in the level of I improved (<I>P</I> < 0.001) eggshell quality (strength 36.1 N vs. 34.0 N and thickness 0.386 mm vs. 0.363 mm). Taste and overall acceptability were lower (<I>P</I> < 0.05) in eggs of hens fed RS. The addition of I did not affect flavour, odour, taste or overall acceptability.

Stability and bifurcation analysis for a model of a nonlinear coupled pitch–roll ship

Using a combination of analytical and numerical methods, the paper studies the stability and bifurcations for a model of a nonlinear coupled pitch–roll ship. The model represents a two-degree-of-freedom system with quadratic coupling subjected to a modulated sinusoidal excitation. Three types of critical points for the bifurcation response equations near the combination resonance in the presence of internal resonance are considered. These points are characterized by a double zero and two negative eigenvalues, a double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. For each case, the stability regions for the initial equilibrium solution and the critical bifurcation curves are obtained. The amplitude response curves with respect to detuning/damping parameters for critical bifurcation parameters are obtained for the first two types, and detailed analyses of the eigenvalues of the linearized system for each parametric region are given. For the third type, with the aid of normal form theory, the explicit expressions of the critical bifurcation curves leading to incipient and secondary bifurcations are obtained. Bifurcations leading to 2D, 3D tori and their stability conditions are also investigated. Some new dynamical behaviors are presented for this system.

Euler characteristics of Teichmüller curves in genus two

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert modular surfaces and our main result is that the Euler characteristic of a Teichmuller curve is proportional to the Euler characteristic of the Hilbert modular surface on which it lies. The idea is to use techniques from algebraic geometry to calculate the fundamental classes of these Teichmuller curves in certain compactifications of the Hilbert modular surfaces. This is done by defining meromorphic sections of line bundles over Hilbert modular surfaces which vanish along these Teichmuller curves. We apply these results to calculate the Siegel-Veech constants for counting closed billiards paths in certain L-shaped polygons. We also calculate the Lyapunov exponents of the Kontsevich-Zorich cocycle for any ergodic, SL_2(R)-invariant measure on the moduli space of Abelian differentials in genus two (previously calculated in unpublished work of Kontsevich and Zorich).

Bifurcations in the Regularized Ericksen Bar Model

We consider the regularized Ericksen model of an elastic bar on an elastic foundation on an interval with Dirichlet boundary conditions as a two-parameter bifurcation problem. We explore, using local bifurcation analysis and continuation methods, the structure of bifurcations from double zero eigenvalues. Our results provide evidence in support of Müller’s conjecture (Müller, Calc. Var. 1:169–204, 1993) concerning the symmetry of local minimizers of the associated energy functional and describe in detail the structure of the primary branch connections that occur in this problem. We give a reformulation of Müller’s conjecture and suggest two further conjectures based on the local analysis and numerical observations. We conclude by analysing a “loop” structure that characterizes (k,3k) bifurcations.

SHILNIKOV-TYPE MULTIPULSE ORBITS AND CHAOTIC DYNAMICS OF A PARAMETRICALLY AND EXTERNALLY EXCITED RECTANGULAR THIN PLATE

The Shilnikov-type multipulse orbits and chaotic dynamics for a simply supported rectangular thin plate under combined parametric and external excitations are studied in this paper for the first time. The rectangular thin plate is subjected to spatially and temporally varying transversal and in-plane excitations, simultaneously. The formulas of the rectangular thin plate are derived from the von Kármán equation and Galerkin's method. The method of multiple scales is used to find the averaged equation in the case of 1:2 internal resonance. Based on the averaged equation, the theory of normal form is used to obtain the explicit expressions of normal form associated with a double zero and a pair of purely imaginary eigenvalues using the Maple program. The dissipative version of the energy-phase method is utilized to analyze the multipulse global bifurcations and chaotic dynamics of a parametrically and externally excited rectangular thin plate. The global dynamical analysis indicates that there exist the multipulse jumping orbits in the perturbed phase space of the averaged equation for a parametrically and externally excited rectangular thin plate. These results show that the chaotic motions of the multipulse Shilnikov-type can occur for a parametrically and externally excited rectangular thin plate. Numerical simulation results are presented to verify the analytical predictions. It is also found from the results of numerical simulation that the Shilnikov-type multipulse orbits exist for a parametrically and externally excited thin plate.

Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams

The critical and post-critical behavior of a non-conservative non-linear structure, undergoing statical and dynamical bifurcations, is analyzed. The system consists of a purely flexible planar beam, equipped with a lumped visco-elastic device, loaded by a follower force. A unique integro-differential equation of motion in the transversal displacement, with relevant boundary conditions, is derived. Then, the linear stability diagram of the trivial rectilinear configuration is built-up in the parameter space. Particular emphasis is given to the role of the damping on the critical scenario. The occurrence of different mechanisms of instability is highlighted, namely, of divergence, Hopf, double zero, resonant and non-resonant double Hopf, and divergence–Hopf bifurcation. Attention is then focused on the two latter (codimension-two) bifurcations. A multiple scale analysis is carried-out directly on the continuous model, and the relevant non-linear bifurcation equations in the amplitudes of the two interactive modes are derived. The fixed-points of these equations are numerically evaluated as functions of two bifurcation parameters and some equilibrium paths illustrated. Finally, the bifurcation diagrams, illustrating the system behavior around the critical points of the parameter space, are obtained.

On the Inverse and Determinant of Certain Truncated Wiener-Hopf Operators

The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible) and in singular cases. This paper treats two cases where the symbol of the Wiener-Hopf operator has Fisher-Hartwig singularities, one double zero or two simple zeros. We find formulas for the inverse that hold uniformly throughout the underlying interval with very small error, and formulas for the determinant with very small error.

Global bifurcations and chaotic dynamics for a string-beam coupled system

The global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations are investigated in detail in this paper. The governing equations are firstly obtained to describe the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differential equations with two-degrees-of-freedom. Using the method of multiple scales, parametrically and externally excited system is transformed to the averaged equation. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam and primary resonance for the string is considered. Based on the averaged equation, the theory of normal form is utilized to find the explicit formulas of normal form associated with one double zero and a pair of pure imaginary eigenvalues. The global perturbation method is employed to analyze the global bifurcations and chaotic dynamics of the string-beam coupled system. The analysis of the global bifurcations indicates that there exist the homoclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation of the string-beam coupled system. These results obtained here mean that the chaotic motions can occur in the string-beam coupled system. Numerical simulations also verify the analytical predications.

Effects of Enzyme Addition to Broiler Diets Containing Varying Levels of Double Zero Rapeseed Meal

Maize-soybean meal diets with 0, 100, 200 and 300 g/kg double zero rapeseed meal ('00' RSM) with and without an enzyme mixture (xylanase, pectinase, cellulase) at a level of 1.6 g/kg were evaluated with 624 day-old broiler chicks for 5 weeks. The birds were randomly allocated to eight dietary treatments with three replicates of 26 birds each. Average daily gain (ADG) and feed intake (FI) were recorded weekly and ileal viscosity, organ weights, serum enzyme activity, hormonal profile and hematological parameters were measured at the end of week 5. Average daily gain during the weekly periods was significantly influenced by the dietary level of '00'RSM (p<0.01). Inclusion of '00' RSM improved the ADG up to day 28 with the increased level; beyond that time no improvement was recorded when compared to control groups. However, ADG from 1-35 days was significantly different between 300 g/kg inclusion level of '00' RSM and the control diet. Inconsistent decline in feed intake and feed conversion ratio was observed up to day 21 and the trend was reversed thereafter. The proportion of '00' RSM in the diet had a significant (p≤0.05) influence on thyroid weight but had no effect on the relative weights of liver and heart, serum enzyme activities (γ-glutamyl transferase, alanine amino transferase and aspartate amino transferase), thyroid hormones (T 3 and T 4 ), hemoglobin level and hematocrit. Significant improvement in ADG was recorded during the 2nd week of age with the addition of enzyme, whereas for all other periods, including the whole period of the trial, higher but non-significant ADG was observed. FI and FCR were not affected by the addition of enzyme but there was a numerical reduction in FCR during the whole period. The addition of enzyme reduced the ileal viscosity at all levels of '00' RSM inclusion. The results suggest that '00' RSM can be included up to 300 g/kg in broiler diets without any adverse effects on health and performance. The addition of commercial enzyme mixture containing xylanase, pectinase, cellulase to broiler diets containing '00'RSM has some effect on growth rate and feed conversion efficiency.

Global bifurcations and chaos for a rotor-active magnetic bearing system with time-varying stiffness

In this paper, we investigate the global bifurcations and chaotic dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and time-varying stiffness. From the averaged equation obtained in another paper, the theory of normal form is applied in this paper to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Since the normal form obtained here is not the simplest one, the methods of choosing other complementary space and utilizing the inner product are presented to further reduce the normal form and obtain a simpler normal form. Based on simpler the normal form obtained above, a global perturbation method is utilized for the analysis of global bifurcations and chaotic dynamics of the rotor-AMB system. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation of the rotor-AMB system with the time-varying stiffness. These results indicate that the chaotic motions can occur in the rotor-AMB system with time-varying stiffness. Numerical simulations verify the analytical predictions. The jumping and catastrophic phenomena of the amplitude for the chaotic oscillations in the system are also found by using numerical simulations.

Canola oil extracted by supercritical carbon dioxide and a commercial organic solvent

Samples of crushed and cooked canola seeds (Okapy Double Zero) were extracted using supercritical carbon dioxide (SCCO2) (34.0 MPa and 40.0 °C) and a commercial organic solvent (AW406). Oil solubility was obtained through several stepwise extractions under the conditions of this study, and then three additional extractions were performed to measure fatty acid compositions, iodine values, chlorophyll concentrations and unsaponifiable matter. The yield of SCCO2 extraction was lower than that after extraction with AW406 solvent, due to the incomplete SCCO2 extraction process. Fatty acid composition analysis showed that the SCCO2-extracted oil was slightly higher in polyunsaturated fatty acids and lower in erucic and behenic acids. However, iodine values and unsaponifiable matter did not indicate significant differences (p >0.05) in the two extracted oils. The chlorophyll concentration of SCCO2-extracted oil was lower than that in the AW406 solvent, and as a result, the color of SCCO2-extracted oil was lighter.

Petroleum-free extraction of oil from canola seedsusing supercritical CO2

Samples of crushed and cooked canola seeds (Okapy Double Zero) were extracted using supercritical carbon dioxide (SCCO2) at 34 MPa and 40oC and a commercial organic solvent (AW406). The oil solubility in SCCO2 was determined and extracted oils were examined with respect to their chlorophyll contents, nonsaponifiable matters, fatty acid composition and iodine value. The yield of SCCO2 extraction was significantly (P 0.05) in both extracted oils. Key words: Canola oil, extraction, organic solvent, quality characteristics, supercritical carbon dioxide

Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt

Abstract In this paper, the Shilnikov type multi-pulse orbits and chaotic dynamics of parametrically excited viscoelastic moving belt are studied in detail. Using Kelvin-type viscoelastic constitutive law, the equations of motion for viscoelastic moving belt with the external damping and parametric excitation are given. The four-dimensional averaged equation under the case of primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin’s approach to the partial differential governing equation of viscoelastic moving belt. From the averaged equations obtained here, the theory of normal form is used to give the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on normal form, the energy-phrase method is employed to analyze the global bifurcations and chaotic dynamics in parametrically excited viscoelastic moving belt. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type multi-pulse homoclinic orbits in the averaged equation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense in parametrically excited viscoelastic moving belt. The chaotic motions of viscoelastic moving belts are also found by using numerical simulation. A new phenomenon on the multi-pulse jumping orbits is observed from three-dimensional phase space.

Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam

This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.