The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on ...The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string (MS) relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, and at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids (including supercooled liquid) is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion is of reference significance for solving and simulating the multi-state MS model.展开更多
The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical featu...The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical features of the models are also discussed. In special cases the model reduces to the string models without viscosity that was previously given in the literatures.展开更多
The class of bi-directional optimal velocity models can describe the bi-directional looking effect that usually exists in the reality and is even enhanced with the development of the connected vehicle technologies. It...The class of bi-directional optimal velocity models can describe the bi-directional looking effect that usually exists in the reality and is even enhanced with the development of the connected vehicle technologies. Its combined string stability condition can be obtained through the method of the ring-road based string stability analysis. However, the partial string stability about traffic fluctuation propagated backward or forward was neglected, which will be analyzed in detail in this work by the method of transfer function and its H∞ norm from the viewpoint of control theory. Then, through comparing the conditions of combined and partial string stabilities, their relationships can make traffic flow be divided into three distinguishable regions, displaying various combined and partial string stability performance. Finally, the numerical experiments verify the theoretical results and find that the final displaying string stability or instability performance results from the accumulated and offset effects of traffic fluctuations propagated from different directions.展开更多
Force analysis and calculation of workover string in the slanted and horizontal well are the basis of designing and checking string strength, selecting tools and determining operation parameters, which determine the o...Force analysis and calculation of workover string in the slanted and horizontal well are the basis of designing and checking string strength, selecting tools and determining operation parameters, which determine the operation safety and success of engineering accidence treatment. In this paper, by comprehensive consideration of wellbore structure, string assembly, string load and workover operation conditions, the workover string mechanical model has been built under three kinds of working states of lifting, lowering and rotating. The downhole string mechanics has been analyzed and calculated. By field verification, the string assembly, tool selection and operation parameter optimization can be achieved, which can improve the safety and success rates of workover engineering accident treatment.展开更多
A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predicti...A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.展开更多
The front-row shading reduction coefficient is a key parameter used to calculate the system efficiency of a photovoltaic(PV)power station.Based on the Hay anisotropic sky scattering model,the variation rule of solar r...The front-row shading reduction coefficient is a key parameter used to calculate the system efficiency of a photovoltaic(PV)power station.Based on the Hay anisotropic sky scattering model,the variation rule of solar radiation intensity on the surface of the PV array during the shaded period is simulated,combined with the voltage-current characteristics of the PV modules,and the shadow occlusion operating mode of the PV array is modeled.A method for calculating the loss coefficient of front shadow occlusion based on the division of the PV cell string unit and Hay anisotropic sky scattering model is proposed.This algorithm can accurately evaluate the degree of influence of the PV array layout,wiring mode,array spacing,PV module specifications,and solar radiation on PV power station system efficiency.It provides a basis for optimizing the PV array layout,reducing system loss,and improving PV system efficiency.展开更多
In this paper, a simple mathematical model was proposed to answer such a question: what’s the relationship between the finger pressing position and the corresponding pitch for stringed instruments? Furthermore, we co...In this paper, a simple mathematical model was proposed to answer such a question: what’s the relationship between the finger pressing position and the corresponding pitch for stringed instruments? Furthermore, we compared the theoretical results with measurement results which were obtained from a guitar to prove that the model we propose is reliable. Result shows that relative errors of theoretical results and measurement results are from 0.18% to 1.8%. The mathematics model is more concise, direct and clear than physical model.展开更多
To unify the four known fundamental forces and provide an explanation for the origin and the evolution of the universe are two long-term goals of theoretical physics. Here a “universe collapse model” has been propos...To unify the four known fundamental forces and provide an explanation for the origin and the evolution of the universe are two long-term goals of theoretical physics. Here a “universe collapse model” has been proposed. The universe consists of Matter and No-matter. No-matter is the universal energy that constructs a consistent universe field, presenting a spiral wave motion at the speed of light at the small scale. The partial collapse of the universal energy forms the particles of the universal energy in a variety of sizes, which are called as the elementary particles. These elementary particles form atom and matter, which construct the galaxies. The collapse of the universe field induces the formation of the universe collapse potential (UCP) and universe collapse force (UCF), and the later is represented by four different aspects of the fundamental forces at the large or small scales. The mathematical equation and the derivation of UCP and UCF are described, and possible experimental tests are also suggested. Therefore, this new model may give a novel explanation for the unification of four fundamental forces and the origin and the evolution of the universe.展开更多
The meson productions in Au+Au and/or Pb+Pb collisions at AGS, SPS, RHIC, and LHC energies have been studied systematically with a hadron and string cascade model LUCIAE. After considering the energy dependence of th...The meson productions in Au+Au and/or Pb+Pb collisions at AGS, SPS, RHIC, and LHC energies have been studied systematically with a hadron and string cascade model LUCIAE. After considering the energy dependence of the model parameter α in string fragmentation function and adjusting it to the experimental data of charged multiplicity to a certain extent, the model predictions for meson yield, rapidity, and transverse mass distributions are compatible with the experimental data at AGS, SPS and RHIC energies. A calculation for Pb+Pb collisions at LHC energy is given as well. The obtained fractional variable in string fragmentation function shows a saturation in energy dependence. It is discussed that the saturation of fractional variable in string fragmentation function might be a qualitative representation of the energy dependence of nuclear transparency.展开更多
We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple...We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.展开更多
The mechanical behavior of the test string in deep wells is generally relatively complex as a result of the high temperature and high pressure,severe dogleg and buckling effects,which in some circumstances can even le...The mechanical behavior of the test string in deep wells is generally relatively complex as a result of the high temperature and high pressure,severe dogleg and buckling effects,which in some circumstances can even lead to string failure.Traditional computational methods for the analysis of these behaviors are often inaccurate.For this reason,here a more accurate mechanical model of the test string is introduced by considering variables such as temperature,pressure,wellbore trajectory,and buckling,as well as combining them with the deformation and string constraint conditions brought in by changes in temperature and pressure during the tripping,setting,and test operations.The model is validated by applying it to a specific high-pressure gas well(located in Northeast Sichuan).展开更多
We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation...We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation to the supermembrane action is clear.展开更多
We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra ass...We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.展开更多
Accurate determination of hydraulic parameters such as pressure losses, equivalent circulation density (ECD), etc. plays profound roles in drilling, cementing and other well operations. Hydraulics characterization req...Accurate determination of hydraulic parameters such as pressure losses, equivalent circulation density (ECD), etc. plays profound roles in drilling, cementing and other well operations. Hydraulics characterization requires that all factors are considered as the neglect of any could become potential sources of errors that would be detrimental to the overall well operation. Drilling Hydraulics has been extensively treated in the literature. However, these works almost entirely rely on the assumption that the drill string lies perfectly at the center of the annulus—the so-called “concentric annulus”. In reality, concentricity is almost never achieved even when centralizers are used. This is because of high well inclination angles and different string geometries. Thus, eccentricity exists in practical oil and gas wells especially horizontal and extended reach wells (ERWs) and must be accounted for. The prevalence of drillstring (DS) eccentricity in the annulus calls for a re-evaluation of existing hydraulic models. This study evaluates the effect of drilling fluid rheology types and DS eccentricity on the entire drilling hydraulics. Three non-Newtonian fluid models were analyzed, viz: Herschel Bulkley, power law and Bingham plastic models. From the results, it was observed that while power law and Bingham plastic models gave the upper and lower hydraulic values, Herschel Bulkley fluid model gave annular pressure loss (APL) and ECD values that fall between the upper and lower values and provide a better fit to the hydraulic data than power law and Bingham plastic fluids. Furthermore, analysis of annular eccentricity reveals that APLs and ECD decrease with an increase in DS eccentricity. Pressure loss reduction of more than 50% was predicted for the fully eccentric case for Herschel Bulkley fluids. Thus, DS eccentricity must be fully considered during well planning and hydraulics designs.展开更多
The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings,...The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10774064 and 30860076)the National Basic Research Program of China (Grant No. 2012CB821503)the Natural Science Foundations of Xinjiang Uygur Autonomous Region,China (Grant Nos. 200821104 and 200821184)
文摘The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string (MS) relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, and at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids (including supercooled liquid) is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion is of reference significance for solving and simulating the multi-state MS model.
文摘The locally rotationally symmetric Bianchi-type II string cosmological models with bulk viscosity are obtained, where an equation of state, , and a relation between metric potentials, , are adopted. The physical features of the models are also discussed. In special cases the model reduces to the string models without viscosity that was previously given in the literatures.
基金Projects(51108465,71371192)supported by the National Natural Science Foundation of ChinaProject(2014M552165)supported by China Postdoctoral Science FoundationProject(20113187851460)supported by Technology Project of the Ministry of Transport of China
文摘The class of bi-directional optimal velocity models can describe the bi-directional looking effect that usually exists in the reality and is even enhanced with the development of the connected vehicle technologies. Its combined string stability condition can be obtained through the method of the ring-road based string stability analysis. However, the partial string stability about traffic fluctuation propagated backward or forward was neglected, which will be analyzed in detail in this work by the method of transfer function and its H∞ norm from the viewpoint of control theory. Then, through comparing the conditions of combined and partial string stabilities, their relationships can make traffic flow be divided into three distinguishable regions, displaying various combined and partial string stability performance. Finally, the numerical experiments verify the theoretical results and find that the final displaying string stability or instability performance results from the accumulated and offset effects of traffic fluctuations propagated from different directions.
文摘Force analysis and calculation of workover string in the slanted and horizontal well are the basis of designing and checking string strength, selecting tools and determining operation parameters, which determine the operation safety and success of engineering accidence treatment. In this paper, by comprehensive consideration of wellbore structure, string assembly, string load and workover operation conditions, the workover string mechanical model has been built under three kinds of working states of lifting, lowering and rotating. The downhole string mechanics has been analyzed and calculated. By field verification, the string assembly, tool selection and operation parameter optimization can be achieved, which can improve the safety and success rates of workover engineering accident treatment.
文摘A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.
基金This work was supported by the Global Energy Interconnection Group Limited Science&Technology Project(Project No.:SGGEIG00JYJS1900046).
文摘The front-row shading reduction coefficient is a key parameter used to calculate the system efficiency of a photovoltaic(PV)power station.Based on the Hay anisotropic sky scattering model,the variation rule of solar radiation intensity on the surface of the PV array during the shaded period is simulated,combined with the voltage-current characteristics of the PV modules,and the shadow occlusion operating mode of the PV array is modeled.A method for calculating the loss coefficient of front shadow occlusion based on the division of the PV cell string unit and Hay anisotropic sky scattering model is proposed.This algorithm can accurately evaluate the degree of influence of the PV array layout,wiring mode,array spacing,PV module specifications,and solar radiation on PV power station system efficiency.It provides a basis for optimizing the PV array layout,reducing system loss,and improving PV system efficiency.
文摘In this paper, a simple mathematical model was proposed to answer such a question: what’s the relationship between the finger pressing position and the corresponding pitch for stringed instruments? Furthermore, we compared the theoretical results with measurement results which were obtained from a guitar to prove that the model we propose is reliable. Result shows that relative errors of theoretical results and measurement results are from 0.18% to 1.8%. The mathematics model is more concise, direct and clear than physical model.
文摘To unify the four known fundamental forces and provide an explanation for the origin and the evolution of the universe are two long-term goals of theoretical physics. Here a “universe collapse model” has been proposed. The universe consists of Matter and No-matter. No-matter is the universal energy that constructs a consistent universe field, presenting a spiral wave motion at the speed of light at the small scale. The partial collapse of the universal energy forms the particles of the universal energy in a variety of sizes, which are called as the elementary particles. These elementary particles form atom and matter, which construct the galaxies. The collapse of the universe field induces the formation of the universe collapse potential (UCP) and universe collapse force (UCF), and the later is represented by four different aspects of the fundamental forces at the large or small scales. The mathematical equation and the derivation of UCP and UCF are described, and possible experimental tests are also suggested. Therefore, this new model may give a novel explanation for the unification of four fundamental forces and the origin and the evolution of the universe.
基金The project supported by National Natural Science Foundation of China under Grant Nos.19975075,10135030,and 10075035,National Research Council of Thailand (1.CH7/2454)
文摘The meson productions in Au+Au and/or Pb+Pb collisions at AGS, SPS, RHIC, and LHC energies have been studied systematically with a hadron and string cascade model LUCIAE. After considering the energy dependence of the model parameter α in string fragmentation function and adjusting it to the experimental data of charged multiplicity to a certain extent, the model predictions for meson yield, rapidity, and transverse mass distributions are compatible with the experimental data at AGS, SPS and RHIC energies. A calculation for Pb+Pb collisions at LHC energy is given as well. The obtained fractional variable in string fragmentation function shows a saturation in energy dependence. It is discussed that the saturation of fractional variable in string fragmentation function might be a qualitative representation of the energy dependence of nuclear transparency.
文摘We find an azimuthal-angle dependent approximate wave like solution to second order on a warped five-dimensional manifold with a self-gravitating U(1) scalar gauge field (cosmic string) on the brane using the multiple-scale method. The spectrum of the several orders of approximation show maxima of the energy distribution dependent on the azimuthal-angle and the winding numbers n of the subsequent orders of scalar field. This breakup of the quantized flux quanta does not lead to instability of the asymptotic wavelike solution, due to the suppression of the n-dependency in the energy mo-mentum tensor components by the warp factor. This effect is triggered by the contribution of the five dimensional Weyl tensor on the brane. This con-tribution can be understood as dark energy and can trigger the self-acceleration of the universe without the need of a cosmological constant. There is a striking relation between the symmetry breaking of the Higgs field described by the winding number and the SO(2) breaking of the axially symmetric configuration into a discrete subgroup of rotations about 180°. The discrete sequence of non-axially symmetric deviations, cancelled by the emission of gravitational waves in order to restore the SO(2) symmetry, triggers the pressure Tzz for discrete values of the azimuthal-angle. There can be a possible relation between the recently discovered angle-preferences of polarization axes of quasars on large scales and our theoretical predicted angle-dependency and can be an evidence for the existence of cosmic strings. The discovery of the increase of polarization rate in smaller subgroups of the several large-quasar groups (LQGs), the red shift dependency and the relative orientation of the spin axes with respect to the major axes of their host LQGs, point at a fractional azimuthal structure, were also found in our cosmic string model. This peculiar discontinuous large scale structure, i.e., polarizations directions of multiples of, for example, π/2 orπ/4, can be explained by the spectrum of azimuthal-angle dependent wavelike modes without the need of conventional density perturbations in standard 4D cosmological models. Carefully com-parison of the spectrum of extremal values of the first and second order φ-dependency and the distribution of the alignment of the quasar polarizations is necessary. This can be accomplished when more observational data become available.
文摘The mechanical behavior of the test string in deep wells is generally relatively complex as a result of the high temperature and high pressure,severe dogleg and buckling effects,which in some circumstances can even lead to string failure.Traditional computational methods for the analysis of these behaviors are often inaccurate.For this reason,here a more accurate mechanical model of the test string is introduced by considering variables such as temperature,pressure,wellbore trajectory,and buckling,as well as combining them with the deformation and string constraint conditions brought in by changes in temperature and pressure during the tripping,setting,and test operations.The model is validated by applying it to a specific high-pressure gas well(located in Northeast Sichuan).
文摘We review on Zariski 3-algebra model of M-theory. The model is obtained by Zariski quantization of a semi-light-cone supermembrane action. The model has manifest N=1 supersymmetry in eleven dimensions and its relation to the supermembrane action is clear.
文摘We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.
文摘Accurate determination of hydraulic parameters such as pressure losses, equivalent circulation density (ECD), etc. plays profound roles in drilling, cementing and other well operations. Hydraulics characterization requires that all factors are considered as the neglect of any could become potential sources of errors that would be detrimental to the overall well operation. Drilling Hydraulics has been extensively treated in the literature. However, these works almost entirely rely on the assumption that the drill string lies perfectly at the center of the annulus—the so-called “concentric annulus”. In reality, concentricity is almost never achieved even when centralizers are used. This is because of high well inclination angles and different string geometries. Thus, eccentricity exists in practical oil and gas wells especially horizontal and extended reach wells (ERWs) and must be accounted for. The prevalence of drillstring (DS) eccentricity in the annulus calls for a re-evaluation of existing hydraulic models. This study evaluates the effect of drilling fluid rheology types and DS eccentricity on the entire drilling hydraulics. Three non-Newtonian fluid models were analyzed, viz: Herschel Bulkley, power law and Bingham plastic models. From the results, it was observed that while power law and Bingham plastic models gave the upper and lower hydraulic values, Herschel Bulkley fluid model gave annular pressure loss (APL) and ECD values that fall between the upper and lower values and provide a better fit to the hydraulic data than power law and Bingham plastic fluids. Furthermore, analysis of annular eccentricity reveals that APLs and ECD decrease with an increase in DS eccentricity. Pressure loss reduction of more than 50% was predicted for the fully eccentric case for Herschel Bulkley fluids. Thus, DS eccentricity must be fully considered during well planning and hydraulics designs.
文摘The recently discovered alignment of quasar polarizations on very large scales could possibly be explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous mass in the bulk, while their warped manifestations in the brane can be consistent with general relativity in 4D. The self-gravitating cosmic string induces gravitational wavelike disturbances which could have effects felt on the brane, i.e., the massive effective 4D modes (Kaluza-Klein modes) of the perturbative 5D graviton. This effect is amplified by the time dependent part of the warp factor. Due to this warp factor, disturbances don’t fade away during the expansion of the universe. From a nonlinear perturbation analysis it is found that the effective Einstein 4D equations on an axially symmetric spacetime, contain a “back-reaction” term on the righthand side caused by the projected 5D Weyl tensor and can act as a dark energy term. The propagation equations to first order for the metric components and scalar-gauge fields contain -dependent terms, so the approximate wave solutions are no longer axially symmetric. The disturbances, amplified by the warp factor, can possess extremal values for fixed polar angles. This could explain the two preferred polarization vectors mod .