Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend...Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.展开更多
The displacement fields u_x,u_y at growing crack tip of LYI2-M specimens with double edge cracks are measured using moire method.The experimental singularity fields are compared with GH theoretical field [12-14].The s...The displacement fields u_x,u_y at growing crack tip of LYI2-M specimens with double edge cracks are measured using moire method.The experimental singularity fields are compared with GH theoretical field [12-14].The size and shape of the experimental GH singularity fields are obtained.The error in both the experimental and theoretical evaluations is controlled within ±10%.The experiments show that there is (In A/r)^(+1)singularity dominant around a growing crack tip.The shape of this dominant region ranges from butterfly wing to oblate and circular.Inside GH-field,there is a 3-D deformed damage zone where no GH sin- gularity exists.展开更多
A crack terminating at an interface of two dissimilar elastic materials is investigated.It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part be- ing charac...A crack terminating at an interface of two dissimilar elastic materials is investigated.It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part be- ing characterized by one singularity.The detailed relation of the two singularities with the bimaterial proper- ties is given for some special cases of the crack.展开更多
V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.
The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling...The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.展开更多
In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we...In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.展开更多
It is generally believed that matter inside or once entering a black hole will gravitationally fall into the center and form a size-less singularity, where the density goes to infinity and the spacetime breaks down wi...It is generally believed that matter inside or once entering a black hole will gravitationally fall into the center and form a size-less singularity, where the density goes to infinity and the spacetime breaks down with infinite curvature or gravitation. In accordance to the Unruh effect, one of the most surprizing predictions of quantum field theory, however, it is found from this study that such singularity cannot be actually formed because it violates the law of energy conservation. The total Unruh radiation energy of the size-less singularity is shown to be infinite, much greater than that the collapsing matter can generate. All the energies of the collapsing matter including the gravitational potential energy, deducted, are far below the Unruh radiation energy, increased, for the collapsing matter to form the singularity. The collapsing matter actually formed is shown to be not a size-less singular point but a small sphere with a finite radius, which is found to be dependent of the mass of the singularity sphere, approximately proportional to the square root of the mass. The radius of the singularity sphere cannot be zero, unless the mass also approaches to zero. The result obtained from this study not only provides us a quantum solution to the problem of black hole singularity, but also leads to profound implications to the spacetime and cosmology. The Unruh effect excludes a black hole to form a size-less singularity, which has a finite mass but infinite density, curvature, and Unruh radiation energy. A point-like or size-less singularity can only be massless and naked.展开更多
The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.T...The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.展开更多
We formulate a model for noncompact spherical charged objects in the framework of noncommutative field theory.The Einstein-Maxwell field equations are solved with charged anisotropic fluid.We choose matter and charge ...We formulate a model for noncompact spherical charged objects in the framework of noncommutative field theory.The Einstein-Maxwell field equations are solved with charged anisotropic fluid.We choose matter and charge densities as functions of the two parameters,instead of defining these quantities in terms of the Gaussian distribution function.It is found that the corresponding densities and the Ricci scalar are singular in origin,whereas the metric is nonsingular,indicating a spacelike singularity.The numerical solution of the horizon equation implies that there are two or one or no horizon（s）,depending on the mass.We also evaluate the Hawking temperature and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.展开更多
In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification w...In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.展开更多
Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model corre...Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.展开更多
Singularity-free superstar is proposed as a model for the collapse of large stars and for GRBs, and as an alternative to black hole and gravastar. Similar to a superconductor, a superstar contains extreme force fields...Singularity-free superstar is proposed as a model for the collapse of large stars and for GRBs, and as an alternative to black hole and gravastar. Similar to a superconductor, a superstar contains extreme force fields that have non-zero momentum and non-zero wavelength to prevent the inactivation of force field at absolute zero and singularity (infinite interacting energy) at infinite density, respectively, based on the uncertainty principle. Emerging only at an extremely low temperature above absolute zero or an extremely high density below infinite density, extreme force fields are shortrange, and located in between a particle and its ordinary force fields (electromagnetic, weak, strong, and gravitational forces) to prevent the inactivation of force fields at absolute zero and singularity (infinite interacting energy) at infinite density in ordinary force fields. Extreme force fields are manifested as the bonds among electrons in a superconductor and among atoms in a Bose-Einstein condensate. When the stellar core of a large star reaches the critical extreme density during the stellar collapse, the stellar core is transformed into the super matter core with extreme force fields and ordinary force fields without singularity. A pre-superstar contains the super matter core, the ordinary matter region, and the thin phase boundary between the super matter core and the ordinary matter region. The stellar collapse increases the super matter core by converting the in falling ordinary energy and matter from the ordinary matter region into the super matter, and decreases the ordinary matter region. Eventually, the stellar breakup occurs to detach the ordinary matter region and the phase boundary from the super matter core, resulting in GRB to account for the observed high amount of gamma rays and the observed complex light curves in GRBs. Unlike black holes and gravastars that lose information, singularity-free superstars that keep all information exist.展开更多
基金Project supported by the China Postdoctoral Science Foundation (Grant No. 2009450159)the Foundation of the State Key Laboratory of Optical Technologies for Micro-Frabrication and Micro-Engineering,Chinese Academy of Sciences (Grant No. KF001)
文摘Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.
基金The project suppoted by National Natural Science Foundation of China
文摘The displacement fields u_x,u_y at growing crack tip of LYI2-M specimens with double edge cracks are measured using moire method.The experimental singularity fields are compared with GH theoretical field [12-14].The size and shape of the experimental GH singularity fields are obtained.The error in both the experimental and theoretical evaluations is controlled within ±10%.The experiments show that there is (In A/r)^(+1)singularity dominant around a growing crack tip.The shape of this dominant region ranges from butterfly wing to oblate and circular.Inside GH-field,there is a 3-D deformed damage zone where no GH sin- gularity exists.
文摘A crack terminating at an interface of two dissimilar elastic materials is investigated.It is found that the asymptotic stress field near the crack tip is in general composed of two parts with each part be- ing characterized by one singularity.The detailed relation of the two singularities with the bimaterial proper- ties is given for some special cases of the crack.
文摘V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.
基金supported by the National Natural Science Foundation of China(Grants No.11572111 and 11372097)the 111 Project(Grant No.B12122)
文摘The embedded water pipe system is often used as a standard cooling technique during the construction of large-scale mass concrete hydrostructures. The prediction of the temperature distribution considering the cooling effects of embedded pipes plays an essential role in the design of the structure and its cooling system. In this study, the singular boundary method, a semi-analytical meshless technique, was employed to analyze the temperature distribution. A numerical algorithm solved the transient temperature field with consideration of the effects of cooling pipe specification, isolation of heat of hydration, and ambient temperature. Numerical results are verified through comparison with those of the finite element method, demonstrating that the proposed approach is accurate in the simulation of the thermal field in concrete structures with a water cooling pipe.
文摘In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.
文摘It is generally believed that matter inside or once entering a black hole will gravitationally fall into the center and form a size-less singularity, where the density goes to infinity and the spacetime breaks down with infinite curvature or gravitation. In accordance to the Unruh effect, one of the most surprizing predictions of quantum field theory, however, it is found from this study that such singularity cannot be actually formed because it violates the law of energy conservation. The total Unruh radiation energy of the size-less singularity is shown to be infinite, much greater than that the collapsing matter can generate. All the energies of the collapsing matter including the gravitational potential energy, deducted, are far below the Unruh radiation energy, increased, for the collapsing matter to form the singularity. The collapsing matter actually formed is shown to be not a size-less singular point but a small sphere with a finite radius, which is found to be dependent of the mass of the singularity sphere, approximately proportional to the square root of the mass. The radius of the singularity sphere cannot be zero, unless the mass also approaches to zero. The result obtained from this study not only provides us a quantum solution to the problem of black hole singularity, but also leads to profound implications to the spacetime and cosmology. The Unruh effect excludes a black hole to form a size-less singularity, which has a finite mass but infinite density, curvature, and Unruh radiation energy. A point-like or size-less singularity can only be massless and naked.
基金Project supported by the Hunan Natural Science Foundation(Nos.01JJY3001 and 01JJY2001)Research Item of the Hunan Education Committee(No.01C083)and the Key Item of Hunan Science and Technology Department.
文摘The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.
基金Project supported by the Higher Education Commission of Pakistan through the Indigenous Ph.D. 5000 Fellowship Program Batch-IV
文摘We formulate a model for noncompact spherical charged objects in the framework of noncommutative field theory.The Einstein-Maxwell field equations are solved with charged anisotropic fluid.We choose matter and charge densities as functions of the two parameters,instead of defining these quantities in terms of the Gaussian distribution function.It is found that the corresponding densities and the Ricci scalar are singular in origin,whereas the metric is nonsingular,indicating a spacelike singularity.The numerical solution of the horizon equation implies that there are two or one or no horizon（s）,depending on the mass.We also evaluate the Hawking temperature and find that a black hole with two horizons is evaporated to an extremal black hole with one horizon.
文摘In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.
基金Project supported by the National Natural Science Foundation of China （Grant No 10574097）.
文摘Based on the propagation law of cross-spectral density function, studied in this paper are the coherence vortices of partially coherent, quasi-monochromatic singular beams with Gaussian envelope and Schell-model correlator in the far field, where our main attention is paid to the evolution of far-field coherence vortices into intensity vortices of fully coherent beams. The results show that, although there are usually no zeros of intensity in partially coherent beams with Gaussian envelope and Schell-model correlator~ zeros of spectral degree of coherence exist. The coherence vortices of spectral degree of coherence depend on the relative coherence length, mode index and positions of pairs of points. If a point and mode index are kept fixed, the position of coherence vortices changes with the increase of the relative coherence length. For the low coherent case there is a circular phase dislocation. In the coherent limit coherence vortices become intensity vortices of fully coherent Laguerre-Gaussian beams.
文摘Singularity-free superstar is proposed as a model for the collapse of large stars and for GRBs, and as an alternative to black hole and gravastar. Similar to a superconductor, a superstar contains extreme force fields that have non-zero momentum and non-zero wavelength to prevent the inactivation of force field at absolute zero and singularity (infinite interacting energy) at infinite density, respectively, based on the uncertainty principle. Emerging only at an extremely low temperature above absolute zero or an extremely high density below infinite density, extreme force fields are shortrange, and located in between a particle and its ordinary force fields (electromagnetic, weak, strong, and gravitational forces) to prevent the inactivation of force fields at absolute zero and singularity (infinite interacting energy) at infinite density in ordinary force fields. Extreme force fields are manifested as the bonds among electrons in a superconductor and among atoms in a Bose-Einstein condensate. When the stellar core of a large star reaches the critical extreme density during the stellar collapse, the stellar core is transformed into the super matter core with extreme force fields and ordinary force fields without singularity. A pre-superstar contains the super matter core, the ordinary matter region, and the thin phase boundary between the super matter core and the ordinary matter region. The stellar collapse increases the super matter core by converting the in falling ordinary energy and matter from the ordinary matter region into the super matter, and decreases the ordinary matter region. Eventually, the stellar breakup occurs to detach the ordinary matter region and the phase boundary from the super matter core, resulting in GRB to account for the observed high amount of gamma rays and the observed complex light curves in GRBs. Unlike black holes and gravastars that lose information, singularity-free superstars that keep all information exist.
