GLLH EM Invisible Cloak With Novel Front Branching And Without Exceed Light Speed Violation

In this paper, we propose new Global and Local (GL) electromagnetic (EM) cloaks with distinctive class material a_{\alpha \beta}\log ^\alpha (b_{\alpha \beta}/h) h^\beta (GLLH Cloak) without exceed light speed violation. The refractive index of the GLLH cloak material, $n(r)$, is large than one or equal to one. Our GLLH cloak is created by GL EM modeling and GL EM cloak inversion with searching class \it a_{\alpha \beta}\log ^\alpha (b_{\alpha \beta}/h) h^\beta. The GLLH cloaks in this paper have finite speed and have no exceed light speed? physical violations and have more advantages. The GLLH EM cloaks can be practicable by using normal materials and are available for all broad frequency band. The GL EM cloak inversion and electromagnetic integral equation for cloak are presented in this paper. The novel EM wave propagation and front branching in the GLLH cloak by GL EM modeling are presented in this paper. The EM wave front propagation in GLLH cloak is behind of the front in free space. At time steps $118 dt$, in the GLLH cloak, the wave front is curved as a crescent like and propagates slower than the light in free space. At the time step $119dt$, the EM wave inside of the GLLH cloak propagates slower than light speed, moreover, its two crescent front peaks intersect at a front branching point. At the front branching point, the front is split to two fronts. The novel front branching and crescent like wave propagation are displayed in the following figure 1, figure 2 and figures 5 -20 in this paper. All copyright and patent of the GLLH EM cloaks and GL modeling and inversion methods are reserved by authors in GL Geophysical Laboratory.Comment: We propose a new EM cloak without exceed light speed violation and without infinite speed violation. 14 pages and 24 figures are in this paper. A novel front branching and crescent like front propagation is presented. Please send comments to [email protected] or [email protected]. It is academical publication. If some colleague refer our paper, please cite it as referenc

Decomposition of De Rham Complexes with Smooth Horizontal Coefficients for Semistable Reductions

We generalize Illusie's result to prove the decomposition of the de Rham complex with smooth horizontal coefficients for a semistable $S$-morphism f:X\ra Y which is liftable over $\Z/p^2\Z$. As an application, we prove the Koll\'ar vanishing theorem in positive characteristic for a semistable $S$-morphism f:X\ra Y which is liftable over $\Z/p^2\Z$, where all concerned horizontal divisors are smooth over $Y$.Comment: 26 page

Problem On The Acoustic Cloak By 00 to R1R_1 Transformation

The $0$ to $R_1$ radial spherical coordinate transformation method can be making electromagnetic (EM) invisible cloak. However the cloak by transformation optic has infinite speed and exceeding light speed etc fundamental difficulties. In this paper, we discover problem on acoustic cloak by transformation and prove that in the $0$ to $R_1$ radial spherical coordinate transformation, the pressure wave field $P(r_p)=P(r)$ is invariant, in the physical inner spherical surface boundary $r=R_1$, $P(R_1)$ is not zero. the acoustic field propagation penetrate into the inner sphere $r < R_1$.Therefore, the inner sphere $r < R_1$ can not be cloaked. The GL simulation figures of the pressure acoustic wave propagation penetrate into the inner sphere $r \le R_1$ are presented in figure 1 to figure 12.The pressure wave is setting to zero that cause the scattering wave to disturb incident pressure acoustic wave outside of the outer sphere $r \ge R_2$ that make the whole sphere $r \ge R_2$ will be deltected. GL method simulation is presented in figure 13. we discovered and proved that $0$ to $R_1$ sphere radial transformation can not be used to induce acoustic no scattering cloak.Comment: 18 pages, 112 formulas and 2 figures in this paper, Welcome comments from colleagues. It is academical publication for open review. Please colleague send comments and question to me by email [email protected]. If colleague use this paper, please be sure cite my paper in his papers. The Paper is different from other paper

A Multigrid Method for the Ground State Solution of Bose-Einstein Condensates

A multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the multilevel correction for eigenvalue problems and the multigrid method for linear boundary value problems. In this scheme, obtaining the optimal approximation for the ground state solution of Bose-Einstein condensates includes a sequence of solutions of the linear boundary value problems by the multigrid method on the multilevel meshes and a series of solutions of nonlinear eigenvalue problems on the coarsest finite element space. The total computational work of this scheme can reach almost the optimal order as same as solving the corresponding linear boundary value problem. Therefore, this type of multigrid scheme can improve the overall efficiency for the simulation of Bose-Einstein condensations. Some numerical experiments are provided to validate the efficiency of the proposed method.Comment: 15 pages and 6 figures. arXiv admin note: substantial text overlap with arXiv:1405.715

A GL Double Layer EM Cloaks In Broad Frequency Band And Reciprocal Law

In this paper, we propose a novel GLWF double layer EM cloak in the broad frequency band. The GLWF double layer cloak consists of two sphere annular layers, two type cloak materials are proposed and installed in its each layer, respectively. The outer layer of the GL cloak has the invisible function in broad frequency band, while its inner layer has the fully absorption and rapid delay function. The GLWF double layer cloak overcomes the following difficulties of the single layer PS cloak. (1) There exists no EM wavefield can be excited inside the concealment of the PS cloak, the concealment of the PS cloak is blind. Our GL double layer cloak recovered that the EM wave field can be excited inside the concealment of the GL double layer cloak. (2) There is exceeding light speed physical violation in PS cloak, its invisibility only in very narrow frequency band. Our GLWF double layer cloak corrects the violation. (3) The reciprocal law is satisfied in our GL double cloak media. However, the PS cloak damaged the reciprocal law.. The simulations and comparisons of the EM wave field propagation through the GLWF double cloak, GL double cloak and GL double layer with PS outer layer are presented to show the advantages of the GLWF double layer EM cloak The GL double layer cloaks are proposed by our GL EM modeling and inversion. The 3D GL EM modeling simulations for the double layer cloak are presented. The copyright and patent of the GLWF double layer cloak materials and GL EM modeling and inversion in this paper are reserved by authors in GL Geophysical Laboratory.Comment: 8 pages and 11 figures are included in this paper. Please send comments to [email protected]

An Electromagnetic GL Double Layered Cloak

In this paper, we propose a new electromagnetic (EM) GL double layered cloak. The GL double layered cloak is consist of two sphere annular layers, $R_1 \le r \le R_2$ and $R_2 \le r \le R_3$. Two type cloak materials are proposed and installed in the each layer, respectively. The outer layer cloak of the GL double layered cloak has the invisible function, the inner layer cloak has fully absorption function. The GL double layered metamaterials are weak degenerative and weak dispersive. When the source is located outside of the GL double layered cloak, the excited EM wave field propagation outside of the double layered cloak is as same as in free space and never be disturbed by the cloak; also, the exterior EM wave can not penetrate into the inner layer and concealment. When local sources are located inside of the GL double cloaked concealment with the normal EM materials, the excited EM wave is propagating under Maxwell equation governing, it is complete absorbed by the inner layer cloak of GL double cloak and never propagate to outside of the inner layer of the GL cloak, moreover, the EM wavefield in concealment never be disturbed by the cloak. The GL doubled layered cloak is a robust cloak and has complete and sufficient invisibility functions. Its concealment is the normal electromagnetic environment. Our EM GL double layered cloak is different from conventional common cloak. The 3D GL EM modeling simulations for the double layered cloak are presented. The GL method is an effective physical simulation method and is fully different from the conventional methods. It has double abilities of the theoretical analysis and numerical simulations to study the cloak metamaterials and wide materials and field scattering problem in physical sciences.Comment: 3D Global and Local Field Modeling and A Novel GL Double Layered Cloak are proposed in this paper. There are 10 pages and 4 figures in the pape

The 00 to R1R_1 cylinder radial coordinate transformation can not be used to make cylinder layer electromagnetic cloak

In this paper, we discover and proved that the $0$ to $R_1$ cylinder radial coordinate transformation can not be used to make cylinder layer electromagnetic EM cloak. Because in the $0$ to $R_1$ cylinder radial coordinate transformation, the value area of the electric wave field $E_z (\rho,\phi,z)$ and magnetic wave field $H_z (\rho,\phi,z)$ are invariant. After $0$ to $R_1$ cylinder radial transformation,$\rho _q = R_1 + Q(\rho)$, $E_z (\rho _q,\phi,z) = E_z (\rho,\phi,z)$,$H_z (\rho _q,\phi,z) = H_z (\rho,\phi,z)$ . in the physical inner cylinder boundary, $E_z (R_1,\phi,z) \ne 0$,$H_z (R_1,\phi,z) \ne 0$, The cylinder EM wave field will propagation penetrate into the inner cylinder $\rho < R_1,\left| z \right| < \infty$ .Therefore, the inner cylinder $\rho < R_1,\left| z \right| < \infty$ . can not be cloaked. In many published papers on EM cylinder cloak, the $0$ to $R_1$ cylinder radial transformation is wrongfully used for their EM cylinder layer cloak.Comment: 4 pages,38 formulas in this paper publication.the academical publication for open review. colleague send comments to me by email [email protected]. If colleague use our GLHUA cloaks and analytical EM in $\rho < R_1$ in this paper, please be sure cite my paper in his papers. arXiv admin note: substantial text overlap with arXiv:1612.02857, arXiv:1701.00534, arXiv:1706.0537

Computable Error Estimates for Ground State Solution of Bose-Einstein Condensates

In this paper, we propose a computable error estimate of the Gross-Pitaevskii equation for ground state solution of Bose-Einstein condensates by general conforming finite element methods on general meshes. Based on the proposed error estimate, asymptotic lower bounds of the smallest eigenvalue and ground state energy can be obtained. Several numerical examples are presented to validate our theoretical results in this paper.Comment: 19 pages, 9 figures. arXiv admin note: text overlap with arXiv:1601.0156

Pathwise uniqueness for a class of SPDEs driven by cylindrical α\alpha-stable processes

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola [Osaka J. Math., 2012] in the case $H=\mathbb{R}^d$. The proof is based on an infinite dimensional Kolmogorov equation with non-local operator

Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradient

By using Duhamel's formula, we prove sharp two-sided estimates for the heat kernel of spectral fractional Laplacian with time-dependent gradient perturbation in bounded $C^{1,1}$ domains. Moreover, we also obtain gradient estimate as well as H\"older continuity of the gradient of the heat kernel