Some rigidity theorems for locally symmetrical Finsler manifolds

In this paper we study some rigidity properties for locally symmetrical Finsler manifolds and obtain some results. We obtain the local equivalent characterization for a Finsler manifold to be locally symmetrical and prove that any locally symmetrical Finsler manifold with nonzero flag curvature must be Riemannian. We also generalize a rigidity result due to Akbar-Zadeh.     

局域共振复合单元声子晶体结构的低频带隙特性研究

本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法. 关键词： 局域共振 低频带隙 复合单元 声子晶体     

Flicker Noise in a Locally Nonequilibrium Medium

A model implying that particles of a medium are subjected to external forces with a flicker noise spectrum has been proposed to describe fluctuations in locally nonequilibrium physical media. The Langevin equation with additional integral terms describing the action of the locally nonequilibrium medium has been derived. The spectral density of fluctuations of an electric current flowing in the locally nonequilibrium medium has been calculated. It has been found that this density in the low-frequency spectral range is flicker noise.     

Locally Conformal Dirac Structures and Infinitesimal Automorphisms

We study the main properties of locally conformal Dirac bundles, which include Dirac structures on a manifold and locally conformal symplectic manifolds. It is proven that certain locally conformal Dirac bundles induce Jacobi structures on quotient manifolds. Furthermore we show that, given a locally conformal Dirac bundle over a smooth manifold M, there is a Lie homomorphism between a subalgebra of the Lie algebra of infinitesimal automorphisms and the Lie algebra of admissible functions. We also show that Dirac manifolds can be obtained from locally conformal Dirac bundles by using an appropriate covering map. Finally, we extend locally conformal Dirac bundles to the context of Lie algebroids.     

Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.     

Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring--mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.     

Continuity conditions for finite-dimensional representations of connected locally compact groups

We obtain simple necessary and sufficient conditions for the continuity of a locally bounded finite-dimensional representation of a connected locally compact group. We also prove that the discontinuity group of a locally bounded finite-dimensional representation of a connected locally compact group is a central subgroup in the closure of the image.     

Effects of locally resonant modes on underwater sound absorption in viscoelastic materials

Recently, by introducing locally resonant scatterers with spherical shape proposed in phononic crystals into design of underwater sound absorption materials, the low-frequency underwater sound absorption phenomenon induced by the localized resonances is observed. To reveal this absorption mechanism, the effect of the locally resonant mode on underwater sound absorption should be studied. In this paper, the finite element method, which is testified efficiently by comparing the calculation results with those of the layer multiple scattering method, is introduced to investigate the dynamic modes and the corresponding sound absorption of localized resonance. The relationship between the resonance modes described with the displacement contours of one unit cell and the corresponding absorption spectra is discussed in detail, which shows that the localized resonance leads to the absorption peak, and the mode conversion from longitudinal to transverse waves at the second absorption peak is more efficient than that at the first one. Finally, to show the modeling capability of FEM and investigate shape effects of locally resonant scatterers on underwater sound absorption, the absorption properties of viscoelastic materials containing locally resonant scatterers with ellipsoidal shape are discussed.     

Reduction for locally conformal symplectic manifolds

It is shown how one can do symplectic reduction for locally conformal symplectic manifolds, especially with an action of a Lie group. This generalizes well-known procedures for symplectic manifolds to the slightly larger class of locally conformal symplectic manifolds. The whole setting is very conformally invariant.     

Harmonic maps and stability on locally conformal Kähler manifolds

We study harmonic and pluriharmonic maps on locally conformal Kähler manifolds. We prove that there are no nonconstant holomorphic pluriharmonic maps from a locally conformal Kähler manifold to a Kähler manifold and that any holomorphic harmonic map from a compact locally conformal Kähler manifold to a Kähler manifold is stable.     

Symmetries of parabolic contact structures

We generalize the concept of locally symmetric spaces to parabolic contact structures. We show that symmetric normal parabolic contact structures are torsion-free and some types of them have to be locally flat. We prove that each symmetry given at a point with non-zero harmonic curvature is involutive. Finally we give restrictions on the number of different symmetries which can exist at such a point.     

Continuity Conditions for Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups

A criterion for the continuity of the restriction of a finite-dimensional locally bounded representation of a connected locally compact group to the commutator subgroup of the group is given.     

Hyper-parahermitian manifolds with torsion

Necessary and sufficient conditions for the existence of a hyper-parahermitian connection with totally skew-symmetric torsion (HPKT-structure) are presented. It is shown that any HPKT-structure is locally generated by a real (potential) function. An invariant first order differential operator is defined on any almost hyper-paracomplex manifold showing that it is two-step nilpotent exactly when the almost hyper-paracomplex structure is integrable. A local HPKT-potential is expressed in terms of this operator. Examples of (locally) invariant HPKT-structures with closed as well as non-closed torsion 3-form on a class of (locally) homogeneous hyper-paracomplex manifolds (some of them compact) are constructed.     

Gauge theory of the conformal and superconformal group

We show that the locally scale invariant Weyl theory of gravity is the gauge theory of the conformal group. Proper conformal transformations are gauged by a non-propagating gauge field.A gauge theory for the superconformal group is obtained which is locally scale, Lorentz, and chiral invariant but not locally supersymmetric despite remarkable cancellations.     

Tunable band gaps in acoustic metamaterials with periodic arrays of resonant shunted piezos

Periodic arrays of resonant shunted piezoelectric patches are employed to control the wave propagation in a two-dimensional (2D) acoustic metamaterial. The performance is characterized by the finite element method. More importantly, we propose an approach to solving the conventional issue of the nonlinear eigenvalue problem, and give a convenient solution to the dispersion properties of 2D metamaterials with periodic arrays of resonant shunts in this article. Based on this modeling method, the dispersion relations of a 2D metamaterial with periodic arrays of resonant shunted piezos are calculated. The results show that the internal resonances of the shunting system split the dispersion curves, thereby forming a locally resonant band gap. However, unlike the conventional locally resonant gap, the vibrations in this locally resonant gap are unable to be completely localized in oscillators consisting of shunting inductors and piezo-patches.     

On locally normal states in quantum statistical mechanics

A sufficient condition is given in order that a von Neumann algebra with cyclic vector is quasi-standard. With the help of this result it is proved that a locally normal state with a cyclic and separating vector in the representation space gives rise to a quasi-standard von Neumann algebra. Furthermore it is proved that the representation space determined by a locally normal state in the G.N.S. construction is separable.     

Irreducible Locally Bounded Finite-Dimensional Pseudorepresentations of Connected Locally Compact Groups

The irreducible locally bounded finite-dimensional pseudorepresentations of connected locally compact groups are described.     

Calculation of the electric potential and Lorentz force acting on a locally ionized region in a magnetohydrodynamic flow placed in a nonuniform magnetic field

An analytical solution to electrodynamic equations for the electric potential in a locally ionized magnetohydrodynamic (MHD) flow in the nonuniform magnetic field produced by a straight-line conductor is found. Analytical formulas are obtained to evaluate the volume density of the Lorentz force and the integral Lorentz force acting on the locally ionized region of the MHD flow. It is shown that the MHD action on the locally ionized flow in the nonuniform magnetic field can be used to control the elevating force as well as the ratio of the elevating force to the drag force.     

Acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials

Using the multilayered cylinder model, we study acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials, which exhibit locally negative effective mass densities. A spring model is introduced to replace the traditional transfer matrix, which may be singular in the negative mass region. The backscattering form function and the scattering cross section are calculated to discuss the acoustic properties of the coated submerged cylindrical shell.