Symmetry detection of auxetic behaviour in 2D frameworks

A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio -1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic. © EPLA, 2013.

Optically activated shutter using a photo-tunable short-pitch chiral nematic liquid crystal

We report the demonstration of an optically activated shutter based upon a short-pitch chiral nematic liquid crystal (LC) device sandwiched between crossed polarizers. This LC is comprised of photo-active chiral dopants. In the trans-state, the LC appears dark between crossed polarizers due to the very short pitch. As the pitch is extended through exposure to ultraviolet light, the device becomes transmissive reaching a maximum for a particular value of the pitch. As a result, it is possible to switch between the light and dark states by subjecting the device to visible light so as to cause a cis-trans photo-isomerisation. © 2013 AIP Publishing LLC.

Symmetry-extended counting rules for periodic frameworks.

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Electrical addressing of polymer stabilized hyper-twisted chiral nematic liquid crystals with interdigitated electrodes: Experiment and model

Electro-optic switching in short-pitch polymer stabilized chiral nematic liquid crystals was studied and the relative contributions of flexoelectric and dielectric coupling were investigated: polymer stabilization was found to effectively suppress unwanted textural transitions of the chiral nematic liquid crystal and thereby enhance the electro-optical performance (high optical contrast for visible light, a near ideal optical hysteresis, fast electro-optic response). Test cells were studied that possessed interdigitated electrodes to electrically address the liquid crystal. Based on simulations, a well-fitted phenomenological description of the electro-optic response was derived considering both flexoelectro-optic and Kerr-effect based electro-optic response. © 2014 AIP Publishing LLC.

Studies on the restoration succession of PFU microbial communities in a pilot-scale microcosm

In order to imitate the restoration succession process of natural water ecosystem, a laboratory microcosm system of constant-flow-restoration was designed and established. A eutrophycation lake, Lake Donghu, was selected as the subject investigated. Six sampling stations were set on the lake, among which the water of station IV was natural clean water, and others were polluted with different degrees. Polyurethane foam unit microbial communities, which had colonized in the stations for a month, were collected from these stations and placed in their respective microcosms, using clean water of station IV to gradually replace the water of these microcosms. In this process, the healthy community in clean water continuously replaced the damaged communities in polluted water, the restoration succession of the damaged communities was characterized by weekly determination of several functional and structural community parameters, including species number (S), diversity index (DI), community pollution value (CPV), heterotrophy index (HI), and similarity coefficient. Cluster analysis based on similarity coefficient was used to compare the succession discrepancies of these microbial communities from different stations. The ecological succession of microbial communities during restoration was investigated by the variable patterns of these parameters, and based on which, the restoration standards of these polluted stations were suggested in an ecological sense. That was, while being restored, the water of station 0 (supereutrophycation) should be substituted with natural clean water by 95%; station I (eutrophycation), more than 90%; station II (eutrophycation), more than 85%; station III (eutrophycation), about 85%; station V (mesoetitrophycation), less than 50%. The effects of the structural and functional parameters in monitoring and assessing ecological restoration are analyzed and compared. (C) 2007 Elsevier Ltd. All rights reserved.

The restoration of aquatic macrophytes for improving water quality in a hypertrophic shallow lake in Hubei Province, China

This paper deals with a case study of the restoration of submerged macrophytes for improving water quality in a hypertrophic shallow lake, Lake Donghu of Wuhan, Hubei Province, China. Macrophyte restoration experiments were conducted in large-scale enclosures established in three sublakes of different trophic status, and the effectiveness for water quality improvement was tested by using the enclosure experiment in the hypertrophic sublake. Water quality was remarkably improved after the reestablishment of aquatic macrophytes. It is suggested that the submerged vegetation of less polluted sublakes could be capable of recovering spontaneously once the stocking of herbivorous fishes has been ceased, and the K-selected plants such as Potamogeton maackianus should be introduced into these sublakes to enhance the stability of aquatic vegetation. However, it may not be possible and economical to restore the submerged macrophytes in severely polluted basins unless external pollution has been cut off and internal nutrient loadings considerably reduced. In this case, the r-selected submerged plants should be used as the pioneer species for macrophyte recovery. (C) 2001 Elsevier Science B.V. All rights reserved.

Direct detection of the relative strength of Rashba and Dresselhaus spin-orbit interaction: Utilizing the SU(2) symmetry

We propose a simple method to detect the relative strength of Rashba and Dresselhaus spin-orbit interactions in quantum wells (QWs) without relying on the directional-dependent physical quantities. This method utilizes the two different critical gate voltages that leading to the remarkable signals of SU(2) symmetry, which happens to reflect the intrinsic-structure-inversion asymmetry of the QW. We support our proposal by the numerical calculation of in-plane relaxation times based on the self-consistent eight-band Kane model. We find that the two different critical gate voltages leading to the maximum spin-relaxation times [one effect of the SU(2) symmetry] can simply determine the ratio of the coefficients of Rashba and Dresselhaus terms. Our proposal can also be generalized to extract the relative strengths of the spin-orbit interactions in quantum-wire and quantum-dot structures.

Sixfold symmetry of excitonic transition energies in c-plane for wurtzite GaN

The optical properties of the strained wurtzite GaN are investigated theoretically within the nearest neighbor tight-binding method. The piezoelectric effect is also taken into account. The empirical rule has been used in the strained band-structure calculation. The results show that the excitonic transition energies are anisotropic in the c-plane in a high electronic concentration system and have a 60 degrees periodicity, which is in agreement with experiment. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3001937]

The impact of imperfect symmetry on band edge modes of a two-dimensional photonic crystal with square lattice

A theoretical analysis has been performed by means of the plane-wave expansion method to examine the dispersion properties of photons at high symmetry points of an InP based two-dimensional photonic crystal with square lattice. The Q factors are compared qualitatively. The mechanism of surface-emitting is due to the photon manipulation by periodic dielectric materials in terms of Bragg diffraction. A surface-emitting photonic crystal resonator is designed based on the phenomenon of slow light. Photonic crystal slabs with different unit cells are utilized in the simulation. The results indicate that the change of the air holes can affect the polarization property of the modes. So we can find a way to improve the polarization by reducing the symmetry of the structure.

Correlations between electronic energy bands spin splitting and magnetic profile symmetry of magnetic superlattice

We have theoretically investigated the energy band structures of two typical magnetic superlattices formed by perpendicular or parallel magnetization ferromagnetic stripes periodically deposited on a two-dimensional electron gas (2DEG), where the magnetic profile in the perpendicular magnetization is of inversion anti-symmetry, but of inversion symmetry in parallel magnetization, respectively. We have shown that the energy bands of perpendicular magnetization display the spin-splitting and transverse wave-vector symmetry, while the energy bands of the parallel magnetization exhibit spin degeneration and transverse wave-vector asymmetry. These distinguishing spin-dependent and transverse wave-vector asymmetry features are essential for future spintronics devices applications. (c) 2008 Elsevier B.V. All rights reserved.

Symmetry and optical transition rule for low-dimensional semiconductor system with spin-orbit interaction and magnetic field

Starting from effective mass Hamiltonian, we systematically investigate the symmetry of low-dimensional structures with spin-orbit interaction and transverse magnetic field. The position-dependent potentials are assumed to be space symmetric, which is ever-present in theory and experiment research. By group theory, we analyze degeneracy in different cases. Spin-orbit interaction makes the transition between Zeeman sub-levels possible, which is originally forbidden within dipole approximation. However, a transition rule given in this paper for the first time shows that the transition between some levels is forbidden for space symmetric potentials. (C) 2009 Elsevier Ltd. All rights reserved.

Aharonov-Bohm oscillation and chirality effect in optical activity of single-wall carbon nanotubes

We study the Aharonov-Bohm effect in the optical phenomena of single-wall carbon nanotubes (SWCN) and also their chirality dependence. Especially, we consider the natural optical activity as a proper observable and derive its general expression based on a comprehensive symmetry analysis, which reveals the interplay between the enclosed magnetic flux and the tubule chirality for arbitrary chiral SWCN. A quantitative result for this optical property is given by a gauge invariant tight-binding approximation calculation to stimulate experimental measurements.

Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group C-Nv, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group C-Nv. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.

Blind image restoration based on the theory of high-dimensional space geometry

In practical situations, the causes of image blurring are often undiscovered or difficult to get known. However, traditional methods usually assume the knowledge of the blur has been known prior to the restoring process, which are not practicable for blind image restoration. A new method proposed in this paper aims exactly at blind image restoration. The restoration process is transformed into a problem of point distribution analysis in high-dimensional space. Experiments have proved that the restoration could be achieved using this method without re-knowledge of the image blur. In addition, the algorithm guarantees to be convergent and has simple computation.