Realization of the Topological Hopf Term in a Two-Dimensional Lattice Model

It is known that a 2-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics due to the fermion-doubling in the low-energy spectrum. In this work we propose a scenario to realize the Hopf term in lattice models. The central aim is tuning the coupling between the spins and the Dirac fermions such that the topological terms contributed by the two cones do not cancel each other. To this end, we consider $p_x$ and $p_y$ orbitals for the Dirac fermions on the honeycomb lattice such that there are totally four bands.By utilizing the orbital degrees of freedom, a $\theta=2\pi$ Hopf term is successfully generated for the spin system after integrating out the Dirac fermions. If the fermions have a small gap $m_0$ or if the spin-orbit coupling is considered, then $\theta$ is no longer quantized, but it may flow to multiple of $2\pi$ under renormalization. The ground state and the physical response of a spin system having the Hopf term are discussed

Defining Urban Boundaries by Characteristic Scales

Defining an objective boundary for a city is a difficult problem, which remains to be solved by an effective method. Recent years, new methods for identifying urban boundary have been developed by means of spatial search techniques (e.g. CCA). However, the new algorithms are involved with another problem, that is, how to determine the characteristic radius of spatial search. This paper proposes new approaches to looking for the most advisable spatial searching radius for determining urban boundary. We found that the relationships between the spatial searching radius and the corresponding number of clusters take on an exponential function. In the exponential model, the scale parameter just represents the characteristic length that we can use to define the most objective urban boundary objectively. Two sets of China's cities are employed to test this method, and the results lend support to the judgment that the characteristic parameter can well serve for the spatial searching radius. The research may be revealing for making urban spatial analysis in methodology and implementing identification of urban boundaries in practice.Comment: 26 pages, 5 figures, 7 table

A global adaptive velocity space for general discrete velocity framework in predictions of rarefied and multi-scale flows

The rarefied flow and multi-scale flow are crucial for the aerodynamic design of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete velocity space, the Boltzmann method, such as the discrete velocity method and unified methods, can capture complex and non-equilibrium velocity distribution functions (VDFs) and describe flow behaviors exactly. However, the extremely steep slope and high concentration of the gas VDFs in a local particle velocity space make it very difficult for the Boltzmann method with structured velocity space to describe high speed flow. Therefore, the adaptive velocity space (AVS) is required for the Boltzmann solvers to be practical in complex rarefied flow and multi-scale flow. This paper makes two improvements to the AVS approach, which is then incorporated into a general discrete velocity framework, such as the unified gas-kinetic scheme. Firstly, a global velocity mesh is used to prevent the interpolation of the VDFs at the physical interface during the calculation of the microscopic fluxes, maintaining the program's high level of parallelism. Secondly, rather than utilizing costly interpolation, the VDFs on a new velocity space were reconstruction using the ``consanguinity" relationship. In other words, a split child node's VDF is the same as its parent's VDF, and a merged parent's VDF is the average of its children's VDFs. Additionally, the discrete deviation of the equilibrium distribution functions is employed to maintain the proposed method's conservation. Moreover, an appropriate set of adaptive parameters is established to enhance the automation of the proposed method. Finally, a number of numerical tests are carried out to validate the proposed method

A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows

The rarefied flow and multi-scale flow are crucial for the aerodynamic design of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete velocity space, the discrete velocity method (DVM) and unified methods can capture complex and non-equilibrium distribution functions and describe flow behaviors exactly. The unified methods predict flows from continuum to rarefied regimes by adopting unified modeling, and they can be further applied to other multi-scale physics such as radiation heat transfer, phonon heat transfer and plasma. In the flow field, the concrete dynamic process needs to describe the gas-gas interaction and gas-surface interaction (GSI). However, in both DVM and unified methods, only a simple but not accurate GSI is used, which can be regarded as a Maxwell GSI with a fixed accommodation coefficient of 1 (full accommodation) at the present stage. To overcome the bottleneck in extending DVM and unified methods to the numerical experiment and investigate real multi-scale flow physics, this paper realizes precise GSI in the DVM framework by constructing the boundary conditions of a concrete Maxwell GSI with an adjustable accommodation coefficient. In the constructing process, the problems of macro-conservation and micro-consistency in the DVS at the boundary are well solved by reflected macroscopic flux and interpolation distribution function and interpolation error correction, respectively. Meanwhile, considering that the multi-scale flows in the background of aeronautics and aerospace are often at supersonic and hypersonic speeds, the unstructured velocity space (UVS) is essential. From the perspective of generality, the GSI is forced on UVS. Besides, by combined with the unified method (the unified gas-kinetic scheme in the paper), the effectiveness and validity of the present GSI on the DVM framework are verified by a series of simulations

Taburan dan kepelbagaian foraminifera bentik di dalam sedimen permukaan sekitar Delta Sungai Pahang, Pahang, Malaysia

Suatu kajian mengenai taburan dan kepelbagaian spesies Foraminifera bentik di dalam sedimen permukaan telah dijalankan di sekitar Delta Sungai Pahang, Pahang. Sebanyak 33 sampel sedimen telah diambil bagi tujuan ini. Hasilnya, sebanyak 82 spesies, 45 genus dan 29 famili telah berjaya dikenal pasti daripada sejumlah 28,501 individu Foraminifera. Stesen 5 mencatatkan jumlah kehadiran Foraminifera paling tinggi iaitu sebanyak 5,543 individu. Stesen 11 pula mencatatkan jumlah kehadiran paling rendah dengan hanya 46 individu sahaja. Spesies yang paling dominan dan melimpah (>10%) ialah Amphistegina lessonni (4,790 individu) dan Amphistegina gibbosa (4,490 individu). Kemudian, diikuti oleh Elphidium advenum, Operculina ammonoides dan Asterorotalia pulchella (>5%). Bagi famili pula, Amphisteginidae merupakan famili paling dominan dengan mencatatkan jumlah individu tertinggi iaitu 9,280 (mewakili 32.6% daripada keseluruhan individu). Famili Hauerinidae mencatatkan kepelbagaian spesies yang paling tinggi iaitu sebanyak 24 spesies telah berjaya dijumpai. Indeks kepelbagaian spesies, H’ yang dicatatkan adalah antara 1.1 dan 3.1. Manakala indeks kekayaan spesies, α adalah antara 2.0 dan 9.4

Genetic Mechanism of Geothermal Resources in the Qutan and Reshuizhou Geothermal Fields, Jiangxi Province, China: Evidence from Hydrogeochemical Characteristics of Geothermal Water

AbstractThe hydrogeochemical characteristics and isotopic analyses of geothermal water are effective in the genetic study of a geothermal system. This study systematically investigated the geochemical and isotopic compositions of the geothermal water in the Qutan and Reshuizhou geothermal fields. The geothermal water in these two fields is of HCO3 (·F)-Ca·Na type and has undergone protracted water runoff and deep thermal cycle. Based on the mineral-water solubility equilibrium, the reservoir in the Qutan geothermal field has a temperature of 60–74°C and a depth range of 770–1003 m. The geothermal water in the Reshuizhou geothermal field has been mixed with cold water, which accounts for 58% in weight. The reservoir in the Reshuizhou geothermal field has a temperature range of 131-150°C and a depth range of 1953–2287 m. The geothermal water in the Qutan and Reshuizhou geothermal fields have 14C ages of 8251–7961 BC and 3514–2254 BC, respectively, which are consistent with the result of the 3H isotopic analyses. When recharging and transiting to geothermal water, the meteoric water underwent changes in geochemical compositions, which were dominantly controlled by water-rock interactions, including the precipitation of chalcedony and muscovite and the dissolution of calcite, fluorite, K-feldspar, and albite. In the Reshuizhou geothermal field, the hydrogeochemical compositions of the geothermal water are affected by cold water mixing

Features of a Self-Mixing Laser Diode Operating Near Relaxation Oscillation

When a fraction of the light reflected by an external cavity re-enters the laser cavity, both the amplitude and the frequency of the lasing field can be modulated. This phenomenon is called the self-mixing effect (SME). A self-mixing laser diode (SM-LD) is a sensor using the SME. Usually, such LDs operate below the stability boundary where no relaxation oscillation happens. The boundary is determined by the operation condition including the injection current, optical feedback strength and external cavity length. This paper discovers the features of an SM-LD where the LD operates beyond the stability boundary, that is, near the relaxation oscillation (RO) status. We call the signals from such a SM-LD as RO-SM signals to differentiate them from the conventional SM signals reported in the literature. Firstly, simulations are made based on the well-known Lang and Kobayashi (L-K) equations. Then the experiments are conducted on different LDs to verify the simulation results. It shows that a RO-SM signal exhibits high frequency oscillation with its amplitude modulated by a slow time varying envelop which corresponds to the movement of the external target. The envelope has same fringe structure (half-wavelength displacement resolution) with the conventional SM signals. However, the amplitudes of the RO-SM signals are much higher compared to conventional SM signals. The results presented reveal that an SM-LD operating near the RO has potential for achieving sensing with improved sensitivity