The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $\Gamma$ in a Hilbert space $H$. We prove the existence and uniqueness of a strong solution of this problem when $\Gamma$ is a regular convex set. The result is also extended to the non-symmetric case. Finally, we extend our results to the case when $\Gamma=K_\alpha$, where $K_\alpha={f\in L^2 (0,1)|f\geq -\alpha},\alpha\geq0$

Modelling barriers for coal dust suppression

Airborne dust originating from the transport and storage of raw coal has detrimental effects on the environment. Warkworth Mining is seeking to reduce the dust emissions caused by the dumping of raw coal at their facility in Singleton, NSW. The suggested strategy was the construction of windbreaks, for which commercial designs exist. The MISG was asked to advise on the placement and design of such windbreaks. The problem was approached by studying results in the literature on windbreak design, selecting a few possible configurations, and then testing these by solving numerically for the wind velocity around the dumping site. It was concluded that a long fence on the upwind side of the dumping hoppers would provide moderate protection, but would interfere with current operating procedures. As a better option, a long downwind fence immediately behind the hoppers would provide a similar reduction in the dust emission, and allow more effective use of water sprays. Although fine details of the fence design could not be modelled numerically, we concluded that it was desirable for the fence to have an angled overhang in the vicinity of the hoppers, and a porous section near the base to reduce turbulent flows

Analytical modeling of open-Circuit air-Gap field distributions in multisegment and multilayer interior permanent-magnet machines

We present a simple lumped magnetic circuit model for interior permanent-magnet (IPM) machines with multisegment and multilayer permanent magnets. We derived analytically the open-circuit air-gap field distribution, average air-gap flux density, and leakage fluxes. To verify the developed models and analytical method, we adopted finite-element analysis (FEA). We show that for prototype machines, the errors between the FEA and analytically predicted results are $≪$1% for multisegment IPM machines and $≪$ 2% for multilayer IPM machines. By utilizing the developed lumped magnetic circuit models, the IPM machines can be optimized for maximum fundamental and minimum total harmonic distortion of the air-gap flux density distribution

Improved analytical model for predicting the magnetic field distribution in brushless permanent-magnet machines

A general analytical technique predicts the magnetic field distribution in brushless permanent magnet machines equipped with surface-mounted magnets. It accounts for the effects of both the magnets and the stator windings. The technique is based on two-dimensional models in polar coordinates and solves the governing Laplacian/quasi-Poissonian field equations in the airgap/magnet regions without any assumption regarding the relative recoil permeability of the magnets. The analysis works for both internal and external rotor motor topologies, and either radial or parallel magnetized magnets, as well as for overlapping and nonoverlapping stator windings. The paper validates results of the analytical models by finite-element analyses, for both slotless and slotted motor

Moving vehicle load identification from bridge responses based on method of moments (MOM)

A MOM-based algorithm (MOMA) is proposed for identifying of the time-varying moving vehicle loads on a bridge in this paper. A series of numerical simulations and experiments in laboratory have been studied and the proposed MOMA are compared with the existing time domain method (TDM). A few main parameters, such as basis function terms, executive CPU time, Nyquist fraction of digital filter, two different solutions to the ill-posed system equation, etc, have been investigated. Both the numerical simulation and experimental results show that the MOMA has higher identification accuracy and robust noise immunity as well as producing an acceptable solution to ill-conditioning cases to some extent, but its CPU execution time is just less than one tenth of the TDM

Optical interface states protected by synthetic Weyl points

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arcs surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.Comment: 36 pages, 9 figures. arXiv admin note: text overlap with arXiv:1610.0434