Quasi-TEM modes in rectangular waveguides: a study based on the properties of PMC and hard surfaces

Hard surfaces or magnetic surfaces can be used to propagate quasi-TEM modes inside closed waveguides. The interesting feature of these modes is an almost uniform field distribution inside the waveguide. But the mechanisms governing how these surfaces act, how they can be characterized, and further how the modes propagate are not detailed in the literature. In this paper, we try to answer these questions. We give some basic rules that govern the propagation of the quasi-TEM modes, and show that many of their characteristics (i.e. their dispersion curves) can be deduced from the simple analysis of the reflection properties of the involved surfaces

Active fluids at circular boundaries: Swim pressure and anomalous droplet ripening

We investigate the swim pressure exerted by non-chiral and chiral active particles on convex or concave circular boundaries. Active particles are modeled as non-interacting and non-aligning self-propelled Brownian particles. The convex and concave circular boundaries are used as models representing a fixed inclusion immersed in an active bath and a cavity (or container) enclosing the active particles, respectively. We first present a detailed analysis of the role of convex versus concave boundary curvature and of the chirality of active particles on their spatial distribution, chirality-induced currents, and the swim pressure they exert on the bounding surfaces. The results will then be used to predict the mechanical equilibria of suspended fluid enclosures (generically referred to as 'droplets') in a bulk with active particles being present either inside the bulk fluid or within the suspended droplets. We show that, while droplets containing active particles and suspended in a normal bulk behave in accordance with standard capillary paradigms, those containing a normal fluid exhibit anomalous behaviors when suspended in an active bulk. In the latter case, the excess swim pressure results in non-monotonic dependence of the inside droplet pressure on the droplet radius. As a result, we find a regime of anomalous capillarity for a single droplet, where the inside droplet pressure increases upon increasing the droplet size. In the case of two interconnected droplets, we show that mechanical equilibrium can occur also when they have different sizes. We further identify a regime of anomalous ripening, where two unequal-sized droplets can reach a final state of equal sizes upon interconnection, in stark contrast with the standard Ostwald ripening phenomenon, implying shrinkage of the smaller droplet in favor of the larger one.Comment: 15 pages, 7 figure

Numerical Investigation of Evaporation Induced Self-Assembly of Sub-Micron Particles Suspended in Water

Self-assembly of sub-micron particles suspended in a water film is investigated numerically. The liquid medium is allowed to evaporate leaving only the sub-micron particles. A coupled CFD-DEM approach is used for the simulation of fluid-particle interaction. Momentum exchange and heat transfer between particles and fluid and among particles are considered. A history dependent contact model is used to compute the contact force among sub-micron particles. Simulation is done using the open source software package CFDEM which basically comprises of two other open source packages OpenFOAM and LIGGGHTS. OpenFOAM is a widely used solver for CFD related problems. LIGGGHTS, a modification of LAMMPS, is used for DEM simulation of granular materials. The final packing structure of the sub-micron particles is discussed in terms of distribution of coordination number and radial distribution function (RDF). The final packing structure shows that particles form clusters and exhibit a definite pattern as water evaporates away

Hyers-Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems

In this paper, we prove some existence, uniqueness and Hyers-Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is based on a new version of the Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de Andalucí

Power system security enhancement by HVDC links using a closed-loop emergency control

In recent years, guaranteeing that large-scale interconnected systems operate safely, stably and economically has become a major and emergency issue. A number of high profile blackouts caused by cascading outages have focused attention on this issue. Embedded HVDC (High Voltage Direct Current) links within a larger AC power system are known to act as a “firewall” against cascading disturbances and therefore, can effectively contribute in preventing blackouts. A good example is the 2003 blackout in USA and Canada, where the Québec grid was not affected due to its HVDC interconnection. In the literature, many works have studied the impact of HVDC on the power system stability, but very few examples exist in the area of its impact on the system security. This paper presents a control strategy for HVDC systems to increase their contribution to system security. A real-time closed-loop control scheme is used to modulate the DC power of HVDC links to alleviate AC system overloads and improve system security. Simulations carried out on a simplified model of the Hydro-Québec network show that the proposed method works well and can greatly improve system security during emergency situations.Peer reviewedFinal Accepted Versio

Semiclassical limits of eigenfunctions on flat nn-dimensional tori

We provide a proof of the conjecture formulated in \cite{Jak97,JNT01} which states that on a $n$-dimensional flat torus \T^{n}, the Fourier transform of squares of the eigenfunctions $|\phi_\lambda|^2$ of the Laplacian have uniform $l^n$ bounds that do not depend on the eigenvalue $\lambda$. The proof is a generalization of the argument by Jakobson, {\it et al}. for the lower dimensional cases. These results imply uniform bounds for semiclassical limits on \TT^{n+2}. We also prove a geometric lemma that bounds the number of codimension-one simplices which satisfy a certain restriction on an $n$-dimensional sphere $S^n(\lambda)$ of radius $\sqrt{\lambda}$ and use it in the proof.Comment: 10 pages; Canadian Mathematical Bulletin, 201