Dynamical Casimir–Polder force in a semi-infinite rectangle waveguide

In this paper, we study the dynamical Casimir–Polder force between an ensemble of identical two-level atoms and the wall of a rectangle waveguide with semi-infinite length. With the presence of both the rotating wave and counter rotating wave terms in the light–matter interaction Hamiltonian, we utilize the perturbation theory to solve the Heisenberg equation. Up to the seconder of coupling strength, we obtain the energy shift analytically and the Casimir–Polder force numerically. Our result shows that the dynamical behavior of the Casimir force is closely connected to the photon propagation in the waveguide. Therefore, we hope this work will stimulate the studies about the quantum effect in waveguide scenario.

Analytical Solution for Vibrations of a Modified Timoshenko Beam on Visco-Pasternak Foundation Under Arbitrary Excitations

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.

Mathematical model of the influence of the rheology of lubricating compositions on the safety of rolling stock movement

The article deals with the search for rational and balanced solutions to ensure maximum safety of rolling stock movement, taking into account the minimization of costs and technical measures. The paper presents a mathematical model for calculating the effect of rheological characteristics of lubricants on the service life of heavy-loaded friction units of rolling stock. The scheme of interaction of a wheel with a rail at a single-point contact is presented in the form of contacts of two cylinders of infinite length. The results of numerical analysis of the found analytical dependences of the influence of the plasticity parameter on the coefficient of friction, the influence of the plasticity parameter on the supporting force created by the lubricant layer during the movement of surfaces are presented. The influence of the coefficient of friction on the safety of rolling stock movement in the curved sections of the track is established.

Infinite length slotted ultra-wideband monopole antenna using step-feed with band notch characteristics

In this work, a printed ultra-wideband (UWB) antenna has been proposed exhibiting band notch characteristics. The proposed design covers the entire UWB band except for the 3.5 GHz band providing the band notch for the WiMAX band. This design consists of two-quarter elliptical patches placed symmetrically over the FR4 substrate. The elliptical shape of the patch is responsible for the UWB band achieved. The slot has been created on the optimized patch area to achieve the desired characteristics providing a notch for the WiMAX band. The slot in the patch is so perfectly designed that it gives the patch a perfect shape of butterfly wings. After designing, the proposed antenna was simulated and then fabricated. The fabricated and simulated results are in close agreement with each other which shows, the proposed UWB antenna is good enough for biomedical applications.

Ways to Improve Wear Resistance and Damping Properties of Radial Bearings Taking into Account Inertial Forces

This article considers a radial sliding bearing of infinite length whose moving part consists of the support, the porous layer, and the liquid lubricant. The analysis of the existing design calculation methods for such sliding bearings shows that they are very approximate because they do not consider the inertial forces applied, the electric conductivity of the lubricant, the permeability anisotropy, as well as the impacts of the electric field vector, magnetic induction vector, and incomplete filling of the working gap (pre-accident condition). The authors demonstrate how these factors impact the stable operation of the device facilitating the hydrodynamic regime. The authors find the asymptotic solution for the zero, first, and second approximation taking into account the inertial forces for the “thin layer”. By solving the produced equations using the Gauss-Seidel method, the authors determine the key operating parameters of the friction couple in question: the carrying capacity and the friction force. The authors provide an impact assessment for the parameters characterizing the permeability of the porous coating, the electric conductivity, and viscosity of the lubricant, as well as the length of the loaded area and the impacts of inertial forces on the carrying capacity and the friction force.

-modules on rigid analytic spaces III: weak holonomicity and operations

We develop a dimension theory for coadmissible $\widehat {\mathcal {D}}$ -modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic $\mathcal {D}$ -modules in the algebraic setting. We discuss a number of pathologies contained in this subcategory (modules of infinite length, infinite-dimensional fibres). We prove stability results for closed immersions and the duality functor, and show that all higher direct images of integrable connections restricted to a Zariski open subspace are coadmissible of minimal dimension. It follows that the local cohomology sheaves $\underline {H}^{i}_Z(\mathcal {M})$ with support in a closed analytic subset $Z$ of $X$ are also coadmissible of minimal dimension for any integrable connection $\mathcal {M}$ on $X$ .

Dynamic Analysis of a Deeply Buried Tunnel Influenced by a Newly-built Adjacent Cavity with a Special Emphasis on the Minimum Seismically Safe Tunnel Distance

Contemporary life streams, more often than ever, impose the necessity for construction of new underground structures in the vicinity of existing tunnels, with an aim to accommodate transportation systems and utility networks. A previously uninvestigated case, in which a newly-constructed tunnel opening is closely positioned behind an existing tunnel, referred to as the tunnel–cavity configuration, has been considered in this study. An exact analytical solution is derived considering a pair of parallel circular cylindrical structures of infinite length, with the horizontal alignment, embedded in a boundless homogeneous, isotropic, elastic medium and excited by time-harmonic plane SV-waves under the plane-strain conditions. The Helmholtz decomposition theorem, the wave functions expansion method, the translational addition theorem for bi-cylindrical coordinates, and the pertinent boundary conditions are jointly employed in order to develop a closed-form solution of the corresponding boundary value problem. The primary goal of the present study is to examine the increase in dynamic stresses at an existing tunnel structure due to the presence of a closely driven unlined cavity, as well as in a localized region around the tunnel (at the position of the cavity in close proximity), under incident SV-waves. A new quantity called dynamic stress alteration factor is introduced and the aspect of the minimum seismically safe distance between the two structures is particularly considered.

IMPROVED DESIGN TECHNIQUE FOR CONDUCTING PARTS OF ELECTROMAGNETIC CONTACTORS

The existing design techniques for the conductive parts of the main circuit of electromagnetic contactors are based on two assumptions: the infinite length of the conductor and the absence of its heating, which is determined by the contact resistance. This can lead to significant errors in the design of conductors of finite length, primarily in the design of conductive parts with contact bridges, which contain almost all modern electromagnetic contactors. For a more efficient determination of the geometric parameters of the conductive parts, it is proposed to use an improved technique without the above assumptions. The technique uses a model of a contact formed by overlapping the ends of two rectangular conductors and containing a contact piece as a design one. A key feature of the technique is the use in the calculations of the temperature distribution constant along the length of the conductor, introduced for the first time, which determines the nature of the change in its heating temperature. The main stages of calculation and an example of determining the geometric dimensions of the conductive parts by this method for ABB contactors for different rated currents are given.

A Unified Method to Decentralized State Detection and Fault Diagnosis/prediction of Discrete-event Systems

The state detection problem and fault diagnosis/prediction problem are fundamental topics in many areas. In this paper, we consider discrete-event systems (DESs) modeled by finite-state automata (FSAs). There exist plenty of results on decentralized versions of the latter problem but there is almost no result for a decentralized version of the former problem. In this paper, we propose a decentralized version of strong detectability called co-detectability which means that if a system satisfies this property, for each generated infinite-length event sequence, in at least one location the current and subsequent states can be determined by observations in the location after a common observation time delay. We prove that the problem of verifying co-detectability of deterministic FSAs is coNP-hard. Moreover, we use a unified concurrent-composition method to give PSPACE verification algorithms for co-detectability, co-diagnosability, and co-predictability of FSAs, without any assumption on or modification of the FSAs under consideration, where co-diagnosability is first studied by [Debouk & Lafortune & Teneketzis 2000], co-predictability is first studied by [Kumar & Takai 2010]. By our proposed unified method, one can see that in order to verify co-detectability, more technical difficulties will be met compared with verifying the other two properties, because in co-detectability, generated outputs are counted, but in the latter two properties, only occurrences of events are counted. For example, when one output was generated, any number of unobservable events could have occurred. PSPACE-hardness of verifying co-diagnosability is already known in the literature. In this paper, we prove PSPACE-hardness of verifying co-predictability.