Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay

In this paper, we study the dynamics of an SIR epidemic model with a logistic process and a distributed time delay. We first show that the attractivity of the disease-free equilibrium is completely determined by a threshold $R_0$. If $R_0?1$, then the disease-free equilibrium is globally attractive and the disease always dies out. Otherwise, if $R_0>1$, then the disease-free equilibrium is unstable, and meanwhile there exists uniquely an endemic equilibrium. We then prove that for any time delay $h>0$, the delayed SIR epidemic model is permanent if and only if there exists an endemic equilibrium. In other words, $R_0>1$ is a necessary and sufficient condition for the permanence of the epidemic model. Numerical examples are given to illustrate the theoretical results. We also make a distinction between the dynamics of the distributed time delay system and the discrete time delay system.     

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

Diffuse optical tomography (DOT) is an emerging technique for functional biological imaging. The imaging quality of DOT depends on the imaging reconstruction algorithm. The SIRT has been widely used for DOT image reconstruction but there is no criterion to truncate based on any kind of residual parameter. The iteration loops will always be decided by experimental rule. This work presents the CR calculation that can be great help for SIRT optimization. In this paper, four inhomogeneities with various shapes of absorption distributions are simulated as imaging targets. The images are reconstructed and analyzed based on the simultaneous iterative reconstruction technique (SIRT) method. For optimization between time consumption and imaging accuracy in reconstruction process, the numbers of iteration loop needed to be optimized with a criterion in algorithm, that is, the root mean square error (RMSE) should be minimized in limited iterations. For clinical applications of DOT, the RMSE cannot be obtained because the measured targets are unknown. Thus, the correlations between the RMSE and the convergence rate (CR) in SIRT algorithm are analyzed in this paper. From the simulation results, the parameter CR reveals the related RMSE value of reconstructed images. The CR calculation offers an optimized criterion of iteration process in SIRT algorithm for DOT imaging. Based on the result, the SIRT can be modified with CR calculation for self-optimization. CR reveals an indicator of SIRT image reconstruction in clinical DOT measurement. Based on the comparison result between RMSE and CR, a threshold value of CR (CR_T) can offer an optimized number of iteration steps for DOT image reconstruction. This paper shows the feasibility study by utilizing CR criterion for SIRT in simulation and the clinical application of DOT measurement relies on further investigation.     

Ejection of uniform micrometer-sized droplets from Faraday waves on a millimeter-sized water drop

This Letter reports the first observation and theoretical analysis of a new phenomenon: one large spherical water drop ejecting simultaneously a very large number of monodisperse microdroplets. An ultrasonic nozzle with multiple-Fourier horns in resonance enables controlled excitation of megahertz Faraday waves on the free water surface. The temporal instability of such waves leads to the ejection of 3.5-4.4 μm monodisperse droplets at a high rate (>4.0×10(7) droplets/sec). This is in stark contrast to the Rayleigh-Plateau instability, which ejects one droplet at a time.     

Controlled Deterministic Secure Quantum Communication Based on Quantum Search Algorithm

In this study, we propose a controlled deterministic secure quantum communication (CDSQC) protocol based on the idea of Grover’s quantum search algorithm (QSA). The proposed protocol has the following two advantages over the existing CDSQC protocols: (1) high qubit frequency and (2) less quantum memory. Moreover, the security analysis of the proposed protocol shows that any eavesdropper will be detected with a very high probability under both ideal and noisy quantum channel conditions.     

Exposure assessment and engineering control strategies for airborne nanoparticles: an application to emissions from nanocomposite compounding processes

In this study, nanoalumina and nanoclay particles were compounded separately with ethylene vinyl acetate (EVA) polymer to produce nanocomposites using a twin-screw extruder to investigate exposure and effective controls. Nanoparticle exposures from compounding processes were elevated under some circumstances and were affected by many factors including inadequate ventilation, surrounding air flow, feeder type, feeding method, and nanoparticle type. Engineering controls such as improved ventilation and enclosure of releasing sources were applied to the process equipment to evaluate the effectiveness of control. The nanoparticle loading device was modified by installing a ventilated enclosure surrounding the loading chamber. Exposures were studied using designed controls for comparison which include three scenarios: (1) no isolation; (2) enclosed sources; and (3) enclosed sources and improved ventilation. Particle number concentrations for diameters from 5 to 20,000 nm measured by the Fast Mobility Particle Sizer and aerodynamic particle sizer were studied. Aerosol particles were sampled on transmission electron microscope grids to characterize particle composition and morphology. Measurements and samples were taken at the near- and far-field areas relative to releasing sources. Airborne particle concentrations were reduced significantly when using the feeder enclosure, and the concentrations were below the baseline when two sources were enclosed, and the ventilation was improved when using either nanoalumina or nanoclay as fillers.     

A Layer-Integrated Model of Solute Transport in Heterogeneous Media

This study presents a numerical solution to the three-dimensional solute transport in heterogeneous media by using a layer-integrated approach. Omitting vertical spatial variation of soil and hydraulic properties within each layer, a three-dimensional solute transport can be simplified as a quasi-three-dimensional solute transport which couples a horizontal two-dimensional simulation and a vertical one-dimensional computation. The finite analytic numerical method was used to discretize the derived two-dimensional governing equation. A quadratic function was used to approximate the vertical one-dimensional concentration distribution in the layer to ensure the continuity of concentration and flux at the interface between the adjacent layers. By integration over each layer, a set of system of equations can be generated for a single column of vertical cells and solved numerically to give the vertical solute concentration profile. The solute concentration field was then obtained by solving all columns of vertical cells to achieve convergence with the iterative solution procedure. The proposed model was verified through examples from the published literatures including four verifications in terms of analytical and experimental cases. Comparison of simulation results indicates that the proposed model satisfies the solute concentration profiles obtained from experiments in time and space.     

Point Singularities of 3D Stationary Navier–Stokes Flows

This article characterizes the singularities of very weak solutions of 3D stationary Navier–Stokes equations in a punctured ball which are sufficiently small in weak L ³.     

Simple model for predicting microchannel heat sink performance and optimization

A simple model was established to predict microchannel heat sink performance based on energy balance. Both hydrodynamically and thermally developed effects were included. Comparisons with the experimental data show that this model provides satisfactory thermal resistance prediction. The model is further extended to carry out geometric optimization on the microchannel heat sink. The results from the simple model are in good agreement as compared with those obtained from three-dimensional simulations.     

Noise mapping in urban environments: A Taiwan study

This study analyzed the spatial characteristics of urban environmental noise by using noise maps produced at 345 noise monitoring stations in Tainan, Taiwan. Noise data were collected at varying intervals: morning, afternoon, and evening in both summer and winter. The spatial distributions of the noise levels during each time interval were evaluated and visualized by geographic information systems. The analytical results indicated that the highest and lowest average noise levels were 69.6 dB(A) and 59.3 dB(A) during summer mornings and winter evenings, respectively. Comparison of monitored noise levels with regulatory standards revealed that noise standard violations, which usually occur on summer evenings, are as high as 23 dB(A). Furthermore, the results of noise exposure analysis showed that over 90% of the Tainan City population are exposed to unacceptable noise as defined by US Department of Housing and Urban Development. The findings of this study show that noise maps can be useful for investigating noise in urban environments.