Study of the Streaming Operator with General Maxwell's Boundary Conditions

We study the streaming operator in slab domain with general Maxwell's boundary conditions described by linear boundary operators K ⁺ and K ^–. We prove that the streaming operator generates a strongly continuous semigroup. We show that the positivity and irreducibility of the boundary operators imply the positivity and irreducibility of the generated semigroup. We establish the spectral properties of the streaming operator and characterize its spectral bound. Under the compactness of boundary operators, we explicitly give the essential type of the generated semigroup and describe its asymptotic behavior in the operator norm topology.     

Stabilization and Riesz basis of a star-shaped network of Timoshenko beams

In this paper we consider a star-shaped network of Timoshenko beams, with feedback acting on the common vertex of the star. Suppose that the exterior vertices of this network are clamped, and at the common vertex the displacement and rotational angles are continuous. For this network, feedback controllers are designed at the common vertex so as to move the beams back to their equilibrium position. We show that the operator determined by the closed loop system has a compact resolvent and generates a C ₀ semigroup in an appropriate Hilbert space. Under certain conditions, we prove that the closed loop system is asymptotically stable. We also show that there is a sequence of the generalized eigenvectors of the system operator, which forms a Riesz basis with parentheses. Hence the spectrum determined growth condition holds.     

The Asymptotic Behavior for the Streaming Operator in Slab Geometry

In this paper, we complete Generation theorem for the streaming operator in slab geometry, where we have proved that the one-dimensional streaming operator in slab domain, with general boundary conditions described by a linear operator K, generates a strongly continuous semigroup. Here, under the positivity and irreducibility of the boundary operator K, we prove the positivity and the irreducibility of the generated semigroup. We also study the spectral properties of the streaming operator and characterize its spectral bound. Under the compactness of the boundary operator K, we determine the essential type of the generated semigroup and find its behavior asymptotic in the operator norm topology.     

Generation Theorem for the Streaming Operator in Slab Geometry

We study the one-dimensional streaming operator in slab domain with general boundary conditions described by a linear operator K. We prove that the streaming operator generates a strongly continuous semigroup and determine its upper bound. We also give the expression of the generated semigroup, which we use to describe its asymptotic behavior in the next article in this issue.     

Interior and Analytic Stabilization of the Wave Equation over a Cylinder

We analyze the analytic stabilization of the wave equation on a cylinder subject to an interior dissipation that does not satisfy the classical geometric control condition BLR. For this model, we prove that the space of exponential stabilized functions is lower than the whole energy space. We use spectral properties to find the set of functions that can be stabilized. We define a constant α _S which gives an estimate for the analyticity required for an initial data to hold in the space of stabilized functions.     

A domain of influence theorem for a natural stress–heat-flux disturbance in thermoelasticity of type-II

The aim of the present work is to establish the domain of influence theorem for a stress–heat-flux disturbance under Green and Naghdi thermoelasticity theory of type-II. We consider a mixed problem of natural type represented as stress–heat-flux disturbance in the context of Green–Naghdi thermoelasticity theory of general type. We establish a general energy identity for the problem. Then we establish the domain of influence theorem for natural stress–heat-flux disturbance in the context of Green–Naghdi model of thermoelasticity oftype-II. We prove that for a finite time t > 0, the pair of stress and the heat-flux field generates no disturbance outside a bounded domain. The domain of influence is shown to be dependent on the thermoelastic parameters.     

Stability and Riesz basis property for general network of strings

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator . Under certain conditions, we prove that the spectrum of is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator , we prove further that there exists a sequence of generalized eigenvectors of that forms a Riesz basis with parentheses in the Hilbert state space. This research is supported by the Natural Science Foundation of China grant NSFC-60874034.     

Exponential stability and spectral analysis of the inverted pendulum system under two delayed position feedbacks

In this paper, we examine the stability of a linearized inverted pendulum system with two delayed position feedbacks. The semigroup approach is adopted in investigation for the well-posedness of the closed loop system. We prove that the spectrum of the system is located in the left complex half-plane and its real part tends to − ∞ when the feedback gains satisfy some additional conditions. The asymptotic eigenvalues of the system is presented. By estimating the norm of the Riesz spectrum projection of the system operator that does not have the uniformly upper bound, we show that the eigenfunctions of the system do not form a basis in the state Hilbert space. Furthermore, the spectrum determined growth condition of the system is concluded and the exponential stability of the system is then established. Finally, numerical simulation is presented by applying the MATLAB software.     

Theoretical possibilities of InxGa1−xN tandem PV structures

We designed a model of In_xGa_1−xN tandem structure made of N successive p–n junctions going from two junctions for the less sophisticated structure to six junctions for the most sophisticated. We simulated the photocurrent density and the open-circuit voltage of each structure under AM 1.5 illumination in goal to optimize the number of successive junctions forming one structure.For each value of N, we assumed that each junction absorbs the photons that are not absorbed by the preceding one. From the repartition of photons in the solar spectrum and starting from the energy gap of GaN, we fixed the gap of each junction that gives the same amount of photocurrent density in the structure. Then we calculated the current density accurately and optimized the thicknesses of p and n layers of each junction to make it give the same output current density. The evaluation of n_i: the intrinsic concentration permitted to calculate the saturation current density and the open-circuit voltage of each junction. Assuming an overall fill factor of 80%, we divided the output peak power by the incident solar power and obtained the efficiency of each structure.The numerical values for In_xGa_1−xN were taken from the relevant literature. The calculated efficiency goes from 27.49% for the two-junction tandem structure to 40.35% for a six-junction structure. The six-junction In_xGa_1−xN tandem structure has an open-circuit voltage of about 5.34 V and a short circuit current density of 9.1 mA/cm².     

Spectral characteristics of a-Si:H/c-Si heterostructures

We have examined the current-voltage characteristic of i-a-Si:H/n-c-Si heterojunction Schottky solar cells in the dark and under different illumination (spectrum AM 1.5) intensities as well as the voltage- and temperature-dependent spectral response of these devices. The photo-current from the crystalline silicon depends on both voltage and temperature due to their influence on the impact of the band offsets. From our measurements of the spectral response we conclude that there is a small conduction band offset ΔE_c and a large valence band offset ΔE_v at the i-a-Si:H/n-c-Si heterojunction. The large valence band offset inhibits the collection of photogenerated holes from the crystalline silicon under normal photovoltaic conditions. Thus, the current-voltage characteristic under illumination between V = 0 V and V = V_oc is caused only by the photocurrent from the a-Si:H layer.     

Influence of the light source on the low-irradiance performance of Cu(In,Ga)Se2 solar cells

Illumination intensities in indoor environments are usually given in terms of lux, a unit of measurement which only takes into account the spectral distribution of the light source in the sensitivity range of the human eye (380–780 nm). At a given level of illuminance, however, the performance of a solar cell will strongly depend on the spectral distribution of the incoming light and on its spectral response. This work considers the spectral distribution of some typical light sources encountered in indoor environments (natural daylight/AM 1.5, fluorescent tube, halogen lamp with and without cold reflector, and the common incandescent lamp) and calculates the actual amount of light available to a generic solar cell. We then calculate the performance for different indoor illumination levels and spectra of a Cu(In,Ga)Se₂ solar cell especially optimised for low-irradiance conditions. Considering as a reference the performance of the cell under a AM 1.5 spectrum at a given level of illuminance, we can expect the performance of the cell to be reduced by a factor 3 and 2, respectively, when using a fluorescent tube and a halogen lamp with cold reflector as the light source, and to be increased by a factor 2 to 3 if the cell is operated under a halogen/incandescent lamp.     

Effect of internal migration on the environment in China

We examine the effect of inter-provincial migration on air and water pollution for a panel of Chinese provinces over the period 2000–2013. To do so, we employ linear and non-linear panel data models in a Stochastic Impacts by Regression on Population, Affluence and Technology (STIRPAT) framework. Results from linear and non-linear models suggest that inter-provincial migration has contributed to pollution. Second-generation linear panel data model results suggest that for every additional 10,000 inter-provincial migrants, chemical oxygen demand (COD) increases 0.27–0.58%, sulphur dioxide (SO₂) increases 0.08–0.25% and aggregate waste disposed (WST) increases 0.04–0.26%. Non-linear threshold panel model results suggest that for every additional 10,000 inter-provincial migrants, COD increases 0.2–0.5%, SO₂ increases 0.10–0.20% and WST increases 3.1–4.2%.     

Calibration of solar simulator for evaluation of dye-sensitized solar cells

The photo-to-electricity energy conversion efficiencies of ruthenium-dye-sensitized solar cells (DSC) are measured under a solar simulator. The error in conversion efficiencies was compared under a variety of spectral conditions. Measurements of the conversion efficiencies of DSC between a solar simulator and outdoor sunlight result in about 10% error. This error was seen when the spectral intensity of a xenon-lamp solar simulator (imitating an air mass (AM) 1.5 spectrum) was adjusted by the short-circuit photocurrent I_Si of a crystalline silicon (c-Si) standard cell. In order to adjust the energetic intensity of AM 1.5 for DSC that has a spectrum response only in the visible region light, the c-Si reference cell is modified with a glass UV filter (KG-5, Schott) and the solar simulator was adjusted by I_{IR-cut Si}. The energetic spectrum of the solar simulator has a good accuracy over the wavelength range 300–750 nm, giving the conversion efficiency of DSC an accuracy of about 2%. The dependency of the ratio of I_Si to I_{IR-cut Si} on natural sun power is discussed in view of scattering of the visible light under changing natural sun light.     

Generalized Thermoelastic Models for Linear Elastic Materials with Micro-Structure Part II: Enhanced Lord–Shulman Model

In this article, we derive constitutive thermoelastic models for linear elastic materials with micro-structure. The elastic behavior is assumed to be consistent with Mindlin Form II, whereas for the thermal behavior, the generalization of Fourier–Duhamel law proposed by Maxwell-Vernotte-Cattaneo is adopted. The resulting model is actually a generalization of the thermoelastic theory of Lord and Shulman, suitable for linear elastic materials with micro-structure taking into account micro-inertia effects as well. Uniqueness of the solution for the general case of anisotropic materials is proved. An application example is analyzed by means of the Finite Element method and comparisons are made with the generalized Green–Lindsay model derived in “Generalized Thermoelastic Models for Linear Elastic Materials with Micro-Structure Part I: Enhanced Green–Lindsay Model,” also in this issue.     

A solar cell sensitized with three different dyes

Construction of a semiconductor—dye heterostructure of the configuration n-TiO₂/D₁/p-CuSCN/D₂/p-CuSCN/D₃/p-CuSCN (n-TiO₂ is the nanocrystalline TiO₂ film deposited on conducting glass, p-CuSCN=ultra-thin (2 nm) layers of Cu(I) thiocyanate, p-CuSCN=thick layer of p-CuSCN , D₁=Fast Green, D₂=Rhodamine 6G and D₃=Acridine Yellow) is described. It is found that this heterojunction generates photovoltaic response to light absorption by all the three dyes. The mechanism involved is suggested to be transfer of electrons to n-TiO₂ and holes to p-CuSCN via tunneling. This technique could be a strategy to broaden the spectral response and enhance the efficiency of dye-sensitized solar cells.     

Distributionally <Emphasis Type="Italic">n</Emphasis>-Scrambled Set for Weighted Shift Operators

The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ? 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained.     

Advances in mathematical modeling of hydrogen adsorption and desorption in metal hydride beds with lattice Boltzmann method

This study presents numerical modeling and simulations of thermal fluid flows in high-volumetric-density metal hydride beds during hydrogen (H₂) adsorption and desorption within the lattice Boltzmann method (LBM) framework. A novel LBM is developed for predicting the flow and conjugate heat transfer in a practical lab apparatus involving a combination of solid chamber, free expansion zone, and porous media metal hydride that have not been addressed to date. With a correction term in the collision operator and a new equilibrium distribution function, the present model has a consistent expression of the heat capacity ratio for different fluid regions and derives the correct form of macroscopic energy and generalized momentum equations (including Darcy, Brinkman, and Forchheimer terms). The model is then validated through comparisons of the simulated results with previous experimental data under different initial pressure and temperature conditions for LaNi₅–H₂ storage systems as well Mg–H₂ reactors, achieving excellent agreement. In addition, accounting for conjugate heat transfer and other porous forces in the present LBM yields improved predictions over prior numerical approaches.     

A novel parallel two-step algorithm based on finite element discretization for the incompressible flow problem

Based on a two-step finite element method and fully overlapping domain decomposition technique, a parallel two-step algorithm for the incompressible flow problem is introduced and analyzed. In the new algorithm, all of the computations are performed in parallel on global composite meshes which are fine around the subdomain that we concentrate on but coarse elsewhere. Each processor first solves an original problem based on the P₁–P₁ stabilized finite element method and then solves a generalized Stokes problem based on the P₂–P₂ stabilized finite element method on a global composite mesh. The proposed algorithm is easy to implement. What’s more, the new algorithm can yield more accurate solutions compared with the numerical solution obtained by the common two-step method. Numerical tests are presented to verify the efficiency and validity of the proposed algorithm.     

On the Spatial Behavior of Constrained Motion in Type III Thermoelasticity

Green and Naghdi proposed three theories of thermoelasticity labelled as type I, II and III, respectively. Here we investigate the spatial behavior of solutions of a problem determined by the type III thermoelasticity. We study the growth/decay alternative in the spatial variable for the linear theory in the case that the thermoelastic deformations at the instant T are constrained to be proportional to the ones at the instant zero. In the case that the solutions decay, an upper bound for the amplitude term by means of the data of the problem can be obtained. We sketch how to obtain it. We finish by noting (through examples) that for several families of cases the solutions can be periodic in the spatial variable and the Phragmen–Lindelof alternative is not satisfied.     

Plane waves and eigenfrequency study in a transversely isotropic magneto-thermoelastic medium under the effect of a constant angular velocity

In this article, we investigate the influence of (i) relaxation times according to the theory of Green–Lindsay, (ii) rotation, and (iii) magnetic field on incident and reflected plane waves in a transversely isotropic magneto-thermoelastic medium. We moreover make a numerical study to analyze the amplitude ratios for incident plane waves and a numerical eigenfrequency study presenting some shape modes for the displacement and temperature fields of a physical suitable cylindrical system. The medium rotates with a constant angular velocity, in the presence of a magnetic field orthogonal to the stress-free and thermally insulated plane. We solve the equations of this system and show the arising of three quasi-plane waves in the medium. The theoretical aspects of this article are focused on the reflection of these qp-waves from one of the surfaces of the medium, which we impose to be stress-free and thermally insulated: We obtain the reflection coefficients by numerical simulations considering a cylinder of cobalt.