Simple Equation Model Research Articles

Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression: Analytical post-bifurcation solutions and imperfection sensitivity

This paper studies the axisymmetric deformations of a nonlinearly hyperelastic tube subjected to axial compression. We aim at investigating the critical buckling stresses and modes, deriving the analytical solutions for the post-bifurcation deformations and studying the imperfection sensitivity. For a general isotropic hyperelastic tube, a coupled series-asymptotic method is utilized to derive two simplified model equations with specified constraints on the tube geometry. Then, we specialize to the Blatz–Ko material. With greased end conditions, through linear bifurcation analysis, we obtain the critical stress values and the corresponding mode numbers. The analytical solutions for the post-bifurcation states are constructed by the multiple scales method. By examining the solution behavior in the post-bifurcation regime, it is found that a thick tube could be considerably softer than a thin one. The singularities theory is used to consider the imperfection sensitivity, which reveals the mechanism is the existence of two modes corresponding to the same critical stress. Numerical solutions are also obtained which confirm the validity of the analytical solutions.

Immobilized photocatalyst on stainless steel woven meshes assuring efficient light distribution in a solar reactor

Abstract. An immobilized TiO2 photocatalyst with a high specific surface area was prepared on stainless steel woven meshes in order to be used packed in layers for water purification. Immobilization of such a complex shape needs a special coating technique. For this purpose, dip coating and electrophoretic deposition (EPD) techniques were used. The EPD technique gave the TiO2 coating films a better homogeneity and adhesion, fewer cracks, and a higher ·OH formation than the dip coating technique. The woven mesh structure packed in layers guaranteed an efficient light-penetration in water treatment reactor. A simple equation model was used to describe the distribution of light through the mesh layers in the presence of absorbing medium (e.g., colored water with humic acids). Maximum three or four coated meshes were enough to harvest the solar UV light from 300 nm to 400 nm with a high penetration efficiency. The separation distance between the mesh layers played an important role in the efficiency of solar light penetration through the coated mesh layers, especially in case of colored water contaminated with high concentrations of humic acid.

Impedance analysis of the multilayered organic solar cells with and without hole buffer layer

We studied the effects of a buffer layer [molybdenum oxide (MoO3) and poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS)] and the thickness of a p-type tetraphenyldibenzoperiflanthene (DBP) layer on the performance of multilayered organic solar cells in indium–tin oxide (ITO)/buffer/DBP/fullerene C60/bathocuproine (BCP)/Al multilayered photovoltaic devices. The insertion of a hole buffer layer reduced the resistance across the cell in forward biasing under illumination and in the dark, and the negative capacitance behaviors were observed at a voltage higher than VOC, probably owing to the enhancement of the double injection. On the other hand, a hole-blocking ITO/DBP interface reduced the hole injection and extraction, and DBP became similar to a dielectric layer in the dark, as determined from the capacitance–frequency measurement. The photogenerated carriers caused an increase in the capacitance C and the conductance G in the devices with and without the MoO3 buffer layers. Both C and G reached their local minima at a voltage close to VOC, and increased with a decrease in external voltage probably owing to the enhancement of charge extraction efficiency. At a lower voltage, however, C and G reached their peak values and then decreased again with a decrease in external voltage, probably owing to the reduction (ejection) in the number of photogenerated space charges in active layers. The increase in the thickness of the dielectric DBP layer resulted in a reduction in charge extraction efficiency, and an S-shaped curve was observed for the thick DBP cell. The peak voltages in C and G moved toward negative values with an increment in thickness, and this was discussed using the simplified rate equation model.

Similarity properties in the dynamics of delayed-feedback semiconductor lasers

Semiconductor lasers with delayed feedback exhibit two fundamentally different dynamical states: weak and strong chaos. We characterize experimentally the mechanism for the emergence of strong chaos. Based on these insights, we demonstrate similarity properties for long delays, i.e., similar dynamics for different pump currents when adjusting the feedback strength. For different delay times, even the same time- and amplitude-rescaled version of the dynamics can be generated. Using a simple rate-equation model, these properties can be corroborated. The results have major consequences for the characterization and tailoring of the dynamics for applications.

Luminescence Concentration Quenching Mechanism in Gd2O3:Eu3+.

Luminescence concentration quenching in Gd2O3:Eu(3+) nanocrystals results from strong interactions among O(2-) ions and Eu(3+) ions. Because all synthesized Gd2O3:Eu(3+) nanocrystals present the same cubic crystalline phase regardless of Eu(3+) concentration, it is possible to study the optical properties as a function of the dopant concentration. The emission intensities and lifetime curves for Gd2O3:Eu(3+) were analyzed by a simple rate equation model to study the interaction between the O(2-) ions and Eu(3+) ions. The rate equation model considers that such interaction is driven by the following energy transfer processes: the direct energy transfer (O(2-) → Eu(3+)), back-transfer (Eu(3+) → O(2-)), and direct energy migration (Eu(3+) → Eu(3+)). The exact solution of this model agrees with the experimental results, luminescence concentration quenching is reproduced and the corresponding energy transfer rates are reported. Quantitative results suggest that the direct energy transfer and direct energy migration processes are the main responsible for the luminescence concentration quenching, whereas the back-transfer process promotes the Eu(3+) emission.

Nonlocal spectroscopy of Andreev bound states

We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes $u$ and $v$.

Modeling enhancement and suppression of vibrational Feshbach resonances in positron annihilation on molecules

Experiments have shown that positrons can attach to molecules via vibrational Feshbach resonances. This leads to increased annihilation rates, the magnitudes of which depend upon molecular structure. Presented here is a simplified rate-equation model to describe the competition between annihilation while the positron is attached to the molecule, positron ejection from the entrance state, and diffusion of the vibrational energy to multimode states followed by similar ejection due to vibrational deexcitation. The latter ejection process can involve vibrations more strongly coupled to the positron continuum, producing suppression of the annihilation, or those more weakly coupled to the continuum, resulting in enhanced annihilation rates. This model elucidates the role that mode coupling can play in determining resonant annihilation amplitudes. Simple limits are obtained and compared with experimental results for selected molecules.

Multi-component Reynolds-averaged Navier–Stokes simulations of Richtmyer–Meshkov instability and mixing induced by reshock at different times

Turbulent mixing generated by shock-driven acceleration of a perturbed interface is simulated using a new multi-component Reynolds-averaged Navier–Stokes (RANS) model closed with a two-equation \(K\)–\(\epsilon \) model. The model is implemented in a hydrodynamics code using a third-order weighted essentially non-oscillatory finite-difference method for the advection terms and a second-order central difference method for the gradients in the source and diffusion terms. In the present reshocked Richtmyer–Meshkov instability and mixing study, an incident shock with Mach number \(M\!a_{\mathrm{s}}=1.20\) is generated in air and progresses into a sulfur hexafluoride test section. The time evolution of the predicted mixing layer widths corresponding to six shock tube test section lengths are compared with experimental measurements and three-dimensional multi-mode numerical simulations. The mixing layer widths are also compared with the analytical self-similar power-law solution of the simplified model equations prior to reshock. A set of model coefficients and initial conditions specific to these six experiments is established, for which the widths before and after reshock agree very well with experimental and numerical simulation data. A second set of general coefficients that accommodates a broader range of incident shock Mach numbers, Atwood numbers, and test section lengths is also established by incorporating additional experimental data for \(M\!a_{\mathrm{s}}=1.24\), \(1.50\), and \(1.98\) with \(At=0.67\) and \(M\!a_{\mathrm{s}}=1.45\) with \(At=-0.67\) and previous RANS modeling. Terms in the budgets of the turbulent kinetic energy and dissipation rate equations are examined to evaluate the relative importance of turbulence production, dissipation and diffusion mechanisms during mixing. Convergence results for the mixing layer widths, mean fields, and turbulent fields under grid refinement are presented for each of the \(M\!a_{\mathrm{s}}=1.20\) cases.

A New Design of Dual Band Phase Shifter using MEMS Technology

Abstract - This paper presents a new design of microwave microelectromechanical systems (MEMS) phase shifter for dual band wireless local area network (WLAN) applications. A bit is designed which product a constant phase shift of 11.25° by switching between two line that consist of 12 and 6 unitcells in each frequency band. A unitcell is constructed by gold membrane suspended over the coplanar waveguide (CPW) that can be moved vertically by electrostatic actuation which can ultimately be used for changing the operating frequency band. Two states of unitcell are used to switch between two frequency bands of 2.4 GHz and 5.2 GHz (IEEE 802.11 standard employed in dual band WLAN systems). First, a closed form equation of simplified model of structure is obtained. Then using this equation and advanced design system (ADS) simulator, the dual band phase shifter is designed. The validation of modeling and equations are demonstrated using the High Frequency Structure Simulator (HFSS). At the frequency of 2.4 GHz, maximum return and insertion losses are -16.96 and -0.12 dB, respectively that exhibit a phase shift efficiency of 93.75 °/dB (60.22 °/cm). At the frequency of 5.2 GHz, maximum return and insertion loss are -16.86 and -0.15 dB, respectively exhibiting a phase shift efficiency of 75 °/dB (60.22 °/cm). The new proposed design is only to achieve a dual band phase shifter using MEMS technology which has low loss and weight with high linearity respect to the other technologies.

The Basic Dynamics Study of Flip-Flow Screen and Particles Based on MATLAB

This paper outlined the basic working principle of flip-flow Screen and and then established the screen surface kinetic equation of simplified geometric model. The midpoint motion law of the flip-flow Screen surface, the screen surface-particle trajectory and the inclination of the particle trajectory were studied. The characteristic curve made by Matlab showed unique dynamic characteristics of the screen surface, which provided a theoretical basis for its design and application.

The Basic Dynamics Study of Flip-Flow Screen and Particles Based on MATLAB

This paper outlined the basic working principle of flip-flow Screen and and then established the screen surface kinetic equation of simplified geometric model. The midpoint motion law of the flip-flow Screen surface, the screen surface-particle trajectory and the inclination of the particle trajectory were studied. The characteristic curve made by Matlab showed unique dynamic characteristics of the screen surface, which provided a theoretical basis for its design and application.

Study on China's Carbon Emmission Three Factors Simulation in 12<sup>th</sup> Five-Year Plan: 2011-2020 in an Economy-Energy-Environment Framework

In an Economy-Energy-Environment framework, we use system dynamics simulation analysis, thermal coal equivalent, by 2000-2010 history data, divide GDP into three industries, energy into coal, petrol, natural gas and electricity subdivision 9 energy, environment per person carbon emissions, build 9 simplified in-tree model and simulation equation. On the goal of per person GDP double index, simulation per person carbon emission in 2011-2020 . subject to the The 12th Five-Year Plan (E1)- GDP growth 7% and the industry structure of 6%, 45%, 49% and in 2020 10000RMB carbon emission degrade 40%-45% to one in 2015, energy (E2) the goal of energy consumption total, energy consumption structure and 10000 GDP energy consumption in energy The 12th Five-Year Plan , in the hypothesis of scheme A-secondary industry decrease rate 0.1% per-year and tertiary industry growth rate 0.15% per-year and scheme B-percent of secondary industry adjust to forty five percent and tertiary industry adjust to forty nine percenttwo scheme, get the goal of double GDP per population in 2017, it is positive to increase energy efficiency and decrease to carbon emission for industry adjustment, scheme is better to achieve the 12th Five-Year goal.

Four-wave mixing analysis on injection-locked quantum dot semiconductor lasers

We derive a simplified rate equation model for the four-wave mixing (FWM) analysis on quantum dot (QD) semiconductor lasers subject to optical injection. The regenerative and the amplitude modulation spectra of the FWM signals with different intrinsic laser parameters and external injection conditions are investigated. By curve fitting the regenerative and the amplitude modulation spectra obtained experimentally, the intrinsic parameters of a commercial single-mode QD laser under different injection conditions are extracted. The linewidth enhancement factor α at different injection levels and detunings are shown, where a reduction of up to 39% from its free-running value is demonstrated. By increasing the injection strength, the α can be further reduced to minimized the chirp in optical communications.

Understanding the enhancement effect of high-temperature steam on the carbonation reaction of CaO with CO2

The steam-enhanced carbonation reaction of CaO with CO2 is a widely observed phenomenon, but its mechanism is unclear. This study proposed that OH− formation caused by the dissociation of H2O molecules may explain enhanced carbonation. The relationship of oxygen vacancies with OH− at different temperatures and steam fractions was established and integrated into a new carbonation model. This new model included a simplified rate equation model to describe product island formation and a multi-ion diffusion model that describes product layer growth. Experiments on carbonation and sorption-enhanced water gas shift reactions in a laboratory-scale fluidized bed reactor were conducted to validate the idea of OH− formation. The new developed models were validated by thermogravimetric analysis.

Aspergillus niger P6 and Rhodotorula mucilaginosa CH4 used for olive mill wastewater (OMW) biological treatment in single pure and successive cultures

The aim of this study was to investigate the Rhodotorula mucilaginosa CH4 and Aspergillus niger P6 abilities to purify olive mill wastewater (OMW) in single pure and mixed cultures during the treatment. Both fungi were molecularly identified. OMW was used at five dilutions from 5% to 30% with chemical oxygen demand (COD) ranging from 11,600 to 24,600 mg L−1. Firstly, each fungus was used separately, then they were successively used to treat the OMW. In single pure culture, A. niger showed a better efficiency in OMW purification than R. mucilaginosa. Furthermore, when successively used, the two studied strains exhibited improvements in the decrease of COD, polyphenolic compounds concentration and effluent colour. COD removals were 95.68–56.71% by R. mucilaginosa and 98.02–69.51% by A. niger for OMW dilutions varying from 5% to 30%. Both strains showed an important polyphenolic compounds removal of 83–45% by R. mucilaginosa and 94–58% by A. niger, in accordance with the OMW COD initially used. The COD and phenolic compound removals fitted simple equation models, with high regression coefficients. The strains’ growth kinetics decreased according to the OMW concentration, but, when successively used, fungal growth was improved, allowing efficient effluent treatment.

Dynamical quorum sensing and clustering dynamics in a population of spatially distributed active rotators

A model of clustering dynamics is proposed for a population of spatially distributed active rotators. A transition from excitable to oscillatory dynamics is induced by the increase of the local density of active rotators. It is interpreted as dynamical quorum sensing. In the oscillation regime, phase waves propagate without decay, which generates an effectively long-range interaction in the clustering dynamics. The clustering process becomes facilitated and only one dominant cluster appears rapidly as a result of the dynamical quorum sensing. An exact localized solution is found to a simplified model equation, and the competitive dynamics between two localized states is studied numerically.

Rate equation analysis of injection-locked quantum cascade lasers

The modulation properties of optical injection-locked quantum cascade lasers (QCLs) are investigated theoretically via a simple low dimensional rate equation model. It is found that both strong injection level and positive optical frequency detuning increase the modulation bandwidth, while a large linewidth enhancement factor (LEF) contributes to the enhancement of the peak magnitude in the intensity modulation (IM) response. As opposed to conventional injection-locked interband lasers, it is demonstrated that no dip occurs in the QCL's IM response, which is beneficial for a series of broadband microwave photonic applications. Computations also show that the value of the LEF can critically modify both the locking and stability regions on the optical frequency detuning injection level map.

Mass-based hygroscopicity parameter interaction model and measurement of atmospheric aerosol water uptake

Abstract. In this study we derive and apply a mass-based hygroscopicity parameter interaction model for efficient description of concentration-dependent water uptake by atmospheric aerosol particles with complex chemical composition. The model approach builds on the single hygroscopicity parameter model of Petters and Kreidenweis (2007). We introduce an observable mass-based hygroscopicity parameter κm which can be deconvoluted into a dilute hygroscopicity parameter (κm0) and additional self- and cross-interaction parameters describing non-ideal solution behavior and concentration dependencies of single- and multi-component systems. For reference aerosol samples of sodium chloride and ammonium sulfate, the κm-interaction model (KIM) captures the experimentally observed concentration and humidity dependence of the hygroscopicity parameter and is in good agreement with an accurate reference model based on the Pitzer ion-interaction approach (Aerosol Inorganic Model, AIM). Experimental results for pure organic particles (malonic acid, levoglucosan) and for mixed organic-inorganic particles (malonic acid – ammonium sulfate) are also well reproduced by KIM, taking into account apparent or equilibrium solubilities for stepwise or gradual deliquescence and efflorescence transitions. The mixed organic-inorganic particles as well as atmospheric aerosol samples exhibit three distinctly different regimes of hygroscopicity: (I) a quasi-eutonic deliquescence & efflorescence regime at low-humidity where substances are just partly dissolved and exist also in a non-dissolved phase, (II) a gradual deliquescence & efflorescence regime at intermediate humidity where different solutes undergo gradual dissolution or solidification in the aqueous phase; and (III) a dilute regime at high humidity where the solutes are fully dissolved approaching their dilute hygroscopicity. For atmospheric aerosol samples collected from boreal rural air and from pristine tropical rainforest air (secondary organic aerosol) we present first mass-based measurements of water uptake over a wide range of relative humidity (1–99.4%) obtained with a new filter-based differential hygroscopicity analyzer (FDHA) technique. For these samples the concentration dependence of κm can be described by a simple KIM model equation based on observable mass growth factors and a total of only six fit parameters summarizing the combined effects of the dilute hygroscopicity parameters, self- and cross-interaction parameters, and solubilities of all involved chemical components. One of the fit parameters represents κm0 and can be used to predict critical dry diameters for the activation of cloud condensation nuclei (CCN) as a function of water vapor supersaturation according to Köhler theory. For sodium chloride and ammonium sulfate reference particles as well as for pristine rainforest aerosols consisting mostly of secondary organic matter, we obtained good agreement between the KIM predictions and measurement data of CCN activation. The application of KIM and mass-based measurement techniques shall help to bridge gaps in the current understanding of water uptake by atmospheric aerosols: (1) the gap between hygroscopicity parameters determined by hygroscopic growth measurements under sub-saturated conditions and by CCN activation measurements at water vapor supersaturation, and (2) the gap between the results of simplified single parameter models widely used in atmospheric or climate science and the results of complex multi-parameter ion- and molecule-interaction models frequently used in physical chemistry and solution thermodynamics (e.g., AIM, E-AIM, ADDEM, UNIFAC, AIOMFAC).

Study on the Hydration Kinetics of Portland Cement

A kinetic model originally developed by Tomosawa is analyzed for the hydration of Portland cement. The complicated kinetic equation of Tomosawa model is transformed into three simple equations of simplified model which represent mass transfer, phase-boundary reaction and diffusion process at different stage, respectively. Based on the isothermal calorimetry and the simplified model, the relationship between the degree of reaction and reaction rate is discussed. The derived result could reflect the development of degree of reaction and reaction rate during the cement hydration. The calculation results of simplified model are compared well with the experimental results. Studying the connection among the three processes is helpful to understanding the complicated hydration mechanism of Portland cement.

Multicomponent Reynolds-averaged Navier–Stokes simulations of reshocked Richtmyer–Meshkov instability-induced mixing

A third-order weighted essentially nonoscillatory (WENO) finite-difference implementation of a two-equation K–ε multicomponent Reynolds-averaged Navier–Stokes (RANS) model is used to simulate reshocked Richtmyer–Meshkov turbulent mixing of air and sulfur hexafluoride at incident shock Mach numbers Mas = 1.24, 1.50, 1.98 with Atwood number At = 0.67 and Mas = 1.45 with At = −0.67. The predicted mixing layer width evolutions are compared with experimental measurements of the width before and after reshock [M. Vetter, B. Sturtevant, Shock Waves 4 (1995) 247; F. Poggi, M.H. Thorembey, G. Rodriguez, Phys. Fluids 10 (1998) 2698] and with the analytical self-similar power-law solution of the simplified model equations before reshock. A new procedure is introduced for the specification of the initial turbulent kinetic energy and its dissipation rate, in which these quantities are related by the linear instability growth rate. The predicted mixing layer widths before reshock are shown to be sensitive to changes in the initial turbulent kinetic energy and its dissipation rate, while the widths after reshock are sensitive to changes in the model coefficients Cε0 and σρ appearing in the buoyancy (shock) production terms in the turbulent kinetic energy and dissipation rate equations. A set of model coefficients and initial conditions is shown to predict mixing layer widths in generally good agreement with the pre-reshock experimental data, and very good agreement with the post-reshock data for all cases. Budgets of the turbulent kinetic energy equation just before and after reshock for the Mas = 1.24 case are used to identify the principal physical mechanisms generating turbulence in reshocked Richtmyer–Meshkov instability: buoyancy production (pressure work) and shear production. Numerical convergence of the mixing layer widths under spatial grid refinement is also demonstrated for each of the Mach numbers considered.