Steady Distribution Research Articles

Assessing the impact of the 4CL enzyme complex on the robustness of monolignol biosynthesis using metabolic pathway analysis

Lignin is a polymer present in the secondary cell walls of all vascular plants. It is a known barrier to pulping and the extraction of high-energy sugars from cellulosic biomass. The challenge faced with predicting outcomes of transgenic plants with reduced lignin is due in part to the presence of unique protein-protein interactions that influence the regulation and metabolic flux in the pathway. Yet, it is unclear why certain plants have evolved to create these protein complexes. In this study, we use mathematical models to investigate the role that the protein complex, formed specifically between Ptr4CL3 and Ptr4CL5 enzymes, have on the monolignol biosynthesis pathway. The role of this Ptr4CL3-Ptr4CL5 enzyme complex on the steady state flux distribution was quantified by performing Monte Carlo simulations. The effect of this complex on the robustness and the homeostatic properties of the pathway were identified by performing sensitivity and stability analyses, respectively. Results from these robustness and stability analyses suggest that the monolignol biosynthetic pathway is resilient to mild perturbations in the presence of the Ptr4CL3-Ptr4CL5 complex. Specifically, the presence of Ptr4CL3-Ptr4CL5 complex increased the stability of the pathway by 22%. The robustness in the pathway is maintained due to the presence of multiple enzyme isoforms as well as the presence of alternative pathways resulting from the presence of the Ptr4CL3-Ptr4CL5 complex.

Steady state numerical solutions for determining the location of MEMS on projectile

This paper is devoted to compare the numerical solutions for the steady and unsteady state heat distribution model on projectile. Here, the best location for installing of the MEMS on the projectile based on the surface temperature is investigated. Numerical iteration methods, Jacobi and Gauss-Seidel have been elaborated to solve the steady state heat distribution model on projectile. The results using Jacobi and Gauss-Seidel are shown identical but the discrepancy iteration cost for each methods is gained. Using Jacobi’s method, the iteration cost is 350 iterations. Meanwhile, using Gauss-Seidel 188 iterations are obtained, faster than the Jacobi’s method. The comparison of the simulation by steady state model and the unsteady state model by a reference is shown satisfying. Moreover, the best candidate for installing MEMS on projectile is observed at pointT(10, 0) which has the lowest temperature for the other points. The temperature using Jacobi and Gauss-Seidel for scenario 1 and 2 atT(10, 0) are 307 and 309 Kelvin respectively.

Analytical solutions and dimensional analysis of pseudo 2D current density distribution model in PEM fuel cells

Abstract In this paper, a new dimensionless pseudo 2D steady state current density distribution model along the channel of a polymer electrolyte membrane (PEM) fuel cell is presented. This model includes four fundamental phenomena observed in PEM fuel cell cathode such as the air concentration depletion along the channel, the mass transport through the gas diffusion layer (GDL), the charge transport through the membrane and the electrochemical transfer in the catalyst layer (CL). A dimensional analysis is performed, and three dimensionless parameters are found to govern the current density distribution along the channel: a Peclet number at the channel/GDL interface, a Damkholer number at the GDL/CL interface, and a Wagner number at the CL/PEM interface. Four regimes of operation are defined based on the values of these dimensionless numbers, and for each of them new analytical solutions are developed. A good agreement with the experimental measurements of current density distribution reported in literature is found, concluding that the macroscopic PEM fuel cell physic is well described by our model. The specific operating regime described with relatively simple equations of current density distributions paves the way for a better control of fuel cell operation and performance, and in situ characterisation of fuel cell material properties.

Stationary mass distribution and nonlocality in models of coalescence and shattering.

We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the large and small mass asymptotic behavior of the mass distribution depend on whether the collision kernel is local (the aggregation mass flux is essentially generated by collisions between particles of similar masses) or nonlocal (collision between particles of widely different masses give the main contribution to the mass flux). We show that the nonlocal regime is further divided into two subregimes corresponding to weak and strong nonlocality. We also observe that at the boundaries between the local and nonlocal regimes, the mass distribution acquires logarithmic corrections to scaling and calculate these corrections. Exact solutions for special kernels and numerical simulations are used to validate some nonrigorous steps used in the analysis. Our results show that for local kernels, the scaling solutions carry a constant flux of mass due to aggregation, whereas for the nonlocal case there is a correction to the constant flux exponent. Our results suggest that for general scale-invariant kernels, the universality classes of mass distributions are labeled by two parameters: the homogeneity degree of the kernel and one further number measuring the degree of the nonlocality of the kernel.

Predator-prey model with age structure

Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated. doi:10.1017/S1446181117000360

Perishable inventory model with Markovian arrival process, retrial demands and multiple working vacations

In this paper, we consider a continuous review perishable inventory system in which two types of customers, positive and negative, arrive according to a Markovian arrival process. The life time of an item and the lead time of reorder are exponentially distributed. Demands that occur during stock out period or busy period either enter an orbit of size N or are lost. The orbital demands compete their service with an exponential rate depending on the number of demands in the orbit. The waiting demands in the orbit may renege the system after an exponentially distributed amount of time. The server takes multiple working vacations at zero inventory. The steady state joint probability distribution of the number of customers in the orbit and the inventory level is obtained. Various performance measures and cost analysis are shown with numerical results.

Tailored properties of hot stamping steel by resistance heating with local temperature control

Local austenization by local heating temperature control of blanks is one of the methods to obtain hot stamping parts with tailored properties. Resistance heating is a novel heating technology with high efficiency and rapid heating rate. In this paper, a heat transfer model was firstly developed to describe the steady temperature distribution of the blank during resistance heating. Then two resistance heating schemes to achieve tailored properties of hot stamping steel were investigated by experiments. One scheme is local resistance heating by adjusting the electrode position. And the other scheme is resistance heating with middle insulation. The results showed that the developed model could provide adequate accuracy in calculating the blank temperature field. For the local resistance heating, the percentage of high temperature region in heating zone was about 70 %. From the non-heating region to the middle heating region, hardness increased from 200 to 515 HV10. And the length ratio between high and low hardness regions could he controlled by adjusting electrode positions. For the resistance heating with middle insulation, a 340~360 HV10 medium hardness region with the length of 80mm was observed. The total length of transition hardness regions was about 60 mm. In summary, the local resistance heating scheme showed more advantages including shorter transition region and significant hardness difference.

Optical transmission characteristics of multi-band triangular-lattice photonic crystal coupling cavity waveguide based on annular microcavity

The light localization characteristics of the near-infrared triangular-lattice photonic crystal annular microcavity are studied theoretically in this paper. The photonic crystal has a lattice constant of <i>a</i>=540 and it is composed of silicon rods each with a radius of <i>r</i>=135 immersed in air background. The two kinds of annular microcavities are obtained by removing 12 silicon rods which are located respectively at a distance of 2a and at a distance of √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> to the central rod. Five resonant wavelengths and the corresponding eigen mode profiles of the microcavity are studied. A coupled resonant optical waveguide is formed by integrating the microcavities with a periodic length of 7<i>a</i> in space. The group velocity of light beam propagation within multiple guiding bands are analyzed by the tight-binding approximation method. The maximum and minimum velocity of 0.0028<i>c</i> and 0.00082<i>c</i> are obtained, where <i>c</i> is the light velocity in vacuum. The light transmittance values and spatial steady distributions of the electric field's amplitude through the structure at several wavelengths within the guiding bands are studied by the finite-difference time-domain method. The results are consistent with that calculated by the plane wave expand method. Interleaving circular microcavities perpendicular to the direction of optical transmission at a lateral distance of 2√<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i>, the coupling region between the adjacent microcavities is changed, the difference in group velocity between guiding bands apparently decreases and the transmittance values of two frequency bands are enhanced.<br/>Keeping the size of silicon rods unchanged, two kinds of microcavities are constructed by removing the six rods with the distances of 2<i>a</i> and √<span style="border-top:1px solid; padding-top:0px;">3</span><i>a</i> from the center of the central silicon rod, respectively. The resonant wavelengths supported by the above two microcavities are studied. Two coupled-resonant optical waveguides with a periodic length of 7<i>a</i> are proposed. Connecting these two coupled cavity optical waveguides with the W1-typed input/output waveguides, the selecting and sharing function of guiding band are finally achieved for wavelengths within different frequency bands. Keeping the group velocity slowing down, a maximum value of one guiding band reaches 0.00047<i>c</i>.

Influence of accounting for translational motion of grains on grain growth kinetics and size distribution

The thermodynamic dissipation-based approach, being one of the approved effective methods for treatment of grain growth, is refined by accounting for dissipation due to translational motion of individual grains during grain growth. The present model introduces an interaction function correlating the velocity of translational motion and the rate of growth for individual grains. The comparison of results of simulations based on the present model with existing phase-field simulations indicates that about 1/4 to 1/3 of the driving force is dissipated by translational motion of grains lowering the grain growth kinetics and changing of the steady state grain radii distribution function.

Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system – the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β → ∞) limit.

Geophysical assessment for contaminant hydrology in Ujevwu, Nigeria

Indiscriminate dumping of both domestic and industrial waste has been increasing since the beginning of the exploration and exploitation of hydrocarbon in the Niger Delta area of Nigeria and has impacted the groundwater quality. Therefore, this study seeks to evaluate contaminant hydrology from dumpsite around Ujevwu area in relation to a Control site. Three Electrical methods, which include the spontaneous potential, dipole-dipole and the vertical electrical sounding were adopted. Also laboratory water analysis and groundwater/contaminant modelling using VISTA, version 4 were used to evaluate groundwater quality and flow direction/velocity. The low values of 11–515 Ωm and 10 to −160 mV for resistivity and spontaneous potential respectively around the dumpsite area to a depth of about 20 m is a reflection of the redox phenomenon occurring at depth in the contaminated groundwater. Hydrogeochemical parameters from water analysis showed values that are higher around the dumpsites when compared to the control site. Results for conductivity, lead and total viable bacteria count are higher than the permissible limits of the World Health Organisation (WHO) and they range from 380 to 440 μs/cm, 0.2–0.3 mg/l and 4.2–15.8 cfu/mL respectively. The steady state groundwater distribution model of the dumpsite and control site gives an approximate head gradient of about 0.00036 and 0.0007 respectively, and the flow direction in the south west. It is observed that the water level indicates that there is no significant change of the hydraulic gradient with time and therefore, the groundwater flow is assumed to be in steady state with the flow direction in the NE-SW, and a flow rate of 0.0093 m/d or 3.3 m/year, and 0.0197 m/d or 7.0 m/year respectively. From these results, immediate evacuation of the dumps in the area and remediation program should be carried out, as there is a risk of outbreak of water borne diseases in the area.

The Finite Element Simulation of the Upper Airway of Patients with Moderate and Severe Obstructive Sleep Apnea Hypopnea Syndrome.

Objectives To investigate the snoring modes of patients with Obstructive Sleep Apnea Hypopnea Syndrome and to discover the main sources of snoring in soft tissue vibrations. Methods A three-dimensional finite element model was developed with SolidEdge to simulate the human upper airway. The inherent modal simulation was conducted to obtain the frequencies and the corresponding shapes of the soft tissue vibrations. The respiration process was simulated with the fluid-solid interaction method through ANSYS. Results The first 6 orders of modal vibration were 12 Hz, 18 Hz, 21 Hz, 22 Hz, 36 Hz, and 39 Hz. Frequencies of modes 1, 2, 4, and 5 were from tongue vibrations. Frequencies of modes 3 and 6 were from soft palate vibrations. Steady pressure distribution and air distribution lines in the upper airway were shown clearly in the fluid-solid interaction simulation results. Conclusions We were able to observe the vibrations of soft tissue and the modeled airflow by applying the finite element methods. Future studies could focus on improving the soft tissues vibration compliances by adjusting the model parameters. Additionally, more attention should be paid to vibrational components below 20 Hz when performing an acoustic analysis of human snore sounds due to the presence of these frequencies in this model.

Control F-policy for Fault Tolerance Machining System with General Retrial Attempts

The fault tolerance problem of repairable redundant system with admission restriction is investigated by considering the general distributed retrial policy. Upon failure of a machining unit, if the repairman is occupied, the failed unit is forced to enter into the retrial orbit. From the orbit, the failed units repeat the request for the repair job. When the system reaches its capacity K, the failed units are stopped from entering in the system until the number of failed units is again ceases to the prefixed threshold value F. The life time of operating units and the repair times of failed units follow exponential distributed, whereas retrial time is governed by general distribution. By using the supplementary variable corresponding the remaining retrial time, we establish Chapman–Kolmogorov equations to obtain the steady state queue size distribution of the number of failed units. Various performance measures are obtained explicitly which are further used to facilitate the sensitivity analysis by taking numerical illustration.

PREDATOR–PREY MODEL WITH AGE STRUCTURE

Mealybug is an important pest of cassava plant in Thailand and tropical countries, leading to severe damage of crop yield. One of the most successful controls of mealybug spread is using its natural enemies such as green lacewings, where the development of mathematical models forecasting mealybug population dynamics improves implementation of biological control. In this work, the Sharpe–Lotka–McKendrick equation is extended and combined with an integro-differential equation to study population dynamics of mealybugs (prey) and released green lacewings (predator). Here, an age-dependent formula is employed for mealybug population. The solutions and the stability of the system are considered. The steady age distributions and their bifurcation diagrams are presented. Finally, the threshold of the rate of released green lacewings for mealybug extermination is investigated.

Pathways and supply of dissolved iron in the Amundsen Sea (Antarctica)

AbstractNumerous coastal polynyas fringe the Antarctic continent and strongly influence the productivity of Antarctic shelf systems. Of the 46 Antarctic coastal polynyas documented in a recent study, the Amundsen Sea Polynya (ASP) stands out as having the highest net primary production per unit area. Incubation experiments suggest that this productivity is partly controlled by the availability of dissolved iron (dFe). As a first step toward understanding the iron supply of the ASP, we introduce four plausible sources of dFe and simulate their steady spatial distribution using conservative numerical tracers. The modeled distributions replicate important features from observations including dFe maxima at the bottom of deep troughs and enhanced concentrations near the ice shelf fronts. A perturbation experiment with an idealized drawdown mimicking summertime biological uptake and subsequent resupply suggests that glacial meltwater and sediment‐derived dFe are the main contributors to the prebloom dFe inventory in the top 100 m of the ASP. The sediment‐derived dFe depends strongly on the buoyancy‐driven overturning circulation associated with the melting ice shelves (the “meltwater pump”) to add dFe to the upper 300 m of the water column. The results support the view that ice shelf melting plays an important direct and indirect role in the dFe supply and delivery to polynyas such as the ASP.

Study of virtual cathodes formation during beam-wave interaction in the reltron oscillator

In the present work, a high power microwave oscillator—reltron has been analyzed to investigate the virtual cathode formation mechanism during the beam-wave interaction. In reltron, a side coupled modulation cavity is used as its RF interaction structure containing three metal grids along the longitudinal direction. The space charge current responsible for the virtual cathode and its steady state electric field distribution has been analyzed. Space charge and beam impedance conditions for efficient device operation have been demonstrated. It has been shown that during the beam-wave interaction in the device, first a virtual cathode forms in the post-acceleration gap, and then the second virtual cathode develops between the first and second grids of the modulation cavity. These two virtual cathodes co-exist and cause the formation of a third virtual cathode between the second and third grids. At this instant, only the third virtual cathode remains, and for sustained device oscillation, this process repeats periodically in the device. The present study would be useful in understanding the beam-wave interaction mechanism as well as the design and development of efficient reltron devices.

Toxicokinetics, disposition and metabolism of fluoxetine in crabs

The disposition and metabolism of fluoxetine in the European shore crab and the Dungeness crab were assessed. Crabs received intracardiac doses of either 0.13 μg/kg or 0.5 mg/kg fluoxetine, respectively. In addition, fluoxetine was administered to Metacarcinus cancer by oral gavage at 7.8 mg/kg. The distribution of fluoxetine was quantified in haemolymph and digestive gland for both crabs, as well as brain, muscle, and testis of Carcinus maenas, over 12 days. The metabolite norfluoxetine, was also measured in C. maenas. Fluoxetine was mainly found in lipid rich tissues. Distribution coefficients increased for digestive gland until three days after fluoxetine administration and then decreased until the end of the observations. The highest distribution coefficients were obtained for brain. Norfluoxetine displayed continuously high levels in digestive gland and brain. The strong decrease in fluoxetine and the concomitant increase in norfluoxetine demonstrates that decapod crustaceans metabolise fluoxetine into the more biologically active norfluoxetine. Fluoxetine levels in the haemolymph of M. cancer declined within 20 h, but showed a second peak 25 h later, suggesting remobilisation from tissues sequestering the compound. The steady state volume distribution and the total body clearance of fluoxetine were high, consistent with high diffusion of fluoxetine into the peripheral tissues and biotransformation as an important elimination pathway. Oral administration of fluoxetine prolonged its half-life in M. cancer, but bioavailability was low. These results confirm the high distribution into nervous tissue, extensive biotransformation into the highly active norfluoxetine and a half-life similar to that observed in vertebrates.

Mode coupling in multimode step-index plastic-clad silica fibers with corrugated surfaces

The state of mode coupling in step-index plastic-clad silica fibers with corrugated surfaces is investigated in this article using the power flow equation. The coupling coefficient in this equation was obtained using our previously reported method. This enabled us to obtain the length of the corrugated piece of the fiber at which equilibrium mode distribution is achieved as well as the length at which a steady state distribution is established. It was found that the plastic-clad silica fibers with corrugated surfaces showed much stronger mode coupling than plastic-clad silica fibers without corrugated surfaces. Consequently, the equilibrium as well as steady state mode distributions were achieved at shorter fiber lengths in plastic-clad silica fibers with corrugated surfaces than in the same type of optical fibers without corrugated surfaces.

Parametric Study of Cantilever Plates Exposed to Supersonic and Hypersonic Flows

Analysis of hypersonic flows associated with re-entry vehicles has gained a lot of significance due to the advancements in Aerospace Engineering. An area that is studied extensively by researchers is the simultaneous reduction aerodynamic drag and aero heating in re-entry vehicles. Out of the many strategies being studied, the use of aerospikes at the stagnation point of the vehicle is found to give favourable results. The structural stability of the aerospike becomes important as it is exposed to very high pressures and temperatures. Keeping this in view, the deflection and vibration of an inclined cantilever plate in hypersonic flow is carried out using ANSYS. Steady state pressure distribution obtained from Fluent is applied as load to the transient structural module for analysis. After due validation of the methods, the effects of parameters like flow Mach number, plate inclination and plate thickness on the deflection and vibration are studied.

Transient effects on confined groundwater age distributions: Considering the necessity of time‐dependent simulations

AbstractThe key concept of transient age distributions is that the age distribution of water at a fixed spatial location may change over time. Most previous studies involving groundwater age have relied on the assumption of a steady state age distribution over time. This assumption simplifies the problem and can also be used for predictive modeling, but few studies have addressed the validity of this assumption directly. We explore the variability of transient age distributions in simplified, confined groundwater flow systems. The main focus is determining when it is necessary to explicitly model the transience. A combination of analytical and numerical methods is used to demonstrate the transient variability of age for several hypothetical velocity fields and trial domains. Transient effects are strongest for samples taken near fluctuating interfaces or boundaries. Lastly, we investigate how heterogeneity and transient boundary signals interact in a 2‐D domain. These impacts are difficult to generalize, so the article closes with a set of considerations to assist readers in determining whether or not transience is likely to play a significant role in other applications. The main conclusion is that high‐frequency oscillations in flow boundaries have negligible impacts on confined age distributions but long‐term trends in flow velocities (increasing or decreasing) can cause significant changes over time.