Concise Equation Research Articles

Investigation of the main factor affecting the NO x distribution in the street canyon with the photo-catalytic wall

ABSTRACT To find out the most contaminated street region and protect the pedestrian with the photo-catalytic equipment to decrease the hazard of oxynitride (NO x ), Computational Fluid Dynamics (CFD) simulation could be used to research the main factor affecting the statistical characteristics of the oxynitride distribution in the urban street canyon with the photo-catalytic building walls. Additionally, the connection was investigated and focused on the swirling flow and oxynitride concentration to find out the root of the main factor affecting oxynitride distribution. The simulation results showed that there was one three-dimensional swirling flow in the whole canyon and the statistical concentration was straightforwardly related to the swirling or whirling flow structure (such as eddy). The characteristics had been confirmed that the whirling flow structure affected the complex oxynitride distribution in the street canyon with the photo-catalytic building walls. Furthermore, one formula was found which described the oxynitride concentration constrained by the street canyon. This study illustrated that different sections in the canyon had various patterns of the whirling flow structure (swirling flow) and oxynitride. In the symmetrical portion of the street canyon (in the middle of the street length), there is one concise equation to describe the NOx concentration affected by the turbulence intensity. Moreover, the equation was presented as CR = 1.094 + 0.11e−I , where I was the turbulence intensity and CR was the oxynitride relative concentration in the street canyon.

Markov-reward based estimation of the idle-time in vehicular networks to improve multimetric routing protocols

Analyzing vehicular ad hoc networks (VANETs) poses a considerable challenge due to their constantly changing network topology and scarce network resources. Furthermore, defining suitable routing metrics for adaptive algorithms is a particularly hard task since these adaptive decisions should be taken according to the current conditions of the VANET. The literature contains different approaches aimed at optimizing the usage of wireless network resources. In a previous study, we introduced an analytical model based on a straightforward Markov reward chain (MRC) to capture transient measurements of the idle time of the link formed between two VANET nodes, which we denote as Tidle. This current study focuses on modeling and analyzing the influence of Tidle on adaptive decision mechanisms. Leveraging our MRC models, we have derived a concise equation to compute Tidle. This equation provides a quick evaluation of Tidle, facilitating quick adaptive routing decisions that align with the current VANET conditions. We have integrated our Tidle evaluation into multihop routing protocols. We specifically compare performance results of the 3MRP protocol with an enhanced version, I3MRP, which incorporates our Tidle metric. Simulation results demonstrate that integrating Tidle as a decision metric in the routing protocol enhances the performance of VANETs in terms of packet losses, packet delay, and throughput. The findings consistently indicate that I3MRP outperforms 3MRP by up to 50% in various scenarios across high, medium, and low vehicular densities.

Estimating spent fuel burnup with Neutron measurements: A Practical Rule of Thumb Equation

We present a concise equation correlating the burnup of spent nuclear fuel (SF) with the neutron count rate, developed through comprehensive data analysis from Origen-ARP and MCNP codes. This equation is applicable to Fork detectors, commonly used for verifying SF assemblies before their transfer to new storage sites. The detector is assumed to be a helium-3 detector. The reaction rate (RR) in the 3He detector is influenced by Total Neutron Source Intensity (TNSI), net neutron multiplication, and neutron capture during transit to the detector. TNSI emerges as the most influential factor. Two scenarios were explored: one involving pure water and the other with water containing 2000 ppm of boron. The characteristics of the concise equation are also analyzed.

A Novel Trajectory Tracking Control of AGV Based on Udwadia-Kalaba Approach

Several control approaches have been used in order to achieve the trajectory tracking control of automated guided vehicle (AGV). But they are all based on the D'Alembert principle which requires to determine the Lagrangian multipliers. Unlike those control methods, in this paper, a novel approach of trajectory tracking control is presented, which is based on Udwadia-Kalaba approach. This approach presents a novel, concise and explicit equation of motion for constrained mechanical systems with holonomic and/or nonholonomic constraints as well as constraints that may be ideal or non-ideal. The Udwadia-Kalaba equation is uncoupled and free from the Lagrangian multipliers. In this paper, we classify constraints into structural constraints and performance constraints. Structural constraints are set up regardless of trajectory control and we use structural constraints to establish the dynamic model. Then the desired trajectory is set as performance constraints and constraint torques are solved by analyzing Udwadia-Kalaba equation. For AGV, a nonholonomic mechanical system, second-order constraints are used to get constraint forces and the numerical simulation is conducted by using Matlab. The results show that the AGV's movement meets the requirement and the tracking trajectory is exact and perfect. Compared with other approaches, this approach requires very little computation. Through two cases of tracking a circle and a line, how to use Udwadia-Kalaba equation to realize trajectory tracking control is shown in detail.

Dyakonov surface polaritons in bi-hyperbolic metamaterial

A periodically layered metamaterial (MM) structured with antiferromagnetic (AF) and ionic-crystal (IC) layers was proposed, which exhibits bi-hyperbolicity with effective hyperbolic permeability and permittivity. We investigated Dyakonov surface polaritons (DSPs) localized at this bi-hyperbolic metamaterial surface. For such a complicated material system, we analytically acquired one concise dispersion equation and corresponding wave solutions. From them, we found four DSPs, or DSP-I, DSP-II, DSP-III, and DSP-IV, and meanwhile one Dyakonov surface magnon and one Dyakonov surface phonon were found in this bi-hyperbolic metamaterial. The ATR spectra numerically calculated clearly proved the actual existence of the DSPs acquired from the dispersion equation and offered the path to excite and observe the DSPs. The DSP’s energy propagating direction is parallel to the air/MM interface, but not along the wave vector direction, and further it can approximatively be vertical to the wave-vector.

A novel lattice model to predict chloride diffusion coefficient of unsaturated cementitious materials based on multi-typed pore structure characteristics

This paper develops a novel lattice diffusive model to quantitatively study the chloride diffusion coefficient in unsaturated cementitious materials, in which the pore voxels are redistributed to make a better representation of a real microstructure of hardened cement paste. Considering the hierarchical microstructure and different drying-wetting cycles, water distributions in multiscale pore structures are modelled and the structure characteristics of water-filled pores, including water connectivity, water tortuosity and effective porosity, are computationally extracted based on that. A lattice diffusion network is established to predict relative chloride diffusion coefficient by combining the effect of both water saturation degree and pore structure characteristics. The predicted results are validated against experimental data, and a concise analytical equation is proposed to predict the relative chloride diffusion coefficient. The equation indicated that the relative chloride diffusion coefficient is proportional to water connectivity but inversely proportional to the square of water tortuosity. Besides, the lattice model's quantitative results reveal that the water connectivity and water tortuosity are highly related to pre-water loading processes, and influenced by the gel pore fraction, which in turn will affect the relative chloride diffusion coefficient. Compared with existing equations and non-redistributed models, the present model could improve the prediction accuracy significantly.

Study on the magnetic levitation of a magnetic flea

We investigated the problem of ‘magnetic levitation’ originating from the International Young Physicists’ Tournament (IYPT). The problem was first investigated by a PRL paper (Baldwin et al.) in 2018, which states that the flea of a magnetic stirrer spinning fast enough in a liquid with a high viscosity coefficient can jump from the bottom and levitate stably. The magnetic force and gravity balance periodically. This phenomenon includes several concepts: magnetic dipoles, rigid-body rotation, fluid mechanics and magnetic levitation. They are more or less unfamiliar to undergraduate students. However, the movement of the flea could be described with a concise forced vibration equation, which is familiar in textbooks. The phenomenon could be divided into two stages: synchronous movement and levitation state. The transition is the jumping of the flea. We demonstrated this process and presented several equations to build this physical model. The progression of the phenomenon is due to the increase in the drive magnet angular velocity called the drive velocity. We verified our theory by simulation and experiments. Several parameters are experimentally verified to influence the phenomenon. We also discussed the origin of dynamic stabilization, which would be slightly complicated but worthy for students. In short, we introduce an interesting problem originating from the PRL paper that can be easily achieved under laboratory conditions. We extend some content in a pedagogical way that would be helpful for students to understand the related physical concepts, such as the influence of the viscosity coefficient of the liquid on the flea’s motion, which is not discussed in the PRL paper.

Effects of stacking sequences on the axial compressive buckling behavior and failure characteristics of channel-section CFRP/Al laminate columns

Open-section composite profiles are often used as columns in civil engineering structures. Their thin-walled nature makes these sections prone to buckling phenomena when loaded in compression. This paper presents a study on the axial compressive performances and failure behavior of channel-section CFRP/Al laminate columns with two different stacking sequences. Typical mechanical responses and failure characteristics were first explored through experiments. Then the damage propagation mechanisms of the two kinds of columns were further compared based on a three-dimensional progressive damage model. The results indicated that column with CFRP layers stacked on the exterior surfaces exhibited smaller delaminated areas compared with the ones with aluminum alloy layers stacked exteriorly, thus resulting in the higher load-bearing capacities. Finally, a concise theoretical calculation equation for buckling load was derived, based on which further structural parametric analysis were performed.

Evaluation and characteristic analysis of compressive strength and resistivity of EG cement conductive mortar based upon hybrid-BP neural network

A concise general equation is difficult to reflect the relationship between physical properties of conductive materials and properties of conductive mortar (CM). To handle this issue, a back propagation neural network (BPNN) model with a topology of 4–10-2 was designed, which was further optimized with the Ant colony optimization (ACO), Genetic algorithm (GA) and Particle swarm optimization (PSO) algorithms. The models intended to establish non-linear relationships among the input layer parameters, viz., expanded graphite (EG), carbon fiber (CF), slag powder (SP), and fly ash (FA) contents, and the output layer parameters including the CM’s compressive strength and resistivity. A total of 112 groups of data points were used for model development, including 80 groups of training set data, and two series of 16 data groups for verification and testing. Influence of conductive materials on compressive strength and resistivity of CM was determined with a correlation analysis. Meanwhile, the importance and total scores of different proportions were analyzed by performing a principal component analysis on the dataset. It was found that both the EG and FA content were correlated negatively with the CM’s compressive strength and resistivity. In addition, the CF and SP contents were correlated positively with the CM’s compressive strength but negatively with resistivity. The order of the conductive substances’ importance in CM’s compressive strength and resistivity was EG > CF > SP > FA, and the group B-3 was determined as the best mix ratio. The PSO-BPNN model had the highest accuracy in predicting both the CM’s compressive strength and resistivity, which can provide guidance for mix design of CM.

Modelling for effects of surface chemical composition on contact angle and applications in membrane flux control

Surface wettability is related to the chemical composition of the surfaces; however, their mathematical connections are not well understood. An accurate and concise equation was derived to relate the contact angle and chemical composition of a composite surface, and subsequently verified by measuring the apparent water contact angle (WCA) on a special uniform surface with an increasing modification ratio. This surface was fabricated using the layer-by-layer method and modified using the ion exchange method. Excellent correlation (R2 = 0.9985) of the linear fit between the WCA cosine value and modification ratio verified the theoretical correlation. This conclusion was further applied to the study of membrane separation performance. The water flux of two cellulose membranes modified by chlorosulfonic acid had a good linear relationship (R2 = 0.9875) with the modification ratio. This result provides insight into precise wettability control, which is significant for the study of surfaces, membranes, and other fields.

A New Analytical Model for Predicting Steam-Assisted Gravity-Drainage Performance in the Plateau and Decline Stages

Summary Analytical models have been widely used to study the steam-assisted gravity-drainage (SAGD) process. Existing analytical models for this process either underperform or are limited in their applicability. In this paper, a new analytical model is developed to address these shortcomings. The new model consists of three major components. First, an equation for predicting oil production rate during the plateau stage was developed. This equation allows for permeability anisotropy in the reservoir, which is neglected in the majority of existing analytical models. Second, a novel and concise equation for calculating oil production rate during the decline stage was derived. This equation for the first time provides a general relationship between oil production rate during the decline stage and the properties of the reservoir together with key operating conditions and simultaneously mitigates the shortcomings of the majority of existing models (e.g., inapplicable in the decline stage of the SAGD process). Third, new correlations representing heat loss from the steam chamber to the overburden and heat transfer to oil-undepleted zone ahead of the chamber interface were derived; new predictive equations for estimating steam/oil ratio (SOR) in the plateau and decline stages of SAGD were obtained. The new model has been validated against a 2D scaled laboratory experiment and a set of field data. The results of this validation show that the new model predicts the oil production rate and SOR over the lifetime of an SAGD operation (excluding the short steam rise period) reasonably well. Predictions from the new model were also compared with several existing analytical models: The new model provided a closer match to actual measurements than other models. This robust model is grounded in more physics and incorporates reservoir geology and well operating conditions. It enables better understanding of the SAGD process and significantly improves the prediction of SAGD performance. Hence, it can be used to design new SAGD projects, predict existing projects, and optimize existing projects.

Central rebound jet of a droplet normal impact on a confined thin liquid film

The phenomenon of the impact of a droplet on a confined thin liquid film is encountered in a variety of industrial applications. Despite exhaustive research, the central rebound jet (CRJ) and its pinch-off are still far from being understood owing to their strong randomness and the uncertainty in secondary pinch-off droplet numbers. This study experimentally investigated the CRJ and its pinch-off formed by the normal impact of a single droplet on a confined thin liquid film. The dynamic evolution of CRJ formation along with its pinch-off is discussed for three typical Weber numbers (We). Its morphology (base diameter and height) was analyzed by focusing on the effects of We and film thickness on the formation mechanism for droplets, and a qualitative comparison of CRJ height with the previous results was made. The critical thresholds of the CRJ pinch-offs are characterized, and a novel concise prediction method was developed. The results show that the increase in the dome diameter is caused not only by the CRJ growth but also by its fallback. Its maximum value is positively correlated with the increase in We and film thickness. The pinch-off height of the CRJ column is characterized by the critical threshold of We (or K), decreasing with the increase in the film thickness. The maximum height of the CRJ increases with the increase in the Froude number (Fr) and shows a power function. An active region of the liquid film thickness taking a Gaussian normal distribution was found for CRJ formation and its pinch-off. The film thickness has a significant influence on the CRJ height in the active region, but little outside this region. A novel concise equation for predicting CRJ pinch-off and its droplet numbers was further obtained by a multiple inverse power-law function of We with Ohnesorge number (Oh), Re/Fr, and viscosity effects.

Analytic expressions for topologically protected edge states in Su–Schrieffer–Heeger model

The Su–Schrieffer–Heeger (SSH) model can demonstrate the topological phase transition of spinless fermions in a two-dimensional square lattice. In this work, we investigate the topologically protected edge states (TESs) in 1D SSH ribbons by using the wave mechanics approach. A concise analytic equation is derived to determine the localization length of TESs. Based on the resulted localization length, the explicit analytic expressions are given for the energy dispersions and wave functions of TESs in 1D SSH ribbons. The effect of the size of the 1D SSH ribbon on the topological phase transition and the critical exponent of the localization length of TESs are further demonstrated. It also shows that the degeneracy of TESs is lifted due to the coupling of the two-side TESs. Our results can elucidate the TESs appearing in nontrivial phase, and can also be employed to optimize the structure of the nanoribbon devices.

Defining, estimating, and understanding the fundamental niches of complex animals in heterogeneous environments

AbstractDuring the past century, the fundamental niche, the complete set of environments that allow an individual, population, or species to persist, has shaped ecological thinking. It is a crucial concept connecting population dynamics, spatial ecology, and evolutionary theory, and a prerequisite for predictive ecological models at a time of rapid environmental change. Yet, its properties have eluded quantification, particularly for mobile, cognitively complex organisms. These difficulties are mainly a result of the separation between niche theory and field data, and the dichotomy between environmental and geographical spaces. Here, I combine recent mathematical and statistical results linking habitats to population growth, to achieve a quantitative and intuitive understanding of the fundamental niches of animals. I trace the development of niche ideas from the early steps of ecology to their use in modern statistical and conservation practice. I examine how animal mobility and behavior may blur the division between geographical and environmental space. I discuss how the central models of population and spatial ecology lead to a concise mathematical equation for the fundamental niche of animals and demonstrate how fitness parameters can be understood and directly estimated by fitting this model simultaneously to data on population growth and spatial distributions. I first illustrate these concepts theoretically for territorial species. I then fit the fundamental niche model to a data set of house sparrow colonies to quantify how a species of selective animals can increase their fitness in heterogeneous environments. This work confirms ideas that had been anticipated in the historical niche literature. Specifically, within traditionally defined environmental spaces, habitat heterogeneity and behavioral plasticity make the fundamental niche more complex and malleable than was historically envisaged. However, once examined in higher‐dimensional environmental spaces, accounting for spatial heterogeneity, the niche is more predictable than recently suspected. This re‐evaluation quantifies how organisms might buffer themselves from change by bending the boundaries of viable environmental space and offers a framework for designing optimal habitat interventions to protect biodiversity or obstruct invasive species. It therefore promotes the fundamental niche as a key concept for understanding animal responses to changing environments and a central tool for environmental management.

Udwadia-Kalaba approach based distributed consensus control for multi-mobile robot systems with communication delays

In this paper, a distributed consensus algorithm for multi-mobile robot systems (MMRSs) with communication delays is proposed based on the Udwadia-Kalaba (UK) approach. The key feature of the proposed algorithm is that the consensus requirement is configured as a second-order constraint, and then a concise and explicit equation of motion for the constrained mechanical systems is formulated. Furthermore, the necessary and sufficient conditions for achieving the consensus of MMRSs with or without communication delays are developed under the network topology possessing a directed spanning tree. Finally, some numerical simulations are performed to verify the validity of the proposed consensus algorithm.

A Trident Quaternion Framework for Inertial-Based Navigation Part I: Rigid Motion Representation and Computation

Strapdown inertial navigation research involves the parameterization and computation of the attitude, velocity, and position of a rigid body in a chosen reference frame. The community has long devoted to finding the most concise and efficient representation for the strapdown inertial navigation system (INS). The current work is motivated by simplifying the existing dual quaternion representation of the kinematic model. This article proposes a compact and elegant representation of the body's attitude/velocity/position, with the aid of a devised trident quaternion tool, which is an extension of dual quaternions. And the position is accounted for by adding a second dual part to the dual quaternion. Eventually, the kinematics of the strapdown INS are cohesively unified in one concise differential equation, which bears the same form as the classical attitude quaternion differential equation. In addition, the numerical solution to this trident quaternion-based kinematic equation is dealt with the recently proposed functional iterative integration approach. Numerical results are provided to verify the analysis. The new representation not only provides an elegant kinematic form of inertial navigation, but gives birth to precision inertial navigation algorithm.

Comparison of dominant frequency attenuation of blasting vibration for different charge structures

Dominant frequency attenuation is a significant concern for frequency-based criteria of blasting vibration control. It is necessary to develop a concise and practical prediction equation describing dominant frequency attenuation. In this paper, a prediction equation of dominant frequency that accounts for primary parameters influencing the dominant frequency was proposed based on theoretical and dimensional analyses. Three blasting experiments were carried out in the Chiwan parking lot for collecting blasting vibration data used to conduct regression analysis of the proposed prediction equation. The fitting equations were further adopted to compare the reliability of three different types of dominant frequencies in the proposed equation and to explore the effects of different charge structures on the dominant frequency attenuation. The apparent frequency proved to be more reliable to express the attenuation law of the dominant frequency. The reliability and superiority of the proposed equation employing the apparent frequency were verified by comparison with the other five prediction equations. The smaller blasthole diameter or decoupling ratio leads to the higher initial value and corresponding faster attenuation of the dominant frequency. The blasthole diameter has a greater influence on the dominant frequency attenuation than the decoupling ratio does. Among the charge structures applied in the experiments, the charge structure with decoupling ratio of 1.5 and blasthole diameter of 48 mm results in the greatest initial value and corresponding fastest attenuation of the dominant frequency. • Prediction equation of dominant frequency attenuation in surface blasting. • Comparing attenuation laws using three different types of dominant frequencies. • Effects of blasthole diameter and decoupling ratio on attenuation characteristics.

A Novel Computation Method for Tag Estimates in DFSA-based RFID Systems

In this paper, we propose a novel computation method for tag estimation in the dynamic framed slotted ALOHA (DFSA) protocol, based on Vogt’s estimate (VE). The estimation target is system load λ and tag estimate N̂ is computed from the estimated values of λ, instead of the direct approach taken in the existing method. Starting from the definition of VE, we derive a single concise equation for the estimate. For the numerical solution, we present a load estimation algorithm, which turns out to be computationally very efficient. The computational complexity is roughly O(10 log<SUB>10</SUB> N<SUB>max</SUB>), in contrast to O(N<SUB>max</SUB>) in the existing method for maximum possible number of tags, N<SUB>max</SUB>. Through computer simulations, we show that the proposed method indeed yields estimation results almost identical to those by the existing method in most cases.

Improvement of the Theis unsteady well flow model with infiltration recharge in a phreatic aquifer

The recharge and discharge of groundwater are mainly vertical surface infiltration recharge, evaporation discharge (evaporation can be shown as negative value of infiltration) and lateral surface water recharge and discharge. One of the most basic problems in hydrogeology is the evaluation criteria of sustainable exploitation of groundwater, which involves the increment of recharge and the decrease of discharge. Therefore, the prediction model of groundwater exploitation must include the above two kinds of recharge and discharge factors, otherwise the evaluation of groundwater cannot meet the requirements. However, the classic Theis unsteady well flow model (1935) only involves the recharge and discharge of the side boundary, and does not considers the surface infiltration recharge of the upper boundary, even when groundwater is pumped near the river. In this way, the analytical model cannot be basically used for prediction, and can only be used for well flow test to obtain the aquifer parameters in dry season. Therefore, the goal of this paper is to develop the Theis unsteady well flow model with surface infiltration recharge. For the problem of phreatic flow, the equation of groundwater flow cannot be established by using head as the dependent variable in a confined aquifer. We use the potential function of the second linearization method to establish groundwater flow equation in the phreatic aquifer. For the solution of the generalized mathematical model of the complex hydrogeological problem with rainfall infiltration and a pumping well, we adopt the method of decomposing it into several simple sub-models and synthesizing them into the solution of the original complex mathematical model. Based on the principle of mass conservation and assuming that the seepage obeys the Darcy’s law and satisfies the Dupuit's assumptions, the differential equation of groundwater flow is established. Then, for the well flow problem with uniform and stable infiltration recharge in two parallel rivers and two kinds of strip regions formed by a river parallel to an impermeable boundary, the general equation of groundwater flow and several kinds of water table equations under specific conditions and their flux equations are obtained. In addition, the “boundary to boundary reflection method” is proposed and applied to solve the same problem in a strip of region between a river boundary in parallel to an impermeable boundary, which reduces many derivation processes. Finally, as a preliminary application of the above theoretical results, it is also an important application, that is, there is a pumping well near the river whose water quality cannot meet the requirements, and the critical flux equation of the pumping well is calculated on the premise of not absorbing the river water. The important and concise relation equation is obtained. The equation can also be used to calculate the critical pumping rate of pumping wells in coastal areas without seawater intrusion. In this paper, the groundwater flow network diagram at a certain time in the process of unstable well flow under the above conditions is given. Compared with the flow network of well flow near the river, which is commonly seen in the literature, the flow network has obvious characteristics.

Fuzzy sliding mode variable structure control of a high-speed parallel PnP robot

This paper presents the analysis and experimental evaluation of robot dynamics and control for a four-limb parallel Schönflies-motion generator dedicating to fast pick-and-place operations, with a different topological architecture from its counterparts for efficient use of shop-floor space. The concise equation of motion is built with principle of virtual work to characterize the robot dynamics, which is integrated into the model-based control design. Fuzzy sliding mode variable structure control is adopted for the design of control scheme, aiming at buffeting suppression of the actuated joints and minimization of pose errors of robot end-effector. Numerical simulations are carried out along a trajectory of an industrial standard testing cycle to evaluate the performance, which is validated experientially by observing the joint dynamics. The results show the effectiveness of the developed dynamic control scheme for fast parallel pick-and-place robots.