Uniform Assumption Research Articles

The influence of the winding and the meridian section of the core on the magnetic moment of the electromagnet

The problem arising in the design of DC electromagnets, which is associated with the limitation of the application of the known methods for calculating the magnetic moment of an electromagnet, is described. The influence of the nonuniformity of the external magnetic field of the magnetizing coil on the magnetic moment of an electromagnet is analyzed to determine the limits of applicability of the assumption of uniformity of the external magnetic field. For this purpose, an iterative algorithm was used to numerically solve the integral equation for the surface density of fictitious magnetic charges on the surfaces of cylindrical elements of the core, considering the nonuniformity of the external magnetic field. It is established that the main cause of the discrepancy between the magnetic moment of the core of the electromagnet and the core, located in a uniform magnetic field, is the degree of nonuniformity of the external magnetic field of the coil, as well as the section of the magnetization curve, which corresponds the strength of the resulting magnetic field for the dominant part of the core. It is indicated that the region of application of the assumption of uniformity of the external magnetic field is limited by a relative core length and level of an external field. The influence of the shape of the meridian section of the core on the magnetic moment of the electromagnet is investigated. For core with washers, an iterative algorithm was used with a partitioning of the core medium into both cylindrical and ring elements to account for the additional edge effect due to the presence of washers. The results of the calculation have shown that their presence makes a significant contribution to the magnetic moment of the electromagnet, sometimes giving growth twice, and the level of contribution depends on the position and size of the washers, as well as on which section of the magnetization curve is the strength of the resulting magnetic field for most of the core in the absence of washers. It is shown that with increasing washer radius and a decrease of the distance from the washer to the ends the magnetic moment of the electromagnet increases, which is more pronounced for short cores and less pronounced for long cores .

Significance of non-uniform scour on the seismic performance of bridges

Multiple hazards such as flood-induced scour followed by earthquakes can adversely impact the performance of bridges spanning over waterways. Scour is the erosion of soil around the foundation of bridges, which can result in loss of the structure’s lateral support and possible failure. The impact is specifically amplified when a flood event resulting in the development of a scour hole is followed by an earthquake event. Recent inspections have shown a non-uniformity in the scour depths at bridge foundations with multiple piers. More specifically, the upstream and downstream pier foundations are exposed to notably different scour depths. However, the practice falls short in capturing this effect as commonly, a uniform scour depth is assumed at all bridge foundations in the water stream when evaluating the lateral stability of the structure. A comparative case is used to identify the unintended consequences of uniform local scour depth assumption for bridges with multiple columns in the direction of flow. This analysis considers bridges with both uniform and non-uniform scour depth at the support foundations. The effects of variable scour depths on the behaviour of bridge components are evaluated by tracking the demand redistribution as the scour depth changes. The results help to understand the performance of bridges crossing waterways when they are subjected to multi-hazard effects from flood-induced scour and earthquakes.

On Linear Convergence of Non-Euclidean Gradient Methods without Strong Convexity and Lipschitz Gradient Continuity

The gradient method is well known to globally converge linearly when the objective function is strongly convex and admits a Lipschitz continuous gradient. In many applications, both assumptions are often too stringent, precluding the use of gradient methods. In the early 1960s, after the amazing breakthrough of Łojasiewicz on gradient inequalities, it was observed that uniform convexity assumptions could be relaxed and replaced by these inequalities. On the other hand, very recently, it has been shown that the Lipschitz gradient continuity can be lifted and replaced by a class of functions satisfying a non-Euclidean descent property expressed in terms of a Bregman distance. In this note, we combine these two ideas to introduce a class of non-Euclidean gradient-like inequalities, allowing to prove linear convergence of a Bregman gradient method for nonconvex minimization, even when neither strong convexity nor Lipschitz gradient continuity holds.

Linear collective collocation approximation for parametric and stochastic elliptic PDEs

Consider the parametric elliptic problem where is a bounded Lipschitz domain, , , and the diffusion coefficients satisfy the uniform ellipticity assumption and are affinely dependent on . The parameter can be interpreted as either a deterministic or a random variable. A central question to be studied is as follows. Assume that there is a sequence of approximations with a certain error convergence rate in the energy norm of the space for the nonparametric problem at every point . Then under what assumptions does this sequence induce a sequence of approximations with the same error convergence rate for the parametric elliptic problem in the norm of the Bochner spaces ? We have solved this question using linear collective collocation methods, based on Lagrange polynomial interpolation on the parametric domain . Under very mild conditions, we show that these approximation methods give the same error convergence rate as for the nonparametric elliptic problem. In this sense the curse of dimensionality is broken by linear methods. Bibliography: 22 titles.

Non-Iterative Subspace-Based DOA Estimation in the Presence of Nonuniform Noise

The uniform white noise assumption is one of the basic assumptions in most of the existing directional-of-arrival (DOA) estimation methods. In many applications, however, the non-uniform white noise model is more adequate. Then the noise variances at different sensors have to be also estimated as nuisance parameters while estimating DOAs. In this letter, different from the existing iterative methods that address the problem of non-uniform noise, a non-iterative two-phase subspace-based DOA estimation method is proposed. The first phase of the method is based on estimating the noise subspace via eigendecomposition (ED) of some properly designed matrix and it avoids estimating the noise covariance matrix. In the second phase, the results achieved in the first phase are used to estimate the noise covariance matrix, followed by estimating the noise subspace via generalized ED. Since the proposed method estimates DOAs in a non-iterative manner, it is computationally more efficient and has no convergence issues as compared to the existing methods. Simulation results demonstrate better performance of the proposed method as compared to other existing state-of-the-art methods.

Closed-form equation for subsidence due to fluid production from a cylindrical confined aquifer

Ground surface subsidence due to groundwater production is a significant problem. Many attempts have been made to develop analytical models to forecast subsidence rates as a consequence of groundwater production. Previous analytical solutions either make limiting assumptions about the stress regime (e.g., radially symmetric with uniaxial strain or radially symmetric with zero incremental vertical total stress) or assume that the pressure distribution within the aquifer is uniform. Imposing assumptions about the stress regime lead to an overestimate of subsidence. Imposing a uniform pressure assumption often leads to an underestimate of subsidence. In this article, the principle of superposition is applied to extend a previous analytical solution, for a cylindrical uniform pressure change, to allow for a non-uniform pressure distribution resulting from constant rate production of a viscous fluid from a cylindrical confined aquifer of finite permeability. Results from the analytical solution are verified by comparison with a set of fully coupled hydro-mechanical finite element simulations. The analytical solution for subsidence directly above the production well (or uplift above an injection well) can be written in closed-form and is straightforward to evaluate. The equation also shows that, for many practical purposes, ground surface subsidence is insensitive to production fluid viscosity and aquifer permeability when the aquifer radius is less than the aquifer depth below the ground surface.

Cooperative Semiglobal Robust Output Regulation of Non-Introspective Nonlinear Agents With Partial Normal Form and State-Dependent High-Frequency Gain

This paper investigates cooperative semig-lobal robust output regulation problem for a class of non-introspective nonlinear multiagent systems. Each agent of this class is allowed to have a partial normal form , instead of only the conventional normal form, with a state-dependent high-frequency gain. Besides, all agents are unaccessible to the controller states of their neighbors. In this setting, if the uniform detectability assumption in the sense of [25] is satisfied, then a robust distributed regulator can be designed with the employment of a distributed nonlinear internal model and a novel distributed extended lower-power high-gain observer, such that the numerical implementation problem is solved and the regulated output of each agent asymptotically converges to the desired reference input robustly with guaranteed domain attraction.

BER Analysis of Interference-Limited Synchronous Wireless Networks With Line-of-Sight Links

The bit error rate (BER) of a Rician-faded and interference-limited synchronous wireless network with binary phase shift keying (BPSK) modulation is investigated. The probability density function (PDF) of the phase of the Rician-faded channel is unwieldy. However, the phase of the Rician-faded channel given the magnitude follows Von Mises distribution. This conditional PDF is exploited to derive an accurate expression for the BER of BPSK-modulated signals with an interference ignorant detector. Moreover, if either the desired signal or the interfering signal is Rayleigh-faded, the BER expression based on the uniform distribution assumption for the phase difference in decision statistic is shown to be accurate.

Numerical investigations of the accuracy of conductivity wire-mesh sensors

The wire-mesh sensor (WMS) is a promising instrumentation for two-phase flows investigation. Since the WMS is a kind of intrusive sensor, some researchers have focused on its intrusive effects on the measurement results. However, apart from the intrusive effects, the uniform sensitive volume assumption also brings a systematic error. For a WMS, it is assumed that there is a linear relationship between the current received by the receiver wire and the void fraction within a square sensitive volume, of which the side length equals to the lateral distance between two adjacent wires. Since the complexity of the potential field, the uniform sensitive volume assumption brings a systematic error. In order to evaluate this systematic error, a cuboid with zero conductivity was introduced in 9 × 9 WMS potential field simulations. The results indicate that the systematic error caused by the uniform sensitive volume assumption increases in the wire plane axial distance. The wire diameter has little effects on the measurements. However, in view of eliminating the intrusive effects, the wire diameter should be as small as possible. The phenomena of over-shoots and cross-talk, which can be observed in experiments, were explained by the potential field simulation results. With the wire plane axial distance increase, the over-shoots and cross-talk will be exacerbated. Even though the over-shoots and cross-talk can cause a deviation for local void fraction measurements, they would not cause any systematic error for sectional average void fraction measurements in a square cross-section.

Predicting Wave‐Induced Sediment Resuspension at the Perimeter of Lakes Using a Steady‐State Spectral Wave Model

AbstractA steady‐state spectral wave model, STWAVE, is evaluated as a tool for predicting wave‐induced sediment resuspension in lake littoral zones. Steady‐state wave height and bed‐shear stress estimates are tested against 2 years of high‐frequency wave height and turbidity data from six littoral measurement stations in Lake Tahoe. Average wave and sediment resuspension response to a broad range of wind conditions are well captured by the model. Despite steady‐state assumptions, the model reproduces patterns in wave height and sediment resuspension under time‐varying wind conditions at sites with different wave exposure. Model results are insensitive to the measurement location of wind data input among six offshore meteorological buoys. Uniform and variable wind field assumptions yield similar resuspension predictions. Results representing the steady‐state response to spatially uniform wind speed‐direction combinations enable output from a single set of model runs to serve as a reasonable static reference for hindcasting and predicting wave resuspension patterns. This obviates the need for repeated model runs, making STWAVE output an efficient tool for exploring long‐term spatio‐temporal patterns in nearshore wave forcing. Application of this tool is limited by wave height overprediction for short fetches and presumably by the validity of uniform wind field assumptions over very long fetches. Applied successfully at Lake Tahoe, we find that the north and east shores, exposed to the prevailing southwesterly winds, see resuspension conditions upward of 3,000 hr/year, while the south and west shores typically see less than 500. Location‐specific resuspension hours can vary by upward of ±200 hr/year due to shifting interannual wind patterns.

Cubature on Wiener space for McKean–Vlasov SDEs with smooth scalar interaction

We present two cubature on Wiener space algorithms for the numerical solution of McKean–Vlasov SDEs with smooth scalar interaction. First, we consider a method introduced in [Stochastic Process. Appl. 125 (2015) 2206–2255] under a uniformly elliptic assumption and extend the analysis to a uniform strong Hormander assumption. Then we introduce a new method based on Lagrange polynomial interpolation. The analysis hinges on sharp gradient to time-inhomogeneous parabolic PDEs bounds. These bounds may be of independent interest. They extend the classical results of Kusuoka and Stroock [J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 32 (1985) 1–76] and Kusuoka [J. Math. Sci. Univ. Tokyo 10 (2003) 261–277] further developed in [J. Funct. Anal. 263 (2012) 3024–3101; J. Funct. Anal. 268 (2015) 1928–1971; Cubature Methods and Applications (2013), Springer, Cham] and, more recently, in [Probab. Theory Related Fields 171 (2016) 97–148]. Both algorithms are tested through two numerical examples.

Refining constitutive relation by integration of finite element simulations and Gleeble experiments

Thermo-mechanical coupled finite element calculations were carried out to simulate the Gleeble compression of the samples of a titanium alloy (Ti60), and the results are analyzed and compared with the actual compression tests conducted on a Gleeble 3800 thermo-mechanical simulator. The changes in temperature, stress and strain distribution in the samples and the source of error on the constitutive relations from Gleeble hot compression test were analyzed in detail. Both simulations and experiments showed that the temperature distribution in the specimen is not uniform during hot compression, resulting in significant deformation inhomogeneity and non-ignorable error in the flow stress strain relation, invalidating the uniform strain assumption commonly assumed when extracting the constitutive relation from Gleeble tests. Based on the finite element simulations with iterative corrections, we propose a scheme to refine the constitutive relations from Gleeble tests.

Equivalent deformation modulus of sandy pebble soil-Mathematical derivation and numerical simulation.

This study aims to investigate the mechanical properties of sandy pebble soil through theoretical deduction and finite element analysis. Based on the assumption of stress uniformity or strain uniformity, the analytical formulas for calculating the equivalent deformation modulus of pebble soil are derived through RVEs. To verify the accuracy of the formulas, a series of numerical experiments are conducted through ABAQUS. Results show that theoretical calculation values match numerical simulation results well and the analytical formulas are effective when the pebble content is 0-60%. For pebble content lower than 20%, the equivalent deformation modulus could be described by "Stress Uniformity Model". When content is 20%-60%, pebble soil is a transition state from "Stress Uniformity" to "Strain Uniformity", for which the constitutive model could be expressed as a modified transition formula. This research is helpful for further investigation of mechanical properties of pebble soil. The theories developed in this study can be used in determining shield excavation parameters, and predicting the ground settlement caused by shield excavation.

Application of non-uniform film thickness concept in predicting deviated gas wells liquid loading

Liquid loading causes undesirable occurrences such as premature death of wells, as well as significant reduction in production. However, most available models consider vertical wells and only a few focus on deviated gas wells. In order to reduce the impact of liquid loading on gas production, gas well load-up should be diagnosed at its early stage so as to proffer adequate solution. Unfortunately, most gas wells will experience liquid loading at some stage or point in their production life. Therefore, it is of utmost importance to predict liquid loading at the early life of such wells in order to develop apt liquid management strategies as corrective measures. Liquid film flow reversal concept has been identified as one of the major concepts responsible for the occurrence of liquid loading in deviated gas wells. This study develops an improvement on Chen’s liquid loading model. The model specifically introduces the concept of non-uniform film thickness around the pipe wall, as against previous works which considered uniform film thickness. A modified friction factor is also introduced to account for large film thicknesses around the pipe wall. Results from the model were compared with those of previous models, and data from published literature was used to validate the new model. The new model gave accurate predictions for 11 of 12 unloaded wells while for the loaded wells, the estimated data gave accuracies for 29 out of 30 loaded wells. This then implies that the new model is accurate for predicting liquid loading in deviated gas wells.•Predictions from the new model show a good improvement over existing models.•The uniform film assumption made in Chen liquid loading model was modified, and a different interfacial friction factor was applied.•The method proposed in this study introduces the concept of non-uniform film thickness around the pipe wall as against previous works which considered uniform film thickness.

Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chi-squared. These asymptotic results are derived using existing asymptotic results for likelihood estimates of the unmarked Hawkes process model together with mild additional conditions on the moments and ergodicity of the marks process and an additional uniform boundedness assumption, shown to be true for the exponential decay Hawkes process.

Heat and Mass Transport in Modeling Membrane Distillation Configurations: A Review

Identification and mitigation of challenges associated with membrane distillation (MD) modeling are very crucial to the applicability of MD technology in the industry. Several research studies have been carried out on direct contact membrane distillation (DCMD) modeling because of its simplicity, while other MD configurations have gained little attention. Most studies conducted on MD modeling were achieved based on uniform membrane pore size and pore size distribution assumption. This study exploits the homogeneity of these assumptions to conduct a modeling review for temperature polarization (TP) and concentration polarization (CP), as they apply to MD configurations. TP and CP phenomena have been identified as two of the main challenges to advance MD modeling for further development of MD technology. Their impact is detailed in the heat and mass transfer mechanisms discussed. Thermal conductivity of common hydrophobic commercial membrane materials at different temperatures are presented in this study. The use of optimal operating flow rate, suitable membranes and proper module design are recommended as viable solutions to reduce the effects of TP and CP on permeate flux decay.

Real-Time Prediction of Lane-Based Queue Lengths for Signalized Intersections

Queue length is one of the most important traffic evaluation indexes for traffic signal control at signalized intersections. Most previous studies have focused on estimating queue length, which cannot be predicted effectively. In this paper, we applied the Lighthill–Whitham–Richards shockwave theory and Robertson’s platoon dispersion model to predict the arrival of vehicles in advance at intervals of 5 seconds. This approach fully described the relationship between disparate upstream traffic arrivals (as a result of vehicles making different turns) and the variation of incremental queue accumulation. It also addressed the shortcomings of the uniform arrival assumption in previous research. In addition, to predict the queue length of multiple lanes at the same time, we integrated the prediction of the traffic volume proportions in each lane using the Kalman filter. We tested this model in a field experiment, and the results showed that the model had satisfactory accuracy. We also discussed the limitations of the proposed model in this paper.

Reliability and Failure Analysis of Jet Vane TVC System

Structural and system reliability of a typical jet vane (JV) thrust vector control (TVC) subsystem subjected to stochastic loadings is investigated. Jet vane TVC (JVTVC) is used in many aerospace liquid and solid propulsion systems. For the purpose of this work, JVTVC structural reliability of a solid rocket propulsion system is computed using an explicit closed-form limit state function. The JV structure is influenced by the internal ballistic loads emanating out of the solid rocket propulsion internal ballistic, whose performance is modeled via a one-dimensional uniform flow assumption at the engine steady operating condition. Subsequently, JV structural reliability is predicted using the methods of mean value first-order second-moment as well as the first- and second-order reliability methods. The reliability results of the analytical methods are compared with Monte Carlo simulation for verification purposes. Finally, a comprehensive sensitivity analysis is performed to identify the key JVTVC and solid rocket propulsion design parameters affecting the TVC total system reliability. The parameters considered for sensitivity analysis include the JV geometric and structural properties as well as the solid rocket propulsion ballistic and geometric features. It turned out that the vane support arm radius and the vane area are the most important strength and load design variables, respectively, that impact the JVTVC failure reliability.

Effect of the misorientation angle and anisotropy strength on the initial planar instability dynamics during solidification in a molten pool

The initial planar instability will appear with the solute accumulation ahead of the solid/liquid (S/L) interface during solidification in a molten pool. The instability process is dominated by the misorientation angle and the surface tension anisotropy strength, where the misorientation angle is the angle between the preferred crystalline orientation of base metal and the thermal gradient direction in front of the S/L interface. In this study, their effects on the initial planar instability during gas tungsten arc welding of an Al-alloy are investigated using a modified analytic model and a quantitative phase-field model, respectively. Specifically, we apply the uniform fluctuation spectrum assumption, Aω(0) = kBTM/{γ0[1 − 15γ4cos(4θ0)]ω2}, to represent the influence of thermal noise on S/L interface evolution. The incubation time, average wavelength and detailed interface morphology of the initial planar instability are investigated with varying surface tension anisotropies (determined by anisotropy strength γ4 and misorientation angle θ0). The results indicate that -γ4cos(4θ0) is a reasonable indicator for the effect of surface tension anisotropy on the initial planar instability. Moreover, rather than influencing solute diffusion, the surface tension anisotropy just affects the planar interface stability during the solidification. Finally, the experimental observations with the same welding parameters was carried out, which are in general agreement with the simulated results.

Coral Reef Island Initiation and Development Under Higher Than Present Sea Levels

AbstractCoral reef islands are considered to be among the most vulnerable environments to future sea level rise. However, emerging data suggest that different island types, in contrasting locations, have formed under different conditions in relation to past sea level. Uniform assumptions about reef island futures under sea level rise may thus be inappropriate. Using chronostratigraphic analysis from atoll rim islands (sand‐ and gravel‐based) in the southern Maldives, we show that while island building initiated at different times around the atoll (~2,800 and ~4,200 calibrated years before present at windward and leeward rim sites, respectively), higher than present sea levels and associated high‐energy wave events were actually critical to island initiation. Findings thus suggest that projected sea level rise and increases in the magnitude of distal high‐energy wave events could reactivate this process regime, which, if there is an appropriate sediment supply, may facilitate further vertical reef island building.