Arbitrary Distribution Research Articles

Three-dimensional thermoelastic analysis of functionally graded solids using a high-order staggered finite volume method

This paper has developed a 3D 2-order cell vertex finite volume method (CV-FVM) for thermoelastic problems of functionally graded materials (FGMs). The construction methods of 15-node triangular prismatic (P15) element and 20-node hexahedral (H20) element are proposed. The 10-node tetrahedral (T10) element is adopted together with P15 and H20 to deal with mixed element problems. Material variation is considered using the staggered grid technique by defining properties at the cell center while defining unknown variables at the node. This treatment makes the present method suitable for FGMs with arbitrary material distribution. The accuracy and capability of the 2-order CV-FVM are verified by numerical tests. The results show that all the T10 elements, P15 elements, H20 elements and 2-order mixed elements can provide accurate results. When the same mesh size is employed, 2-order CV-FVM could provide better numerical precision than the 1-order CV-FVM and H20 elements could provide more accurate results than T10 elements. Based on the same mesh size, the H20 element avoids numerical oscillations caused by the T10 element. The developed method exhibits advantages in analyzing materials with significant property changes, avoiding physically unrealistic stress distributions.

Forced and post-forced responses of multi-stepped composite cylindrical shell under general moving excitations

For the first time, this work presents a comprehensive analysis of the forced and post-forced vibration responses for the multi-stepped composite cylindrical shell (MSCCS) subjected to moving excitation with the general distribution. Based on the method of reverberation-ray matrix (MRRM) of the general connection conditions, the investigated structural system composed of several cylindrical shells having different lengths and thicknesses is modeled analytically by the inhomogeneous dynamic equations with introduced the continuous acting mechanism of the moving excitations precisely. In order to address the discontinuity problem of the moving excitation at the multi-stepped connections, a coupling technique involving the recombination of wave numbers and a matrix excitation coordinate transfer scheme is adopted. This approach allows for a flexible span of axial loading and arbitrary circumferential distribution. The verification results exhibit excellent accuracy for dealing with the transient responses under various moving excitations of the MSCCS. The novel parameters examples reveal that the post-forced vibration phenomenon can be eliminated within a certain parametric range instead of changing the load velocity. Furthermore, the thickness ratio, axial loading span and circumferential distribution also play an important role in the dynamic responses under moving excitations.

Time-domain computation of the reliability of standby systems with and without priority under general repair

In this paper, we consider a two-unit, non-identical cold standby system under general repair with or without priority. In the prioritized case, one unit in the system is designated to serve as standby only, that is, the standby unit is only utilized when the main unit has failed and is being repaired, whereas in the non-prioritized case, both units serve alternately as standby with each unit being put to standby mode when its repair is complete. The effect of each repair is modelled by a degree θ, 0≤θ≤1, where θ=0 means full repair (or full replacement) and θ=1 means minimal repair. For these cases, and for arbitrary distributions of the lifetimes and repair times of the units in the system, we obtain the reliability function in the time domain as opposed to the Laplace domain. Our functions utilize results from classical and generalized renewal theory results. We validated our formulas on various in-house standby configurations, as well as standby configurations occurring in coolant systems of nuclear power plants.

High fidelity laser beam shaping using liquid crystal on silicon spatial light modulators as diffractive neural networks

Spatial light modulators (SLMs) based on liquid crystal on silicon (LCoS) are powerful tools for laser beam shaping as they can be used to dynamically create almost arbitrary intensity distributions. However, laser beam shaping with LCoS-SLMs often suffers from beam shaping artifacts in part caused by unconsidered properties of the LCoS devices: astigmatism that stems from the non-normal incidence of the laser beam on the SLM and the effect commonly referred to as the ’0-th diffraction order’ that is caused by both the crosstalk between neighboring pixels and the direct reflection at the cover glass of the SLM. We here present a method to consider and compensate for these inherent properties of LCoS devices by treating the SLM as a diffractive neural network.

A strategy for fast evaluation of nonviscously damped systems with arbitrary kernels

In this work, a fast algorithm to evaluate the dynamic response of nonviscously damped systems with arbitrary distributions of damping characterised by arbitrary kernel functions (both number and form) is proposed. The proposed algorithm requires mere matrix–vector operations. It can be integrated into existing analysis tools with various time integration methods in forms of either element-based dashpots or global damping model. Compared to other existing methods, the proposed algorithm does not explicitly evaluate the convolution integral and thus does not require the storage of the whole velocity history. It shows superior accuracy while the corresponding computational cost is low.

Coupling multi-fluid dynamics equipped with Landau closures to the particle-in-cell method

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run times and often to set-ups of less than three spatial dimensions. Traditionally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-conserving multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell's equations. This avoids simplifications typically adopted for Ohm's law and enables us to fully resolve the electron temporal and spatial scales while retaining the versatility of initializing any number of ion, electron or neutral species with arbitrary velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison with linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays interacting with thermal plasmas over macroscopic time scales.

Mode-cleaning in antisymmetrically modulated non-Hermitian waveguides

Abstract We demonstrate all-optical spatial mode-cleaning in non-Hermitian waveguides. The effect is accounted by a unidirectional coupling among the modes resulting from a simultaneous modulation of the refractive index and the gain/loss along graded index multimodal waveguides. Depending on the spatial delay between the real and imaginary part of the potential modulation, higher or lower order modes are favored, which in latter case eventually leads to an nearly-monomode propagation. In this way, for any arbitrary initial field distribution an antisymmetric non-Hermitian modulation results in an effective mode-cleaning. The effect is demonstrated analytically, based on coupled mode theory in 1D waveguides, and numerically proven by solving the wave propagation equation with the antisymmetric non-Hermitian potential. The proposal is also generalized to the more involved case of 2D waveguides, leading to a significant reduction of the beam quality factor and improvement of beam spatial quality.

Cooperative Investment Problem With an Authoritative Risk Determined by Central Bank

In this paper, we are interested in providing an analytic solution for cooperative investment risk. We reformulate cooperative investment risk by writing dual representations for each risk preference (Coherent risk measure). Finding an analytic solution for this problem for both cases individual and cooperative investment by using dual representation for each risk preference has a strong effect on the financial market. In addition, we formulate a problem that covers the risk minimization with an expected return maximization problem with risk constraint, for the general case of an arbitrary joint distribution for the asset return under certain conditions and assuming that all coherent risk measure is continuous from below. Thus, the optimal portfolio is written as the optimal Lagrange multiplier associated with an equality-constrained dual problem. Furthermore, a unique equilibrium allocation as a fair optimal allocation solution in terms of equilibrium price density function for each agent is also shown.

Localization for random CMV matrices

We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.

Weibull-Fréchet distribution: A new lifetime distribution with application to gastric cancer data

Lifetime data is a type of data that consists of waiting time until an event occurs. Some of the events of lifetime data are deaths, occurrence of a disease, or failure of a machine. The distribution usually used for modeling lifetime data is the Weibull distribution. However, Weibull distribution has a limitation in its application: it can only model data with a monotonic hazard function. Therefore, a method for generalizing the Weibull distribution is needed so it can model data with a non-monotonic hazard function. One of those generalizations is the Weibull-Fréchet distribution (WFr) which was introduced by Afify in 2016. The WFr distribution has an advantage over the Weibull distribution, due to its capability in modeling data with unimodal hazard function. The method used in generating the WFr distribution is the Weibull-G (WG) that were introduced by Bourguignon in 2014. The WG method combines the distribution of a Weibull distribution with an arbitrary distribution with a cumulative distribution function (cdf) G(x) using a function W[G(x)]. The characteristics of WFr distribution discussed include probability density function (pdf), cumulative distribution function, survival function, hazard function, and the moment. The hazard function of WFr can be monotonic or unimodal. The maximum likelihood estimation method is used in estimating the parameters of the distribution. Finally, lifetime data of gastric cancer patients is given for illustration purposes. The data is modeled using the WFr distribution, and both the Weibull and Fréchet distribution for comparison. The model result shows that the WFr distribution is the best distribution for modeling the lifetime data of gastric cancer patients.

Higher-order random network models

Most existing random network models that describe complex systems in nature and society are developed through connections that indicate a binary relationship between two nodes. However, real-world networks are so complicated that we can only identify many critical hidden structural properties through higher-order structures such as network motifs. Here we propose a framework in which we define higher-order stubs, higher-order degrees, and generating functions for developing higher-order complex network models. Then we develop higher-order random networks with arbitrary higher-order degree distributions. The developed higher-order random networks share critical structural properties with real-world networks, but traditional connection-based random networks fail to exhibit these structural properties. For example, as opposed to connection-based random network models, the proposed higher-order random network models can generate networks with power-law higher-order degree distributions, right-skewed degree distributions, and high average clustering coefficients simultaneously. These properties are also observed on the Internet, the Amazon product co-purchasing network, and collaboration networks. Thus, the proposed higher-order random networks are necessary supplements to traditional connection-based random networks.

Message Transmission and Common Randomness Generation Over MIMO Slow Fading Channels With Arbitrary Channel State Distribution

Message Transmission and Common Randomness Generation Over MIMO Slow Fading Channels With Arbitrary Channel State Distribution

Space Charge Forces analytical model for emittance compensation

Space charge forces represent main induced effects in an RF-injector that degrade the beam quality. In this scenario the laser distribution sent on the photocathode acquires an important role in the emittance compensation process, as the slice analysis shows. Starting from the preliminary studies performed on [1], a novel semi-analytical model of space charge forces is proposed in detail for bunch with arbitrary charge distribution to derive expressions of self-induced forces. The performance of the fields at low energy regime (as the field has not expired RF forces) is under present analysis, we can investigate use of this model in low charge regime. Further, the model has been bench-marked with the behavior of the distributions present in the literature and studied for new ones. It has also been applied for the study of the optimization of a C-band hybrid photoinjector now being commissioned, thus explaining the factor two reduction of the emittance observed at the exit of the gun by changing the initial distribution at the cathode.

Arbitrary power distribution and efficiency optimization for dual-receiver inductive power transfer system with variable coupling

Arbitrary power distribution and efficiency optimization for dual-receiver inductive power transfer system with variable coupling

Optimal Management in the Operation of Complex Technical Systems

Developing a cost management system for a complex technical system (CTS) at the stages of its life cycle is a modern trend aimed at creating sustainable cooperation ties based on requirements, including those of manufacturers and consumers. The article explores the concept of a complex technical system. The principles and properties of a complex technical system were described. A model of a procedure for checking the operability of a complex technical system with an arbitrary distribution of the time of independent manifestation of a failure was proposed for the example of compressor station equipment. Models of operation of complex technical systems based on information about their state were considered. It was also shown how to optimize maintenance decisions for these systems in terms of the minimum average unit cost and how reliable this ensures. Additionally, proof of the existence of an optimal verification strategy was given. An algorithm for determining the moments of verification was developed to ensure the minimum cost. The methods of collecting, processing, and effectively using information for making decisions about the technical condition of complex products and the possibility of further exploitation were improved based on selecting informative diagnostic features and constructing models that comprehensively consider the maximum and current level of their parameters. This allowed for the quality of the final products to be ensured. The practical use of the proposed methods of diagnosis and forecasting made it possible to increase the actual CTS resource by 1.5–2.0 times. This also increased the productivity of the technological process by 1.6 times due to the reduction of the number of stops for maintenance for replacement, adjustments, and sub-adjustments. As a result, the value of the lack of basic production was reduced from 1.2 % to 0.8 %, and the cost of manufacturing products was decreased by 1.2–2.0 times.

Multi-Mode Vector Light Field Generation Using Modified Off-Axis Interferometric Holography and Liquid Crystal Spatial Light Modulators

The increasing enhancement in the modulation accuracy of spatial light modulators has garnered significant attention towards real-time control technology for light fields based on these modulators. It has been demonstrated that this technology possesses a remarkable capability to generate vector beams with arbitrary complex amplitude distributions. Nevertheless, past studies indicate that the generation of only one vector beam at a time has been observed. The simultaneous generation of numerous vector light fields can give rise to several challenges, including compromised picture quality, limited single-mode operation, and intricate optical path configurations. In pursuit of this objective, we present a novel methodology that integrates the coding methodology of modified off-axis interferometric holography with the idea of optical superposition. This technique facilitates the concurrent generation of several vector beams. In this study, we present a demonstration of the simultaneous creation of twelve vector beams using a single spatial light modulator (SLM) as a proof of concept. Significantly, this technology has the ability to generate an unlimited quantity of vector light fields concurrently under the assumption that the resolution of the SLM does not impose any limitations. The findings indicate that the imaging quality achieved by this technology is of a high standard. Furthermore, it is possible to separately control the beam waist radius, topological charge, polarization order, and extra phase of each beam.

De Sitter-eating O-planes in supercritical string theory

It has been proposed that flux compactifications of supercritical string theories (i.e., with spacetime dimension D > 10) have dS vacua, with large D acting as a control parameter for corrections to the classical spacetime effective action. In this paper, we provide a detailed analysis of the self-consistency of such models, focussing on α′ and backreaction corrections. We first show that all supercritical AdS, Minkowski and dS vacua in this setting have gtrsim mathcal{O}(1) curvature and/or field strengths in the string frame. This may be in tension with suppressing α′ corrections unless the coefficients of the higher-derivative terms have a sufficiently strong large-D suppression. We then argue that an additional and more severe problem arises in the dS case due to the backreaction of O-planes. In particular, we argue using a combination of geometric bounds and string-theory constraints that the O-plane backreaction is large in supercritical dS models. This implies that a large part of the naive classical geometry is eaten up by singular holes and thus indicates a breakdown of the classical description. Our finding resonates with several other recent results suggesting that string theory does not admit dS vacua in regimes where string and backreaction corrections are under control. As byproducts of our analysis, we derive a number of technical results that are useful beyond the specific applications in this paper. In particular, we compute the leading backreaction corrections to the smeared solution in a general flux compactification from D to d dimensions for an arbitrary distribution of O-planes and D-branes. We further argue for a general estimate for Green’s functions on compact manifolds (and therefore for the backreaction corrections) in terms of their diameter, volume and dimension.

Probabilistic Load Flow Analysis Using Nonparametric Distribution

In the pursuit of sustainable energy solutions, this research addresses the critical need for accurate probabilistic load flow (PLF) analysis in power systems. PLF analysis is an essential tool for estimating the statistical behavior of power systems under uncertainty. It plays a vital part in power system planning, operation, and dependability studies. To perform accurate PLF analysis, this article proposes a Kernel density estimation with adaptive bandwidth for probability density function (PDF) estimation of power injections from sustainable energy sources like solar and wind, reducing errors in PDF estimation. To reduce the computational burden, a Latin hypercube sampling approach was incorporated. Input random variables are modeled using kernel density estimation (KDE) in conjunction with Latin hypercube sampling (LHS) for probabilistic load flow (PLF) analysis. To test the proposed techniques, IEEE 14 and IEEE 118 bus systems are used. Two benchmark techniques, the Monte Carlo Simulation (MCS) method and Hamiltonian Monte Carlo (HMC), were set side by side for validation of results. The results illustrate that an adaptive bandwidth kernel density estimation with the Latin hypercube sampling (AKDE-LHS) method provides better performance in terms of precision and computational efficiency. The results also show that the suggested technique is more feasible in reducing errors, uncertainties, and computational time while depicting arbitrary distributions of photovoltaic and wind farms for probabilistic load flow analysis. It can be a potential solution to tackle challenges posed by sustainable energy sources in power systems.

Modeling and braking analyses of longitudinal-vertical coupling towbarless aircraft taxiing system

The variation of tire vertical load has effects on the vehicle braking performance, which may lead to the misjudgment of braking distance and increasement of the accident risks. In order to evaluate the braking distance of the towbarless aircraft taxiing system (TLATS) accurately, a longitudinal-vertical coupling model of the TLATS is established, in which the effects of the vertical vibration on braking dynamics is considered. An 11-degrees of freedom (DOF) dynamic model of the TLATS, which consists of the system longitudinal motion, vertical vibration, and an advanced Lugre tire model, is proposed. The tire vertical dynamic loads are obtained by calculating system vibration differential equations as the input for the Lugre tire model, in which an arbitrary pressure distribution function over the contact patch and load related parameters are used. The Lugre tire model parameters are identified based on the virtual experiment results in ADAMS/Car software through a multi-objective optimization (MOO) method. The proposed tire model is more accurate by comparing with the models using other pressure distribution functions. The advanced Lugre model is integrated into the longitudinal-vertical coupling dynamic model of the TLATS, and the fuzzy PID control method is used to achieve the optimal slip rate during the braking procedure. The tire friction and TLATS’s braking performances in terms of the slip rate, braking speed and braking distance are compared between the coupling and uncoupling models under different traction velocities and the road excitations when a same fuzzy control method is used for the system braking. The results show that the proposed longitudinal-vertical coupling TLATS dynamic model could assess the braking behaviors of the TLATS more accurately than the simplified uncoupling model, which could decrease the potential safety risk of the aircraft towing operation on the airport apron.

Utilizing Probabilistic Maps and Unscented-Kalman-Filtering-Based Sensor Fusion for Real-Time Monte Carlo Localization

An autonomous car must know where it is with high precision in order to maneuver safely and reliably in both urban and highway environments. Thus, in this paper, a reliable and relatively precise position estimation (localization) technique for autonomous vehicles is proposed and implemented. In dealing with the obtained sensory data or given knowledge about the vehicle’s surroundings, the proposed method takes a probabilistic approach. In this approach, the involved probability densities are expressed by keeping a collection of samples selected at random from them (Monte Carlo simulation). Consequently, this Monte Carlo sampling allows the resultant position estimates to be represented with any arbitrary distribution, not only a Gaussian one. The selected technique to implement this Monte-Carlo-based localization is Bayesian filtering with particle-based density representations (i.e., particle filters). The employed particle filter receives the surrounding object ranges from a carefully tuned Unscented Kalman Filter (UKF) that is used to fuse radar and lidar sensory readings. The sensory readings are used to detect pole-like static objects in the egocar’s surroundings and compare them to the ones that exist in a supplied detailed reference map that contains pole-like landmarks that are produced offline and extracted from a 3D lidar scan. Comprehensive simulation tests were conducted to evaluate the outcome of the proposed technique in both lateral and longitudinal localization. The results show that the proposed technique outperforms the other techniques in terms of smaller lateral and longitudinal mean position errors.