Closed-form Results Research Articles

Synchronous Inductor Switched Energy Extraction Circuits for Triboelectric Nanogenerator

Triboelectric nanogenerator (TENG), a class of mechanical to electrical energy transducers, has emerged as a promising solution to self-power Internet of Things (IoT) sensors, wearable electronics, etc. The use of synchronous switched energy extraction circuits (EECs) as an interface between TENG and battery load can deliver multi-fold energy gain over simple-minded Full Wave Rectification (FWR). This paper presents a detailed analysis of Parallel and Series Synchronous Switched Harvesting on Inductor (P-SSHI and S-SSHI) EECs to derive the energy delivered to the battery load and compare it with the standard FWR (a 3rd circuit) in a common analytical framework, under both realistic conditions, and also ideal conditions. Further, the optimal value of battery load to maximize output and upper bound beyond which charging is not feasible are derived for all the three considered circuits. These closed-form results derived with general TENG electrical parameters and first-order circuit non-idealities shed light on the physics of the modeling and guide the choice and design of EECs for any given TENG. The derived analytical results are verified against PSpice based simulation results as well as the experimentally measured values. In our experiments, P-SSHI and S-SSHI circuits are found to provide 1.18 and 8.59 fold per-cycle energy gain over the standard FWR circuit at 15 V battery load, respectively.

Distribution of random motion at renewal instants in three-dimensional space

In physics, chemistry, and mathematics, the process of Brownian motion is often identified with the Wiener process that has infinitesimal increments. Recently, many models of Brownian motion with finite velocity have been intensively studied. We consider one of such models, namely, a generalization of the Goldstein--Kac process to the three-dimensional case with the Erlang-2 and Maxwell--Boltzmann distributions of velocities alternations. Despite the importance of having a three-dimensional isotropic random model for the motion of Brownian particles, numerous research efforts did not lead to an expression for the probability of the distribution of the particle position, the motion of which is described by the three-dimensional telegraph process. The case where a particle carries out its movement along the directions determined by the vertices of a regular $n+1$-hedron in the $n$-dimensional space was studied in \cite{Samoilenko}, and closed-form results for the distribution of the particle position were obtained. Here, we obtain expressions for the distribution function of the norm of the vector that defines particle's position at renewal instants in semi-Markov cases of the Erlang-2 and Maxwell--Boltzmann distributions and study its properties. By knowing this distribution, we can determine the distribution of particle positions, since the motion of a particle is isotropic, i.e., the direction of its movement is uniformly distributed on the unit sphere in ${\mathbb R}^3$. Our results may be useful in studying the properties of an ideal gas.

Tangent second-order homogenisation estimates for incompressible hyperelastic composites with fibrous microstructures and anisotropic phases

This work presents new estimates for the effective mechanical response of composites with fibrous microstructures and hyperelastic, anisotropic, incompressible phases. The composites are two-phase materials consisting of aligned cylindrical fibres of circular cross section that are randomly distributed in the transverse plane of the matrix phase. The proposed homogenisation is based on the tangent second-order method proposed by Avazmohammadi and Ponte Castañeda (2013), which utilises variational principles and a suitably chosen “linear comparison material” to provide estimates for effective strain energies of nonlinear materials. To take into account the incompressibility of the fibre phase, we employed an appropriate asymptotic expansion of the fibre deformation field. By doing so, a constraint pressure is identified as the consistent limit of emerging indeterminate forms in the dilatational part of the fibre stress tensor. Furthermore, we performed an asymptotic analysis to obtain regular expressions of the underlying equations in the incompressible matrix limit. While we addressed the general case of incompressible and generally anisotropic phases, we put particular emphasis on composites with transversely isotropic phases whose symmetry axes are collinear with the fibre direction. For such materials, we derived estimates for the effective strain energies in terms of macroscopic strain invariants. In addition, for composites that are described by isotropic phase energies augmented with J4-invariant-based anisotropic terms, which is the case for many biological materials, we show that the anisotropic part of the energy can be easily homogenised by means of a simple Voigt-type average. Moreover, we present closed-form results for composites with isotropic Neo-Hookean phases augmented by transversely isotropic energy contributions. Finally, it is shown that the new estimates correspond to certain exact results under longitudinal shear deformation and that they properly linearise for small strains by recovering the corresponding linear-elastic estimates.

Regge amplitudes in generalized fishnet and chiral fishnet theories

We extend the analysis of [1] to study the Regge trajectories of the Mellin amplitudes of the 0- and 1-magnon correlators of the generalized Fishnet theory in d dimensions and one type of correlators of chiral fishnet theory in 4 dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our d dimensional results reduce to previously known results in d = 4 for 0-magnon and 1-magnon. As a non-trivial check, we show that the results for 1-magnon correlator in d = 8, when evaluated using the exact techniques in [1, 2] are in perfect agreement with our d dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator leftlangle mathrm{Tr}left[{phi}_1left({x}_1right){phi}_1left({x}_2right)right]mathrm{Tr}left[{phi}_1^{dagger}left({x}_3right){phi}_1^{dagger}left({x}_4right)right]rightrangle using the techniques developed in this paper. Since this correlator has two couplings κ and ω, we have obtained closed-form results in the limit κ → 0, ω → 0 with κ/ω held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.

The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

Semi-analytical analysis of vibrations induced by a mass traversing a beam supported by a finite depth foundation with simplified shear resistance

In this paper the new semi-analytical solution for the moving mass problem on massless foundation, published by the author of this paper, is extended to account for inertial foundation modelled by a continuous homogeneous finite depth foundation with simplified shear resistance. Derivations are presented for infinite as well as finite homogeneous beams. Mode expansion method is used to solve the problem on finite beams, thus vibration modes, the corresponding orthogonality condition, reengagement of coupled equations to ensure significant calculation time savings are derived. Methods of integral transforms and contour integration are exploited to obtain the solution on infinite beams. Resulting vibrations are derived as a sum of the steady and unsteady harmonic vibrations and a transient contribution. The unsteady harmonic vibration is proven to be a useful indicator of unstable behaviour through the mass induced frequencies. Besides frequency lines also discontinuity lines are determined and their influence on the proximity of harmonic and full solutions is discussed. Even if the differences between these two versions are larger than for the massless foundation, it is shown that the harmonic solution provides a very good estimate of the full solution (in several cases perfect match is achieved) with the advantage to be obtainable by a simple evaluation of the derived closed-form results. Like for the massless foundation, also here, vibrations on infinite beams can be obtained on long finite beams with eliminated effect of its supports. All mentioned approaches are also validated by the finite element method.

Peristaltic Transport of a Casson Fluid in a Non-uniform Inclined Tube with Rosseland Approximation and Wall Properties

In this article, the peristaltic transport (PT) of Casson fluid (CF) in the presence of mass and heat transfer under the impacts of slip conditions and wall properties in a non-uniform inclined tube has been analyzed. Furthermore, the effects of Dufour and Soret numbers are also considered. The governing two-dimensional equations for the flow of non-Newtonian CF along with the mass and heat transfer are reformulated by the supposition of a long wavelength and a low Reynolds number. Analytic solutions are computed and outcomes are exhibited graphically to analyze the impact of the parameters emerging in the problem. It is shown that the velocity profile is enhanced with a rise in the Casson parameter. The fluid temperature enhances for enhanced values of thermal slip and source/sink parameter. A validity of closed-form results for the velocity of the fluid is made by comparing it with numerical outcomes computed by MATLAB through bvp4c and finite element method.

Superimposed Pilots are Beneficial for Mitigating Pilot Contamination in Cell-Free Massive MIMO

In this letter, we present the first study for uplink cell-free massive multi-input multi-output (MIMO) systems with superimposed pilots (SPs). Closed-form linear minimum mean square error (LMMSE) channel estimation and achievable spectral efficiency (SE) expressions with maximal ratio combining (MRC) receiver filters are derived. The tractability of the closed-form results facilitates analyzing the effects of key design system parameters, such as the number of mobile terminals (MTs), the power balance factor between pilot and data symbols, and the length of coherence interval. Several significant insights are attained by assuming that the introduced pilot interference can or cannot be perfectly canceled from received data symbols. All the theoretical results are corroborated by simulation experiments.

Optimal Mobile Computation Offloading with Hard Deadline Constraints

This paper considers mobile computation offloading where task completion times are subject to hard deadline constraints. Hard deadlines are difficult to meet in conventional computation offloading due to the stochastic nature of the wireless channels involved. Rather than using binary offload decisions, we permit concurrent remote and local job execution when it is needed to ensure task completion deadlines. The paper addresses this problem for homogeneous Markovian wireless channel models. An online energy-optimal computation offloading algorithm, OnOpt, is proposed. Its energy optimality is shown by constructing a time-dilated absorbing Markov process and applying dynamic programming. Closed form results are derived for general Markovian processes, and the Gilbert-Elliott channel model is used to show how the particular structure of the Markov chain can be exploited in computing optimal offload initiation times more efficiently. It is shown that job completion time probabilities can be computed recursively, which leads to a significant reduction in the computational complexity of OnOpt. The performance of the proposed algorithm is compared to three others, namely, Immediate Offloading, Channel Threshold, and Local Execution. Performance results show that the proposed algorithm can significantly improve mobile device energy consumption compared to the other approaches while guaranteeing hard task execution deadlines.

Finding the Exact Distribution of (Peak) Age of Information for Queues of PH/PH/1/1 and M/PH/1/2 Type

Bufferless and single-buffer queueing systems have recently been shown to be effective in coping with escalated Age of Information (AoI) figures arising in single-source status update systems with large buffers and FCFS scheduling. In this paper, for the single-source scenario, we propose a numerical algorithm for obtaining the exact distributions of both the AoI and the peak AoI (PAoI) in (i) the bufferless $PH/PH/1/1/P(p)$ queue with probabilistic preemption with preemption probability $p$, $0 \leq p \leq 1,$ and (ii) the single buffer $M/PH/1/2/R(r)$ queue with probabilistic replacement of the packet in the queue by the new arrival with replacement probability $r$, $0 \leq r \leq 1$. The proposed exact models are based on the well-established theory of Markov Fluid Queues (MFQ) and the numerical algorithms are matrix-analytical and they rely on numerically stable and efficient vector-matrix operations. Moreover, the obtained exact distributions are in matrix exponential form, making it amenable to calculate the tail probabilities and the associated moments straightforwardly. Firstly, we validate the accuracy of the proposed method with simulations, and for sume sub-cases, with existing closed-form results. We then comparatively study the AoI performance of the queueing systems of interest under varying traffic parameters.

Exact closed-form solutions for Lamb’s problem—II: a moving point load

SUMMARYIn this paper, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb’s problem. Starting with the integral solutions of Bakker et al., we followed the method developed by Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker et al., which confirms the correctness of our formulae. The solution obtained in this paper may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.

Importance-Aware Data Selection and Resource Allocation in Federated Edge Learning System

The implementation of artificial intelligence (AI) in wireless networks is becoming more and more popular because of the growing number of mobile devices and the availability of huge amount of data. However, directly transmitting data for centralized learning will cause long communication latency owing to the limited communication resource and may incur severe privacy issue as well. To address these issues, we consider the federated edge learning (FEEL) system in this paper and develop an importance-aware joint data selection and resource allocation algorithm to maximize the learning efficiency. Aiming at selecting important data for local training, we first analyze the relation between loss decay and gradient norm, which indicates that larger gradient norm generally leads to faster learning speed. Based on this, a learning efficiency maximization problem is formulated by jointly considering the communication resource allocation and data selection. The closed-form results for optimal communication resource allocation and data selection are both developed, where some insights are also highlighted. Furthermore, an optimal algorithm with low computational complexity is developed to obtain the optimal end-to-end latency in one training period. We show that the sample size should be set to its upper limit in order to maximize the learning performance. Finally, we conduct extensive experiments on three popular convolutional neural network (CNN) models. The results show that the proposed algorithm can effectively reduce the training latency and improve the learning accuracy as compared with some benchmark algorithms.

Non-orthogonal multiple access in cell-free massive MIMO networks

In this paper, we investigate the downlink performance of cell-free massive multi-input multi-output non-orthogonal multiple access (CF-mMIMO-NOMA) system with conjugate beamforming precoder and compare against the orthogonal multiple access (OMA) counterpart. A novel achievable closed-form spectral efficiency (SE) expression is derived, which characterizes the effects of the channel estimation error, pilot contamination, imperfect successive interference cancellation (SIC) operation, and power optimization technique. Then, motivated by the closed-form result, a sum-SE maximization algorithm with the sequential convex approximation (SCA) is proposed, subject to each AP power constraint and SIC power constraint. Numerical experiments indicate that the proposed sum-SE maximization algorithms have a fast converge rate, within about five iterations. In addition, compared with the full power control (FPC) scheme, our algorithms can significantly improve the achievable sum-SE. Moreover, NOMA outperforms OMA in many respects in the presence of the proposed algorithms.

Synthesis of Angle Arrays by the NDF of the Radiation Integral

Linear arrays have been well studied for their widespread applications, but they suffer from severe limitations in the scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its singular value decomposition and the number of degrees of freedom of the source according to its geometry. Then, a connection with the known closed-form results of the single line case is established. Next, for an angle geometry, the discussion of the point spread function reveals the condition to be achieved for an angle source to radiate identical beams with a coverage larger than the one of a single linear source with the same total length. Finally, we consider the power synthesis of identical focusing beams by linear arrays, arranged in an angle geometry, also including the effect of the element factor, without excitation constraints, so to show how possibly to drive the design of electrically large arrays by such an analytical approach.

Spatial-temporal hedging coordination in prefabricated housing production

This paper studies the spatial-temporal hedging coordination problem. In the prefabricated housing production, the heavy double handling cost is the major reason that causes profit loss of project manager. The spatial-temporal method is capable of mitigating this double handling cost by reducing assembly time uncertainty and on-site congestion probability substantially. However, adopting hedging methods adds extra cost and pressure to the adopters. To encourage the building contractor who makes the temporal hedging decision to choose a larger assembly time hedging (ATH) amount, a hedging effort-sharing (HES) mechanism is proposed. In this research, we built an analytical model to investigate how HES mechanism affects spatial-temporal hedging decisions, the performance of the building contractor, project manager as well as the whole supply chain. Three scenarios with fixed HES terms under decentralized setting are examined: (I) Nash model, (II) Building contractor led Stackelberg model, and (III) Project manager led Stackelberg model. Closed-form results regarding the optimal spatial-temporal hedging decisions are obtained. Besides, we derive the threshold of the HES terms, under which a win-win coordination can be achieved. Furthermore, an integrated setting with negotiable HES terms is explored. We derive the optimal values of HES terms, which incents the individual optimal spatial-temporal hedging decisions identical with that obtained in the centralized setting. By conducting numerical studies, it is found that a higher site congestion probability and a lower demand uncertainty encourage the project manager to share more ATH effort, while a lower unit ATH cost and higher site space hedging effort-sharing rate entice the building contractor to burden more ATH effort. Surprisingly, in the proposed HES mechanism, the building contractor's profit is increasing in site congestion probability and the project manager's profit increases in the demand uncertainty.

Extensible beam-like metastructures at the microscale: Theoretical and modified Hencky bar-chain modeling

Architected metastructures with beam-like shape configurations have demonstrated promising mechanical performance due to their corrugation-induced geometric nonlinearity. Extensibility of the metabeams caused by corrugation plays a role in the geometric nonlinearity, which, however, has been omitted in the literature. Motivated by investigating the influence of stretching (or shrinking) on the mechanical characteristics, this study analytically and numerically investigates the metabeams designed with different corrugation patterns. A new discretized model is developed to considers the extensibility of the metastructures by modifying the Hencky bar-chain method (HBM). A size-dependent (i.e., length scale factor l) analytical model is developed using the modified couple-stress theory and closed-form results are obtained. Good agreements are observed between the HBM and theoretical results. Parametric studies are conducted to investigate the influence of extensibility and length scale factor on the mechanical behavior the metabeams with the rhombille, cylindrical, hexagonal and basketweave corrugations. Optimal pattern ratio (i.e., pattern diameter-to-pattern gap ratio DpatWpat) and geometric ratio (i.e., width-to-thickness ratio Wt) are obtained by minimizing the self-weight of the patterned plates. The reported HBM accurately predict the mechanical behavior of extensible metabeams, which can be used to design plate-shaped advanced structures for applications requiring rigidity and well deformation recovery.

Shear-Thinning Fluid Flow in Variable-Aperture Channels

Non-Newtonian fluid flow in a single fracture is a 3-D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2-D. To capture the key interactions between fluid rheology and spatial heterogeneity, we adopt a simplified geometric model to describe the aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from an assigned aperture distribution. The flow rate is then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that is parallel/perpendicular to the channels; these two arrangements provide upper and lower bounds to the fracture conductance. The fluid rheology is described by the Prandtl–Eyring shear-thinning model. Novel closed-form results for the flow rate and hydraulic aperture are derived and discussed; different combinations of the parameters that describe the fluid rheology and the variability of the aperture field are considered. The flow rate values are very sensitive to the applied pressure gradient and to the shape of the distribution; in particular, more skewed distribution entails larger values of a dimensionless flow rate. Results for practical applications are compared with those valid for a power-law fluid and show the effects on the fracture flow rate of a shear stress plateau.

Hydrodynamics Interactions of Metachronal Waves on Particulate-Liquid Motion through a Ciliated Annulus: Application of Bio-Engineering in Blood Clotting and Endoscopy

This study deals with the mass transport phenomena on the particle-fluid motion through an annulus. The non-Newtonian fluid propagates through a ciliated annulus in the presence of two phenomenon, namely (i) endoscopy, and (ii) blood clot. The outer tube is ciliated. To examine the flow behavior we consider the bi-viscosity fluid model. The mathematical modeling has been formulated for small Reynolds number to examine the inertia free flow. The purpose of this assumption is that wavelength-to-diameter is maximal, and the pressure could be considerably uniform throughout the entire cross-section. The resulting equations are analytically solved, and exact solutions are given for particle- and fluid-phase profiles. Computational software Mathematica has been used to evaluate both the closed-form and numerical results. The graphical behavior across each parameter has been discussed in detail and presented with graphs. The trapping mechanism is also shown across each parameter. It is noticed clearly that particle volume fraction and the blood clot reveal converse behavior on fluid velocity; however, the velocity of the fluid reduced significantly when the fluid behaves as a Newtonian fluid. Schmidt and Soret numbers enhance the concentration mechanism. Furthermore, more pressure is required to pass the fluid when the blood clot appears.

Improving on transfer entropy-based network reconstruction using time-delays: Approach and validation

Transfer entropy constitutes a viable model-free tool to infer causal relationships between two dynamical systems from their time-series. In an information-theoretic sense, transfer entropy associates a cause-and-effect relationship with directed information transfer, such that one may improve the prediction of the future of a dynamical system from the history of another system. Recent studies have proposed the use of transfer entropy to reconstruct networks, but the inherent dyadic nature of this metric challenges the development of a robust approach that can discriminate direct from indirect interactions between nodes. In this paper, we seek to fill this methodological gap through the cogent integration of time-delays in the transfer entropy computation. By recognizing that information transfer in the network is bound by a finite speed, we relate the value of the time-delayed transfer entropy between two nodes to the number of walks between them. Upon this premise, we lay out the foundation of an alternative framework for network reconstruction, which we illustrate through closed-form results on three-node networks and numerically validate on larger networks, using examples of Boolean models and chaotic maps.

Virtual MISO with joint device relaying and beamforming in 5G networks

In this paper, a novel scheme is proposed in which mobile users organize a virtual multiple-input single-output (MISO) structure with the aid of relaying based on device to device (D2D) communication in a 5G cellular network. The performance of distributed quasi-orthogonal space–time code (D-QOSTC) based virtual MISO for the cooperation among four communication nodes is investigated. Error propagation in the second hop of relaying in decode and forward (DF) relaying protocols, is one of the main challenges of virtual MISO systems and it can be mitigated by the joint use of selection relaying and beamforming techniques. We propose a novel beamforming technique for removing the end to end inter-symbol interference (ISI) of D-QOSTC scheme. By means of our proposed scheme, even though we have error propagation in the second hop of relaying, without any loss in bandwidth or rate, the full diversity order can be achieved. Moreover, the performance of bit error rate (BER) with closed form result is analyzed and compared to the simulation results. The results exhibit that the theoretical BER curves coincide with the simulation ones and the system achieves full diversity order. The simulation results also indicate a significant gain in power efficiency for the optimal selection relaying and fixed relaying compared to conventional schemes.