Perturbation Analysis Techniques Research Articles

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

AbstractHigh-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant challenges in both statistics and computation. In this paper, we propose a tensor block model and the computationally efficient methods, high-order Lloyd algorithm (HLloyd), and high-order spectral clustering (HSC), for high-order clustering. The convergence guarantees and statistical optimality are established for the proposed procedure under a mild sub-Gaussian noise assumption. Under the Gaussian tensor block model, we completely characterise the statistical-computational trade-off for achieving high-order exact clustering based on three different signal-to-noise ratio regimes. The analysis relies on new techniques of high-order spectral perturbation analysis and a ‘singular-value-gap-free’ error bound in tensor estimation, which are substantially different from the matrix spectral analyses in the literature. Finally, we show the merits of the proposed procedures via extensive experiments on both synthetic and real datasets.

Neural Mechanism of Repeated Transcranial Magnetic Stimulation to Enhance Visual Working Memory in Elderly Individuals With Subjective Cognitive Decline.

Visual working memory (VWM), the core process inherent to many advanced cognitive processes, deteriorates with age. Elderly individuals usually experience defects in the processing of VWM. The dorsolateral prefrontal cortex is a key structure for the top-down control of working memory processes. Many studies have shown that repeated transcranial magnetic stimulation (rTMS) improves VWM by modulating the excitability of neurons in the target cortical region, though the underlying neural mechanism has not been clarified. Therefore, this study sought to assess the characteristics of brain memory function post-rTMS targeting the left dorsolateral prefrontal cortex. The study stimulated the left dorsolateral prefrontal cortex in elderly individuals by performing a high-frequency rTMS protocol and evaluated behavioral performance using cognitive tasks and a VWM task. Based on the simultaneously recorded electroencephalogram signals, event-related potential and event-related spectral perturbation analysis techniques were used to investigate the variation characteristics of event-related potential components' (N2PC and CDA) amplitudes and neural oscillations in elderly individuals to elucidate the effect of high-frequency rTMS. The results found that rTMS enhanced VWM performance and significantly improved attention and executive function in elderly individuals with subjective cognitive decline. We therefore speculate that rTMS enhances VWM by increasing the N2PC and CDA amplitude, alongside increasing β oscillation activity. This would improve the attention and allocation of resources in elderly individuals such as to improve an individual's VWM.

Phoretic self-propulsion of Janus disks in the fast-reaction limit

Using a combination of singular perturbation analysis and conformal mapping techniques, the self-propulsion velocity is found in the limit of fast reaction for a Janus particle with half of the boundary active and the other half inert.

Conflicting Aspects in the Flat Plate Boundary Layer Conventional Solution

The solution of the steady-state isothermal gas flow with zero-pressure gradient over a flat plate is classical and was presented by Blasius in 1908. Despite being reduced to a third-order Ordinary Differential Equation, nobody has solved it using just three boundary conditions. In consequence, the “solutions” (exact or numerical) are not unique, do not satisfy Prandtl’s boundary layer concept, and give rise to imprecise criteria of the boundary layer thickness definition (0.99.U∞, where U∞ is the free stream velocity) and to idealizations such as the displacement thickness, δ∗, and the momentum thickness, δI. Even though η, the similarity parameter, is defined as a function of x, it is surprising that it is seen as a constant, η∞, at the limit of the boundary layer, being valid for the entire plate. It is shown that uncountable “solutions” satisfying the classical equation and its three natural boundary layer conditions can be built. The reduction technique of the Boundary Value Problem, BVP, to an Initial Value Problem, IVP, and the Perturbation Analysis Technique, used as an attempt to incorporate a fourth boundary condition to the differential equation, are discussed. A more general and direct method to deduce the classical Blasius’s flat plate equation is considered, as one of the steps to rectify its solution, and shed light on the origin of the conflicting issues involved.

Investigation of toroidal rotation modulation and momentum transport with electrode biasing in J-TEXT tokamak

The toroidal rotation modulation and momentum transport have been investigated in the J-TEXT tokamak using a modulated electrode biasing (EB) along with measurements of the toroidal rotation (V ϕ ) by a spectrometer and a Langmuir-Mach probe array. The amplitude A v and phase delay ϕ v (relative to the phase of the biasing current, I EB) of the rotation modulation are extracted through sine-fitting approaches. It is found that the A v increases with increasing I EB and the ϕ v becomes larger when the modulation frequency increases. It has been estimated that the momentum transport time across a radial range from r/a ∼ 0.9 to 0.65 is about 10 ms, shorter than the half of modulation period (∼30 ms). Using the perturbation analysis technique, the toroidal momentum transport coefficients, including momentum diffusivity χ ϕ and convective velocity V conv, have been calculated and an inward pinch effect has been observed. In addition, the impact of the EB on the ion temperature and intrinsic rotation and the toroidal rotation difference between impurity and main ions are analyzed and discussed.

Online Measurement-Based Adaptive Scalable Video Transmission in Energy Harvesting Aided Wireless Systems

We consider the point-to-point adaptive transmission of scalable video coding streams over a fading channel in energy harvesting (EH) aided communication systems, where the transmitter is equipped with an EH device and a rechargeable battery. The aim of this paper is to enable the transmitter having the ability of adaptively adjusting the number of video layers to be transmitted according to the available energy. Since the depletion of the energy in the battery acts as a trigger for the interruption of the video transmission, we define the energy starvation probability for equivalently characterizing a quality-of-experience (QoE) metric. We formulate the problem of EH-aided video transmission as a constrained optimization problem, maximizing the number of video layers for transmission while keeping the energy starvation probability below a threshold. Classic large deviation theory is invoked for estimating the energy starvation probability from online measurements. Consequently, our dynamic layer switch algorithm operates with no prior statistical knowledge of both the EH process and of the channel quality. Furthermore, the technique of perturbation analysis that constructs a perturbed sample path from an original sample path is invoked for improving the performance of the proposed method. Our experimental results verify that the algorithms proposed have the adaptation capability to accommodate both the energy-dynamics and the channel-dynamics for improving the video quality subject to an unobjectionable level of transmission interruption rate.

Optimization of integrated preventive maintenance based on infinitesimal perturbation analysis

This paper considers jointly the production control and preventive maintenance problem in a manufacturing system. This system is composed of a single unreliable machine that produces one or two types of products with constant and different demand, a customer and a buffer between the machine and the customer. Machine failures are time-dependent, i.e. the machine can fail at any time, so a block-type preventive maintenance policy is proposed to increase the system life. This policy is coupled with a hedging point policy which controls the machine production speed. Between each element of the system, constant transportation delays are considered, i.e. a conveyor between the machine and its downstream buffer and a transport between the buffer and the customer. Then, a continuous-flow model is proposed to represent the overall dynamics of the system. This model allows us to take into account explicitly the transportation delays. The main objective of this work is to find the optimal preventive maintenance period by means of infinitesimal perturbation analysis technique as well as the optimal hedging point in order to minimize the expected average cost function. For this, we find the gradient estimators of the cost function from a theoretical sample path study. Then we integrate them in a simulation algorithm to find a numerical estimation of the solution. Simulation results highlight our theoretical results.

Design and validation of a sheet metal shearing experimental procedure

Throughout the industrial processes of sheet metal manufacturing and refining, shear cutting is widely used for its speed and cost advantages over competing cutting methods. Industrial shears may include some force measurement possibilities, but the force is most likely influenced by friction losses between shear tool and the point of measurement, and are in general not showing the actual force applied to the sheet. Well defined shears and accurate measurements of force and shear tool position are important for understanding the influence of shear parameters. Accurate experimental data are also necessary for calibration of numerical shear models. Here, a dedicated laboratory set-up with well defined geometry and movement in the shear, and high measurability in terms of force and geometry is designed, built and verified. Parameters important to the shear process are studied with perturbation analysis techniques and requirements on input parameter accuracy are formulated to meet experimental output demands. Input parameters in shearing are mostly geometric parameters, but also material properties and contact conditions. Based on the accuracy requirements, a symmetric experiment with internal balancing of forces is constructed to avoid guides and corresponding friction losses. Finally, the experimental procedure is validated through shearing of a medium grade steel. With the obtained experimental set-up performance, force changes as result of changes in studied input parameters are distinguishable down to a level of 1%.

An optimal inventory management problem with reputation-dependent demand

The paper addresses a problem of inventory control in a two-echelon retailer-customer setting. The problem incorporates the reputation of the retailer as a key factor influencing its policy. The retailer’s reputation depends on the degree to which past demand was satisfied. In turn, the reputation impacts the distribution of future demand. The optimality conditions developed by means of a perturbation analysis technique enable an optimal base-stock policy, in which the current level of base-stock depends on the retailer’s current reputation.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

SUMMARYDistributed network utility maximization (NUM) is receiving increasing interests for cross‐layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time‐varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. Copyright © 2013 John Wiley & Sons, Ltd.

Geolocation Performance With Biased Range Measurements

We study geolocation based on biased range estimates. Positive bias arises using time delay ranging methods in a multipath fading environment, when the line of sight direct path is severely attenuated. We model the range measurement as contaminated with Gaussian noise and an additive nonnegative bias term, and consider deterministic and random bias cases. We develop weighted least squares (WLS) and maximum likelihood (ML) geolocation estimators, and show that in general they yield biased geolocation estimates. A perturbation analysis technique is applied to find bias and mean square error (MSE) expressions for the WLS and MLE algorithms. MLE generally outperforms WLS, because MLE exploits knowledge of the range measurement bias distribution. The location error expressions are functions of the measurement bias and variance, as well as the network geometry. These results are useful to study achievable geolocation performance, and are applied to optimize sensor placement for improving the overall geolocation accuracy. We also develop the Cramér-Rao bound (CRB) on geolocation for our model. The CRB is a bound on unbiased estimation, whereas the geolocation algorithms may be biased, and we show how the estimators approach the CRB in certain cases. Numerical examples are presented to verify the analysis and study some cases of interest.

Using infinitesimal perturbation analysis of stochastic flow models to recover performance sensitivity estimates of discrete event systems

Stochastic Flow Models (SFMs) form a class of hybrid systems used as abstractions of complex Discrete Event Systems (DES) for the purpose of deriving performance sensitivity estimates through Infinitesimal Perturbation Analysis (IPA) techniques when these cannot be applied to the original DES. In this paper, we establish explicit connections between gradient estimators obtained through a SFM and those obtained in the underlying DES, thus providing analytical evidence for the effectiveness of these estimators which has so far been limited to empirical observations. We consider DES for which analytical expressions of IPA (or finite difference) estimators are available, specifically G/G/1 and G/G/1/K queueing systems. In the case of the G/G/1 system, we show that, when evaluated on the same sample path of the underlying DES, the IPA gradient estimators of states, event times, and various performance metrics derived through SFMs are, under certain conditions, the same as those of the associated DES or their expected values are asymptotically the same under large traffic rates. For G/G/1/K systems without and with feedback, we show that SFM-based derivative estimates capture basic properties of finite difference estimates evaluated on a sample path of the underlying DES.

Supply Performance in Multi-Echelon Inventory Systems with Intermediate Product Demand: A Perspective on Allocation

In this article, we study the performance of multi-echelon inventory systems with intermediate, external product demand in one or more upper echelons. This type of problem is of general interest in inventory theory and of particular importance in supply chain systems with both end-product demand and spare parts (subassemblies) demand. The multi-echelon inventory system considered here is a combination of assembly and serial stages with direct demand from more than one node. The aspect of multiple sources of demands leads to interesting inventory allocation problems. The demand and capacity at each node are considered stochastic in nature. A fixed supply and manufacturing lead time is used between the stages. We develop mathematical models for these multi-echelon systems, which describe the inventory dynamics and allow simulation of the system. A simulation-based inventory optimization approach is developed to search for the best base-stock levels for these systems. The gradient estimation technique of perturbation analysis is used to derive sample-path estimators. We consider four allocation schemes: lexicographic with priority to intermediate demand, lexiographic with priority to downstream demand, predetermined proportional allocation, and proportional allocation. Based on the numerical results we find that no single allocation policy is appropriate under all conditions. Depending on the combinations of variability and utilization we identify conditions under which use of certain allocation polices across the supply chain result in lower costs. Further, we determine how selection of an inappropriate allocation policy in the presence of scarce on-hand inventory could result in downstream nodes facing acute shortages. Consequently we provide insight on why good allocation policies work well under differing sets of operating conditions.

Optimization of a Failure – prone Manufacturing System with Regular Preventive Maintenance: an IPA Approach

AbstractThis paper addresses the optimization of a single-stage single-product manufacturing system with a constant demand and a systematic preventive maintenance policy. The manufacturing system is modeled by a continuous-flow model. The machine is subject to time-dependent failures and its production speed is given by a hedging point policy. Times to failure and times to repair are random variables with exponential distribution. We propose a simulation-based optimization method for determining the optimal buffer level in order to minimize the long run average cost including inventory holding cost, backordering cost and corrective and preventive maintenance costs. The optimization algorithm is based on the Infinitesimal Perturbation Analysis (IPA) technique for estimation of gradients along the simulation. The unbiasedness of the IPA estimators is established. Numerical results based on the simulation algorithm are proposed to determine the optimal buffer level and to derive the optimal value of the period of the systematic preventive maintenance.

Using Infinitesimal Perturbation Analysis of Stochastic Flow Models to Recover Performance Sensitivity Estimates of Discrete Event Systems

AbstractStochastic Flow Models (SFMs) form a class of hybrid systems used as abstractions of complex Discrete Event Systems (DES) for the purpose of deriving performance sensitivity estimates through Infinitesimal Perturbation Analysis (IPA) techniques when these cannot be applied to the original DES. In this paper, we establish explicit connections between gradient estimators obtained through a SFM and those obtained in the underlying DES, thus providing analytical evidence for the effectiveness of these estimators which has so far been limited to empirical observations. We consider DES for which analytical expressions of IPA (or finite difference) estimators are available, specifically G/G/1 and G/G/1/K queueing systems. We show that, when evaluated on the same sample path of the underlying DES, the IPA gradient estimators of states, event times, and various performance metrics derived through SFMs are, under certain conditions, the same as those of the associated DES or their expected values are asymptotically the same under large traffic rates.

Soliton absorption spectroscopy.

We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width using the novel perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively modelocked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurement in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improving of the sensitivity and spectroscopic accuracy making the soliton absorption spectroscopy a promising novel measurement technique.

DISPERSION RELATIONS FOR COLD PLASMA AROUND THE HORIZON OF SCHWARZSCHILD–DE SITTER BLACK HOLE

In this paper, we investigate the wave properties of cold plasma in the vicinity of Schawarzchild–de Sitter black hole horizon using 3 + 1 formalism. The general relativistic magnetohydrodynamical equations are formulated for this space–time with the use of Rindler coordinates. We consider both the rotating and nonrotating surroundings with magnetized and nonmagnetized plasmas. Linear perturbation and Fourier analysis techniques are applied by introducing simple harmonic waves. We derive complex dispersion relation from the determinant of Fourier analyzed equations for each case which provides real and complex values of the wave number. From the wave number we determine the phase and group velocities, the refractive index etc., which are used to discuss the characteristics of the waves around the event horizon.

A Stochastic Inventory Control Problem with Reputation-Dependent Demand

Abstract The paper addresses a problem of capacitated inventory control. It incorporates the reputation of the system as a key factor influencing the distribution of future demand. The reputation depends on the degree to which past demand was satisfied. The optimality conditions developed by means of a perturbation analysis technique allow formulating some structural properties of optimal dynamics of inventory and reputation. A numerical procedure is devised to calculate an optimal rule for inventory control. The rule determines the order quantity at each time period as a function of inventory and reputation of the system at the beginning of the period. A numerical example illustrates the applicability of the developed solution method.

Localization of MHD and fast particle modes using reflectometry in ASDEX Upgrade

The radial structure of toroidal Alfvén eigenmodes (TAEs) is of great importance for comparison with theoretical predictions. A dual-channel fast frequency hopping millimeter-wave reflectometer installed on the ASDEX Upgrade tokamak is capable of measuring density fluctuations from the plasma edge to core, allowing the radial eigenfunction of n = 4 TAE and edge MHD modes to be obtained using phase perturbation and coherence data analysis techniques. The two techniques reveal similar results, and in particular the radial structure of the n = 4 TAE is found to be in good agreement with numerical predictions from linear gyrokinetic simulations. The first results of the radial localization of Alfvén cascades are also presented.