Deviation Function Research Articles

Quantum Bounds on the Generalized Lyapunov Exponents

We discuss the generalized quantum Lyapunov exponents Lq, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents Lq via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger q are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.

Large deviations of a tracer position in the dense and the dilute limits of single-file diffusion.

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large deviation functions for an initial step density profile with the fluctuating (annealed) and the fixed (quenched) initial conditions. These hydrodynamic results are applicable for a general single-file system and they agree with recent exact results obtained by microscopic solutions for specific model systems.

СРАВНИТЕЛЬНЫЙ АНАЛИЗ ЭФФЕКТИВНОСТИ РАЗЛИЧНЫХ МОДЕЛЕЙ ЭЛЕКТРИЧЕСКОГО КОНТУРА ЭЛЕКТРОДУГОВОЙ ПЕЧИ ДЛЯ ИСПОЛЬЗОВАНИЯ В ЦИФРОВОМ ДВОЙНИКЕ

usRelevance Nowadays the metallurgical industry is rapidly developing, which requires a continuous search for innovative solutions aimed at providing consumers with high-quality metal products in the required volumes. To achieve this goal, modern enterprises are faced with a number of scientific and technical tasks, which include increasing the energy efficiency of production. An innovative tool in this case is the development of methods for the digitalization of production, including implementation of digital twins for the control of complicated technological systems. The most energy-intensive equipment at metallurgical enterprises is electric arc furnace (EAF). As operating experience shows, control systems for electrical modes of such units do not always allow EAFs to operate with optimal time, energy and technological parameters, which in turn leads to increased operating costs, such as increased specific energy consumption, consumption of electrodes, etc. As a solution to this problem, a number of scientific studies propose the use of a digital twin for dynamic adaptation of the parameters of the EAF electrical mode control system, capable of calculating the settings of control algorithms during the melting process in such a way as to obtain optimal electrical and technological modes at different stages, as well as optimal dynamic performance quality of impedance regulation on the secondary side of the furnace transformer. One of the important stages in this case is the form of representation of the electrical circuit inside of the digital twin, since the adequacy of the output parameters and the accuracy of the operation of the entire control system will depend on this. Based on the above, an urgent task is to develop an effective method for modeling the electrical circuit of the electric arc furnace for application in a digital twin. Aim of research The paper is devoted to the results of research aimed at the use of various mathematical models of the electrical circuit for application in electric arc furnace’s digital twin. Research methods To process the experimental data, mathematical modeling methods were used in the Matlab environment with the Simulink application. All studies were carried out on the basis of experimental data obtained at operating equipment at domestic and foreign metallurgical plants. Results The significance of the research results lies in increasing the energy efficiency of arc steel-smelting furnaces through the use of a digital twin. This solution will allow to provide the optimal selection of transformer tap reactor tap and operating curve number for each stage of melting, as well as analyze the position of operating points on the electrical characteristics and generate additional control signals for dynamic correction of the lengths of electric arcs. The methods of electric circuit modeling in digital twins presented in the work allow to configure the melting program and optimize the parameters of nonlinear impedance or conductivity controllers of the secondary side of the EAF’s transformer. In addition, it makes possible the analyze and adaptation of the auxiliary blocks in control system — arc ignition, current control and correction of regulator setting signals as a function of the voltage deviation on the primary side of the furnace transformer (relatively to the rated value). Problems associated with calculating matrices of settings for impedances and conductances of the secondary circuit of an EAF for all combinations of transformer taps, reactor taps and all values of operating curves can also be solved. Mathematical models are implemented in the Matlab software environment with the Simulink application.

Roll dynamic coefficients approach of decay test using the Generalized Reduced Gradient method (GRG)

Sea transportation is the vehicle which dominant and vital in the world. The increasing number of ships, types, and uncertain climate change have caused many ship accidents that have caused loss of life and property. The International Maritime Organization (IMO) issued the latest regulation on the second generation of ship stability criteria based on the dynamic of ship roll motions. The survival of dynamic stability depends on the hydrodynamic coefficients, which numerical and experimental calculations can obtain. The problem is finding the hydrodynamic coefficients of the ship roll quickly and accurately from the experimental roll decay data. This paper uses the Generalized Reduced Gradient (GRG) optimization to find the roll motion coefficient with the objective function of a standard deviation. The results show that the roll decay experiment graph is close optimization for variations of the minimum standard deviation used: all data, maximum-minimum amplitude, maximum amplitude, and minimum amplitude. The most similar chart to the experiment is optimization using a standard deviation of maximum-minimum amplitude with the optimal objective function o = 1.006776 closest o=1; obtained variable x 1 = k4 4 =0.1087688 m; x 2 = B4 4 =3.00306E-05 m-ton-sec. Based on sensitivity tests for various scenarios, optimization with a standard deviation of maximum amplitude has a high sensitivity, so it is necessary to avoid or be careful in its use. Generally, the GRG optimization method has the advantage of finding the hydrodynamic roll coefficient quickly and accurately.

Generation of synthetic FLAIR MRI image from real CT image for accurate synovial fluid segmentation in human knee image

Synthetic MRI FLAIR images of an abdominal 3D multimodality phantom and in vivo human knee have been generated from real CT images using predefined mapping functions of CT mean and standard deviation with the corresponding proton density PD, T1 and T2 that were previously generated from spin-echo sequence. First, the validity of generating synthetic MR images from different sequences were tested and the same PD, T1 and T2 maps that were generated from the real CT image have been used in the simulation of MRI inversion-recovery (IR) sequence. The similarity results between the real and synthetic IR sequence images, using different inversion times TI, showed a very good agreement. After confirming the feasibility of generating synthetic IR images from the PD, T1 and T2-maps, that were originally obtained from spin-echo sequence using the phantom, the simulation of a knee image has been generated from the corresponding knee CT real image using the steady-state transverse magnetization formula of the inversion-recovery sequence. The simulated FLAIR IR sequence MR image are generated using proper TI for nulling the signal from the synovial fluid, where the image complement is used as a mask for segmenting the corresponding tissue region in the real CT image.

“试问”非问：语义偏移、语篇特点与互动功能

在现代汉语中, “试问”用形式上的“问”实现了“非问”的语义和功能。它属于诱导参与和信服的元话语标记, 虽然不参与命题表达, 但对语篇的理解和言者立场的构建具有重要作用。“试问”的语义发生了偏移, 它所引导的后续语句的内容不是需要听者回答的问题, 而是言者的观点, 是言者认为不容置疑的或者是符合大众普遍认知和价值取向的内容。“试问”具有人际互动功能, 主要包括诱导参与和信服功能、传信功能和立场构建功能。同时它还具有提请注意与标示言者观点出现的语篇功能。

Nonlinear Stochastic Seismic Response Analysis of Three-Dimensional Reinforced Concrete Piles

A reliable assessment and design of engineering structures requires appropriate estimation and consideration of different sources of uncertainty. The randomness of seismic ground motion is one major uncertainty that needs to be considered from the perspective of performance-based earthquake engineering. To properly account for this uncertainty and its corresponding effect on pile foundations, a stochastic seismic response analytical framework based on a probability density evolution method and a stochastic ground motion model is proposed for the nonlinear stochastic seismic response analysis of pile foundations. A three-dimensional finite element model of a reinforced concrete pile with a large diameter embedded in the soil foundation is firstly established and calibrated using the full-scale lateral load test results from the literature, in which the nonlinear behavior of soil, the soil–pile interaction, the concrete damaged plasticity, and the steel yielding of the pile are properly modeled. Then, the calibrated three-dimensional numerical model is employed as an illustrative example for the stochastic seismic response analysis using the proposed framework. The mean, standard deviation, and probability density function of pile settlement and the dynamic reliabilities of the pile concerning various performance requirements are obtained in the present study. The settlements of the pile show great variability under the excitation of various stochastic ground motions, and the maximum mean value of the pile settlements is about 8 mm. The changing shape of the settlement probability density functions in every moment demonstrates that it is unreasonable to use assumed probabilistic distribution models to characterize the seismic responses of pile foundations during a seismic reliability analysis. Based on the proposed method, it is found that the dynamic reliabilities of the selected reinforced concrete pile concerning four different performance levels are 0, 0.1293, 0.8247, and 1, respectively. The proposed stochastic seismic response analytical method in the present study can provide a proper and comprehensive way to quantify various uncertainties and their corresponding effects on the seismic performance of pile foundations. It can also be used to estimate the actual reliability level of pile foundations that are designed by the current codes when they are subjected to seismic loads.

Extreme Eigenvalues and the Emerging Outlier in Rank-One Non-Hermitian Deformations of the Gaussian Unitary Ensemble.

Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N≫1 the eigenvalue density of J undergoes an abrupt restructuring at γ=1, the critical threshold beyond which a single eigenvalue outlier ("broad resonance") appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold γ=1 and the associated scaling for the real parts ("resonance positions") and imaginary parts ("resonance widths") of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function.

Reactive power assisted frequency regulation scheme for large-scale solar-PV plants

Due to reduction in power system inertia and frequency regulation reserve with high penetration of power-electronic converter (PEC) interfaced renewable sources, advanced control strategies must be developed to exploit the full potential of solar-photovoltaic (PV) systems to improve the frequency stability. In this paper, a new frequency regulation approach is proposed based on reactive-power control (i.e., frequency regulation via reactive-power control (FRQC) scheme) for solar-PV systems, which manipulates the active power demand as a function of the system frequency deviation by varying network voltages via reactive power control. The feasibility of the proposed control scheme is investigated using both theoretical analysis and simulation studies following a loss of a major generation source. Frequency and voltage deadbands, and time delays are added to the FRQC scheme to activate and deactivate the control scheme, and hence it maximises the frequency support without affecting the voltage stability. The reliability and voltage stability (RVS) test system is used to demonstrate the effectiveness of the proposed FRQC scheme under different gains of the controller, PV loading levels, and different PV penetration levels. The comparative results show that the proposed FRQC scheme improves the post-fault frequency trajectory, and hence the system frequency stability.

Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher’s equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher’s process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher’s process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analyzed in terms of the large deviation function.

Improvement, Validation, and Analysis of Colles Fracture Treated with an Integrated Retainer Pad Splint

To observe the effectiveness and safety of the Colles fracture treated with the integrated retainer pad splint and to compare the clinical and radiological outcomes of the integrated retainer pad splint and the traditional bamboo curtain splint in the treatment of the Colles fracture. A total of 100 patients with Colles fractures were randomly divided into two groups: the treatment group was fixed with the integrated retainer pad splint (IS), and the control group was fixed with the traditional bamboo curtain splint (TS).The range of wrist motion was measured at follow-up examinations, and volar inclination, ulnar deviation, and radial height were measured on radiographs. Regular follow-up wrist imaging examinations and functional examinations were performed before reduction, after reduction, and at the 1st, 3rd, 5th, and 8th weeks. The two groups were compared in terms of convenience, fracture healing time, X-ray data of volar inclination, ulnar deviation, radial height, and wrist joint function. The relevant data were analyzed with SPSS 25.0 statistical software. There were no notable differences in gender, age, and injured side between IS and TS groups. In terms of operation time, IS was better than the TS group (P < 0.05), and the operation time in the IS group was shorter. On the basis of X-ray data of volar inclination, ulnar deviation, and radial height measured on radiographs, the difference between the IS and TS groups was statistically significant (P < 0.05), which showed that the IS group was more stable in fracture fixation and had less reduction loss during the treatment process. At the 8th week of treatment, the wrist Gartland-Werley score of the two groups showed that the two fixation methods are equivalent in restoring wrist joint function (P > 0.05); however, in terms of the excellent and good rate of wrist joint function, the IS group scored 96% was higher than the TS group (80%). Compared with the traditional bamboo curtain splint, the integrated retainer pad splint is more convenient and stable, and it has less reduction loss during the treatment. Repair of the Colles fracture using the integrated retainer pad splint with external fixation results in nearly normal return of function, which is significantly better than using the traditional bamboo curtain splint.

The Bicycle Network Improvement Problem

Using a bicycle for commuting is still uncommon in US cities, although it brings many benefits to both the cyclists and to society as a whole. Cycling has the potential to reduce traffic congestion and emissions, increase mobility, and improve public health. To convince people to commute by bike, the infrastructure plays an important role, since safety is one of the primary concerns of potential cyclists. This paper presents a method to find the best way to improve the safety of a bicycle network for a given budget and maximize the number of riders that could now choose bicycles for their commuting needs. This optimization problem is formalized as the Bicycle Network Improvement Problem (BNIP): it selects which roads to improve for a set of traveler origin-destination pairs, taking both safety and travel distance into account. The BNIP is modeled as a mixed-integer linear program that minimizes a piecewise linear penalty function of route deviations of travelers. The MIP is solved using Benders decomposition to scale to large instances. The paper also presents an in-depth case study for the Midtown area in Atlanta, GA, using actual transportation data. The results show that the Benders decomposition algorithm allows for solving realistic problem instances and that the network improvements may significantly increase the share of bicycles as the commuting mode. Multiple practical aspects are considered as well, including sequential road improvements, uneven improvement costs, and how to include additional data.

Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions.

For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.

Computational phantoms for investigating impact of noise magnitude on modulation transfer function

Accurate measurement of spatial resolution in terms of modulation transfer function (MTF) is essential in computed tomography (CT) images. The purpose of this study was to developed a computational phantom that can be used to evaluate the effect of noise on the MTF in CT images. Our computational phantoms for measuring MTF in CT were developed with MATLAB software. The phantom image was blurred by a point spread function of a certain standard deviation. Subsequently, different noise levels were added to the phantoms. Next, an automatic MTF calculation was implemented. The first step of the MTF calculation was to determine the region of interest (ROI). Profile was generated from the ROI, and a line spread function (LSF) curve was formed. The LSF curve was Fourier transformed to produce a MTF curve. Greater noise added to phantom image, it yields greater effect of standard deviation on the measured MTF. The greater noise makes the MTF curve increases differently than MTF with 0 HU noise. The 10% MTF values at the 25% noise reach more than 2.0 cycle/mm. By the developed computational phantoms, the spatial resolution and the amount of noise can be determined independently.

A new symmetry for large deviation functions of time-integrated dynamical variables

A new type of symmetry in the large deviation function of a time-integrated current is introduced. This current is different from the fluctuating entropy production for which the large deviation function is symmetric in the content of the fluctuation theorem. The origin of this symmetry, similar to that of the Gallavotti-Cohen-Evans-Morriss symmetry, is related to time-reversal. The symmetry is more unveiled when one performs an appropriate grouping of stochastic trajectories in the space of microscopic configurations. It turns out that the characteristic polynomial of the modified generator of this current is not symmetric; however, its minimum eigenvalue is symmetric.

Bi-level fuzzy stochastic-robust model for flexibility valorizing of renewable networked microgrids

This paper presents a new bi-level multi-objective model to valorize the microgrid (MG) flexibility based on flexible power management system. It considers the presence of renewable and flexibility resources including demand response program (DRP), energy storage system and integrated unit of electric spring with electric vehicles (EVs) parking (IUEE). The proposed bi-level model in the upper-level maximizes expected flexibility resources profit subject to flexibility constraints. Also, in the lower level, minimizing MG energy cost and voltage deviation function based on the Pareto optimization technique is considered as the objective functions; it is bounded by the linearized AC optimal power flow constraints, renewable and flexibility resources limits, and the MG flexibility restrictions. In the following, the proposed bi-level model using Karush–Kuhn–Tucker (KKT) technique is converted to a single-level counterpart, and the fuzzy decision-making method is employed to achieve the best compromise solution. Further, hybrid stochastic-robust programming models uncertain parameters of the proposed model, so that stochastic programming models uncertainties associated with demand, energy price, and the maximum renewables active generation. Also, to capture the flexible potential capabilities of the IUEE, robust optimization models the EVs’ parameters uncertainty. Finally, numerical results confirm the proposed model could jointly improve operation, economic and flexibility conditions of the MG and turned it to a flexi-optimized-renewable MG. • Bi-level model to value the microgrid flexibility is presented. • Integrated unit of electric spring with electric vehicles is modeled. • The paper deals with maximizing flexibility value in renewable microgrids. • Fuzzy stochastic/robust optimization is proposed to handle uncertainty.

How to harmonise variations in streetscape skeletons under zoning regulations: Considering their external diseconomies

The arrangement of buildings along roads creates one of the most fundamental patterns of three-dimensional streetscape skeletons, primarily defined as a set of building heights and setbacks in a district. Under zoning regulations, building heights and setbacks are indirectly controlled by the building coverage ratio (BCR) and the floor area ratio (FAR). Variations in the BCR result in variations in streetscape skeletons. Moderate complexity of streetscape skeletons is a necessary condition for aesthetic streetscape. Understanding the relationships between variations in the BCR, building heights and setbacks is thus important in order to harmonise streetscape skeletons, smaller variations in building heights, and setbacks, however, this relationship has yet to be theoretically investigated due to the complex relationship between buildings. The objective of this paper is therefore to formulate the relationship between variations in building heights and setbacks as a function of the standard deviation of BCR, and, based on this formulation, to discuss how to indirectly harmonise variations in streetscape skeletons under zoning regulations. This formulation enables us to analytically investigate the relationship between these two functions and the standard deviation of a BCR. An indirect scheme for harmonising variations in streetscape skeletons under zoning regulations is proposed on the basis of this formulation. The external diseconomies of inharmonious streetscape skeletons are quantitatively defined in order to incentivise plot owners to harmonise streetscape skeletons. The optimal building height and setback criteria are computed, which minimises the social cost of inharmonious building heights and building setbacks in a district. This scheme for incentivising plot owners to reduce their social costs is expected to contribute to indirectly harmonising streetscape skeletons.

Surface and Calorimetric Behavior of N,N-Dimethylacetamide with n-Alkanols or 2-Alkanols

The surface tension at the liquid–air interface of eight binary mixtures formed by N,N-dimethylacetamide and n-alkanols (from methanol to 1-pentanol) or 2-alkanols (from 2-propanol to 2-pentanol) was studied at three different temperatures (283.15, 298.15, and 313.15 K) and a pressure of 0.1 MPa. Surface tension deviations were also calculated. Moreover, the excess molar enthalpies for all of these mixtures were measured at T = 298.15 K and a pressure of 0.1 MPa. Both deviation and excess functions were correlated with the mole fraction by means of the Redlich–Kister equation. The surface tension deviations are found to be positive for the system containing methanol, sigmoidal for ethanol and negative for the rest of the alkanols. With regard to excess molar enthalpies, negative values are found for the system containing methanol, sigmoidal values for ethanol, and positive values for the rest of the alkanols.

Exact Solution of the Macroscopic Fluctuation Theory for the Symmetric Exclusion Process.

We present the first exact solution for the time-dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the inverse scattering method. For the step initial condition with two densities, we obtain exact and compact formulas for the optimal density profile and the response field that produce a required fluctuation, both at initial and final times. The large deviation function of the current is derived and coincides with the formula obtained previously by microscopic calculations. This provides the first analytic confirmation of the validity of the MFT for an interacting model in the time-dependent regime.

Mechanisms underlying the impact and interaction of temperature and UV-B on the hatching of spider mite and phytoseiid mite eggs.

A spider mite control method using night-time ultraviolet (UV)-B irradiation was recently developed for strawberry greenhouses (UV method). The control effect of this UV method is negatively affected by increasing temperature. Tetranychus urticae eggs are more resistant to a single dose of UV-B irradiation than Neoseiulus californicus eggs. By contrast, N. californicus can better survive nightly UV-B irradiation with the UV method compared with T. urticae. To elucidate the mechanism underlying these phenomena, we explored the hypotheses that higher temperature promotes photoenzymatic repair (PER) and that mortality is determined by UV-B susceptibility in the embryonic stage exposed to UV-B. PER efficacy was not promoted by increasing temperature. The lowest hatchability (around zero) of T. urticae eggs after a single dose of UV-B irradiation (0.288 and 0.432 kJ m-2 ) without photoreactivation was seen in the morphogenesis stages between "cleavage ended" and "eye points became colored". Based on these results, we developed a linear function of daily UV-B irradiance and deviation of cumulative irradiance during vulnerable embryonic developmental phases from 50% lethal dose (LD50 ) after a single dose of UV-B irradiation. The difference between T. urticae and N. californicus and changes in UV-B vulnerability due to temperature could be explained by this simple relationship. Slower development in T. urticae than N. californicus in nature and developmental delay under low temperatures increase the ovicidal effects of the UV method. This shows the advantage of the simultaneous use of the UV method and biological control, contributing to the development of integrated pest management. © 2022 Society of Chemical Industry.