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Due to the non-linear factors of the single loop gear system and the inter-tooth system, is sometimes difficult to establish an accurate nonlinear dynamic model, which leads to the large deviation between the dynamic characteristics and the actual situation. According to the structural characteristics and dynamic mechanism of nonlinear factors, the bond graph power junction with switching characteristics is adopted. This method is used to establish the model of the single loop gear system and the inter-tooth system respectively. On this basis, the amplitude-phase-frequency characteristics of PX single loop gear systems are obtained by numerical simulation analysis. Eventually, the dynamic stability of single loop gear system is judged based on this characteristic index. The study shows that the dynamic stability of PX type single loop gear system is unsteady in the nonlinear state. In addition, it is concluded that when the whole single loop gear system is unstable, its system module also has the same unstability. [ABSTRACT FROM AUTHOR]

This article is devoted to the large deviation principle for a wide class of stochastic hydrodynamical systems driven by multiplicative Lévy noise. The model covers many equations arising form fluid dynamics such as 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The main difficulty in proving the large deviation principle for the system is overcame by using the weak convergence method introduced by Budhiraja, Dupuis and Maroulas (Ann. Probab. 36: 1390–1420, 2008 and Annales De L Institut Henri Poincare. 47: 725–747, 2011). [ABSTRACT FROM AUTHOR]

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti (J. Theor. Probab. 34(2):682–727). We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles. [ABSTRACT FROM AUTHOR]

JET experiments using the fuel mixture envisaged for fusion power plants, deuterium and tritium (D–T), provide a unique opportunity to validate existing D–T fusion power prediction capabilities in support of future device design and operation preparation. The 2021 JET D–T experimental campaign has achieved D–T fusion powers sustained over 5 s in ITER-relevant conditions i.e. operation with the baseline or hybrid scenario in the full metallic wall. In preparation of the 2021 JET D–T experimental campaign, extensive D–T predictive modelling was carried out with several assumptions based on D discharges. To improve the validity of ITER D–T predictive modelling in the future, it is important to use the input data measured from 2021 JET D–T discharges in the present core predictive modelling, and to specify the accuracy of the D–T fusion power prediction in comparison with the experiments. This paper reports on the validation of the core integrated modelling with TRANSP, JINTRAC, and ETS coupled with a quasilinear turbulent transport model (Trapped Gyro Landau Fluid or QualLiKiz) against the measured data in 2021 JET D–T discharges. Detailed simulation settings and the heating and transport models used are described. The D–T fusion power calculated with the interpretive TRANSP runs for 38 D–T discharges (12 baseline and 26 hybrid discharges) reproduced the measured values within 20 %. This indicates the additional uncertainties, that could result from the measurement error bars in kinetic profiles, impurity contents and neutron rates, and also from the beam-thermal fusion reaction modelling, are less than 20 % in total. The good statistical agreement confirms that we have the capability to accurately calculate the D–T fusion power if correct kinetic profiles are predicted, and indicates that any larger deviation of the D–T fusion power prediction from the measured fusion power could be attributed to the deviation of the predicted kinetic profiles from the measured kinetic profiles in these plasma scenarios. Without any posterior adjustment of the simulation settings, the ratio of predicted D–T fusion power to the measured fusion power was found as 65%–96% for the D–T baseline and 81%–97% for D–T hybrid discharge. Possible reasons for the lower D–T prediction are discussed and future works to improve the fusion power prediction capability are suggested. The D–T predictive modelling results have also been compared to the predictive modelling of the counterpart D discharges, where the key engineering parameters are similar. Features in the predicted kinetic profiles of D–T discharges such as underprediction of ne are also found in the prediction results of the counterpart D discharges, and it leads to similar levels of the normalized neutron rate prediction between the modelling results of D–T and the counterpart D discharges. This implies that the credibility of D–T fusion power prediction could be a priori estimated by the prediction quality of the preparatory D discharges, which will be attempted before actual D–T experiments. [ABSTRACT FROM AUTHOR]

Consider a sequence of continuous-time Markov chains (X t (n) : t ≥ 0) evolving on a fixed finite state space V. Let I n be the level two large deviations rate functional for X t (n) , as t → ∞. Under a hypothesis on the jump rates, we prove that I n can be written as I n = I (0) + ∑ 1 ≤ p ≤ q (1 / θ n (p) ) I (p) for some rate functionals I (p) . The weights θ n (p) correspond to the time-scales at which the sequence of Markov chains X t (n) exhibit a metastable behavior, and the zero level sets of the rate functionals I (p) identify the metastable states. [ABSTRACT FROM AUTHOR]

Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate parabolic-hyperbolic PDE with irregular drift. We develop a robust well-posedness theory for such PDEs in energy-critical spaces based on concepts of renormalized solutions and the equation's kinetic form. We establish these properties by proving that renormalized solutions are equivalent to classical weak solutions, extending concepts of (DiPerna and Lions in Invent. Math. 98(3):511–547, 1989; Ambrosio in Invent. Math. 158(2):227–260, 2004) to the nonlinear setting. The relevance of the results toward large deviations in interacting particle systems is demonstrated by applications to the identification of l.s.c. envelopes of restricted rate functions, to zero noise large deviations for conservative SPDE, and to the Γ -convergence of rate functions. The first of these solves a long-standing open problem in the large deviations for zero range processes. The second makes rigorous an informal link between the non-equilibrium statistical mechanics approaches of macroscopic fluctuation theory and fluctuating hydrodynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang [A. Matoussi, W. Sabbagh and T.-S. Zhang, Large deviation principles of obstacle problems for quasilinear stochastic PDEs, Appl. Math. Optim. 83(2) (2021) 849–879] plays an important role in the proof. [ABSTRACT FROM AUTHOR]

This paper concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity > 0 and with accelerated jumps by intensity 1 . We establish Freidlin–Wentzell estimates for the slow process of the multiscale system in the small noise limit → 0 using the weak convergence approach to large deviations theory. The core of our proof is the reduction of the large deviations principle to the establishment of a stochastic averaging principle for auxiliary controlled processes. As consequence we solve the first exit time/exit locus problem from a bounded domain containing the stable state of the averaged dynamics for the family of the slow processes in the small noise limit. [ABSTRACT FROM AUTHOR]

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated trajectorial LDP. It is shown that if the trajectorial deviation function has certain structure and if the invariant measures are exponentially tight, then the LDP for the invariant measures is implied by the trajectorial LDP, no other properties of the stochastic processes in question being material. As an application, we obtain an LDP for the stationary distributions of jump diffusions. Methods of large deviation convergence and idempotent probability play an integral part. [ABSTRACT FROM AUTHOR]

To address the problem of depletion shutdown precise guidance for a long-range vehicle in large deviation condition, an online guidance algorithm based on Bezier curves and zero-range orientation (ZRO) is proposed under the conditions of thrust magnitude deviation, thrust direction deviation, mass flow rate deviation, and depletion shutdown time deviation of the solid divert control system. First, the mapping relationship between the apparent velocity to be gained (AVTG) and the impact deviation is analyzed based on the variational principle. The AVTG is solved with the Newton iterative method in the designed AVTG solution plane. Then, in the plane spanned by the AVTG and the ZRO, the key parameters of the Bezier curve are solved to obtain the Bezier energy management curve by taking the apparent acceleration direction and the angular velocity of the energy management terminal as the ZRO and zero, respectively, as constraints, which effectively reduces the influence of the solid divert control system performance parameter perturbation. Finally, the feedback linearization method is applied to track the Bezier energy management curve. A detailed simulation experiment is designed to analyze the advantages and computational complexity of the proposed algorithm. The Monte Carlo simulation results show that the proposed algorithm has high precision and good robustness, and the 3 σ error of the proposed algorithm is 2.58 m. On the STM32F407 single-chip microcomputer, the proposed algorithm takes 25.38 ms, which demonstrates good real-time performance and a certain engineering application value. [ABSTRACT FROM AUTHOR]

The Indo-French SARAL/AltiKa mission in Ka band has provided valuable information on global oceans to cater the needs of oceanographic community. The SARAL/AltiKa has been operating in three different orbital configurations, viz. Exact Repeat Mission (ERM, March 2013 – July 2016), Drifting Phase (DP, July 2016 – February 2019) and Mispointing Phase (MP, February 2019 – till date). We investigate the utility of the SARAL/AltiKa data for geodetic applications. Global crossover analysis of Sea Surface Height (SSH) measurements from SARAL/AltiKa suggests a stable performance throughout its life with similar range of standard deviations during ERM (5.8 cm), DP (5.9 cm) and MP (5.9 cm) configurations. Two separate Mean Sea Surface (MSS) models were retrieved by adding DP and MP data from SARAL/AltiKa to the ERM stacks of SARAL/AltiKa and Jason satellite series. The quality of MSS models were evaluated based on the crossover differences with the ERM database. It is observed that the crossover adjustments have reduced the deviations in SSH errors by ∼30% for both DP-MSS and MP-MSS models. Analysis of along-track sea surface slopes suggests that 99.9% of data in ERM and DP phases and 93.8% of data in MP phase are well within 1 μrad bound corresponding to an accuracy of ∼1 mGal in free-air gravity anomaly. Further, time-series analysis of Sea Level Anomaly (SLA) from SARAL/AltiKa showed a stable performance with no significant drifts throughout its phases. Deviations in daily SLA for SARAL/AltiKa DP (10 cm) is considerably lower than that of Jason-3 (10.2 cm) and CryoSat-2 (10.2 cm) satellites. However, daily SLA for the MP phase showed slightly larger deviation (10.4 cm), owing to the larger number of outliers, which could be easily removed using a simple median filter. The present study reveals the usefulness of MP data from SARAL/AltiKa for geodetic applications. [ABSTRACT FROM AUTHOR]

Large scale traveling ionospheric disturbances (LSTIDs) can be detected using the critical frequency of F2 layer (foF2) of the ionosphere. The HF interferometry (HF‐int) technique is applied to the ionosonde data from low and mid latitude stations over Australia. For the first time, we present a comparison of TIDs detected during the geomagnetic storms of 17 March and 23 June 2015. The TID response for these two comparable superstorms is significantly different owing to the differing storm evolution patterns. The storm associated TIDs are more intense and longer compared to the solar terminator. Results demonstrate that the morphology of parameters continually varies over time due to highly dynamic ionospheric response to geomagnetic storms. For the March storms, TIDs velocities were 400–700 m/s at the onset phase, ∼500 m/s during the main phase and ∼600 m/s during the recovery phase. Their propagation directions were equatorward with east/west deviations. Lower period (∼60 min) TIDs were determined during storm onset whereas higher periods (∼140 min) were detected during the recovery phase. The June storm produced a different response. The TID velocity at the onset phase was ∼500 m/s but during the main and recovery phases the velocities were greater than 1,000 m/s. There were large deviations in velocity vectors at the different stations suggesting multiple sources of TID generation and possible resonating effects at middle and low latitude stations. Our findings indicate that while TID detection and storm phases co‐occur, the propagation characteristics of TIDs change dramatically throughout the storm. Key Points: Traveling ionospheric disturbance (TID) characteristics are obtained from foF2 perturbations using HF Interferometry method over the Australian region during two super stormsTID response for the geomagnetic storms of 17 March 2015 and 23 June 2015 differ vastly owing to the differing storm evolution patternsJune storm showed TIDs with very high propagation speeds during the main and recovery phases as compared to the March storm [ABSTRACT FROM AUTHOR]

This paper describes the response of the economy to large shocks in a nonlinear production network. A sector's tail centrality measures how a large negative shock transmits to GDP, that is, the systemic risk of the sector. Tail centrality is theoretically and empirically very different from local centrality measures such as sales share—in a benchmark case, it is measured as a sector's average downstream closeness to final production. It also measures how large differences in sector productivity can generate cross‐country income differences. The paper also uses the results to analyze the determinants of total tail risk in the economy. Increases in interconnectedness can simultaneously reduce the sensitivity of the economy to small shocks while increasing the sensitivity to large shocks. Tail risk is related to conditional granularity, where some sectors become highly influential following negative shocks. [ABSTRACT FROM AUTHOR]

We study the large fluctuations of the work injected by the random force into a Brownian particle under the action of a confining harmonic potential. In particular, we compute analytically the rate function for generic uncorrelated initial conditions, showing that, depending on the initial spread, it can exhibit no, one, or two singularities associated to the onset of linear tails. A dependence on the potential strength is observed for large initial spreads (entailing two singularities), which is lost for stationary initial conditions (giving one singularity) and concentrated initial values (no singularity). We discuss the mechanism responsible for the singularities of the rate function, identifying it as a big jump in the initial values. Analytical results are corroborated by numerical simulations. [ABSTRACT FROM AUTHOR]

Currently, there is a large deviation between official road freight data and real road freight performance at a subnational level in China. In order to deal with this deviation, the new concept of local freight tonnage and ton-kilometers is presented in this paper based on the territoriality principle, where either the origin or the destination of goods transported is local. Also, the statistic procedures and estimation models of the local freight tonnage and ton-kilometers are proposed based on five accessible basic datasets. Finally, an empirical study in Sichuan province of China is conducted. The statistical results show that there is a large amount of local freight transported by local non-commercial trucks and non-local trucks, which is ignored in the existing road freight statistics. Especially, the higher the level of local economic development, the greater the deviation between the official road freight data and the real road freight performance at a subnational level. [ABSTRACT FROM AUTHOR]

As incrementally formed sheets show large geometric deviations resulting from the deflection of the forming tool, an in-process measurement of the tool tip position is required. In order to cover a measuring volume of 2.0 m × 1.0 m × 0.2 m and to achieve measuring uncertainties of less than 50 µm, a multi-sensor system based on triangulation is realized. Each shadow imaging sensor in the multi-sensor system evaluates the direction vector to an LED attached to the tool, and the three-dimensional position of the LED is then determined from the combination of two sensors. Experimental results show that the angle of view from the sensor to the LED limits both the measurement range and the measurement uncertainty. The measurement uncertainty is dominated by systematic deviations, but these can be compensated, so that the measurement uncertainty required for measuring the tool tip position in the ISF is achieved. [ABSTRACT FROM AUTHOR]

We consider a stochastic 2D liquid crystal model with a multiplicative noise of Lévy type, which models the dynamic of nematic liquid crystals under the influence of stochastic external forces of jump type. We derive a large deviation principle for the model. The proof is based on the weak convergence method introduced in [Budhiraja A, Dupuis P, Maroulas V. Variational representations for continuous time processes. Ann Inst Henri Poincar Probab Stat. 2011;47(3):725–747]. [ABSTRACT FROM AUTHOR]

The main aim of this work is to study the asymptotic behavior for multi-scale McKean–Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e. the deviation between the slow component X ε and the solution X ¯ of the averaged equation converges weakly to a limiting process. More precisely, X ε - X ¯ ε converges weakly in C ([ 0 , T ] , R n) to the solution of certain distribution dependent stochastic differential equation, which involves an extra explicit stochastic integral term. Secondly, in order to estimate the probability of deviations away from the limiting process, we further investigate the Freidlin–Wentzell's large deviation principle for multi-scale McKean–Vlasov stochastic system when the small-noise regime parameter δ → 0 and the time scale parameter ε (δ) satisfies ε (δ) / δ → 0 . The main techniques are based on the Poisson equation for central limit type theorem and the weak convergence approach for large deviation principle. [ABSTRACT FROM AUTHOR]

In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403–456 we derived a quenched large deviation principle for the empirical process of words obtained by cutting an i.i.d. sequence of letters according to an independent renewal process. We derived a representation of the associated rate function for stationary word processes in terms of certain specific relative entropies. Our proof of this representation is correct when the mean word length is finite, but is flawed when the mean word length is infinite. In this paper we fix the flaw in the proof. Along the way we derive new representations of the rate function that are interesting in their own right. A key ingredient in the proof is the observation that if the rate function in the annealed large deviation principle is finite at a stationary word process, then the letters in the tail of the long words in this process are typical. [ABSTRACT FROM AUTHOR]

Background: Dosimetry in radionuclide therapy often requires the calculation of average absorbed doses within and between spatial regions, for example, for voxel‐based dosimetry methods, for paired organs, or across multiple tumors. Formation of such averages can be made in different ways, starting from different definitions. Purpose: The aim of this study is to formally specify different averaging strategies for absorbed doses, and to compare their results when applied to absorbed dose distributions that are non‐uniform within and between regions. Methods: For averaging within regions, two definitions of the average absorbed dose are considered: the simple average over the region (the region average) and the average when weighting by the mass density (density‐weighted region average). The latter is shown to follow from the definition of mean absorbed dose according to the ICRU, and to be consistent with the MIRD formalism. For averaging between different spatial regions, three definitions follow: the volume‐weighted, the mass‐weighted, and the unweighted average. With respect to characterizing non‐uniformity, the different average definitions lead to the use of dose‐volume histograms (DVHs) (region average), dose‐mass histograms (DMHs) (density‐weighted region average), and unweighted histograms (unweighted average). Average absorbed doses are calculated for three worked examples, starting from the different definitions. The first, schematic, example concerns the calculation of the average absorbed dose between two regions with different volumes or mass densities. The second, stylized, example concerns voxel‐based dosimetry, for which the average absorbed‐dose rate within a region is calculated. The geometries studied include three 177Lu‐filled voxelized spheres, where the sphere masses are held constant while the material compositions, densities, and volumes are varied. For comparison, the mean absorbed‐dose rates obtained using unit‐density sphere S‐values are also included. The third example concerns SPECT/CT‐based tumor dosimetry for five patients undergoing therapy with 177Lu‐PSMA and six patients undergoing therapy with 177Lu‐DOTA‐TATE, for which the average absorbed‐dose rates across multiple tumors are calculated. For the second and third examples, analyses also include representations by histograms. Results: Example 1 shows that the average absorbed doses, calculated using different definitions, can differ considerably if the masses and absorbed doses for two regions are markedly different. From example 2 it is seen that the density‐weighted region average is stable under different activity and density distributions and is also in line with results using S‐values. In contrast, the region average varies as function of the activity distribution. In example 3, the absorbed dose rates for individual tumors differ by (1.1 ± 4.3)% and (−0.1 ± 0.4)% with maximum deviations of +34.4% and −1.4% for 177Lu‐PSMA and 177Lu‐DOTA‐TATE, respectively, when calculated as region averages or density‐weighted region averages, with largest deviations obtained when the density is non‐uniform. The average absorbed doses calculated across all tumors are similar when comparing mass‐weighted and volume‐weighted averages but these differ substantially from unweighted averages. Conclusion: Different strategies for averaging of absorbed doses within and between regions can lead to substantially different absorbed‐dose estimates. At reporting of radionuclide therapy dosimetry, it is important to specify the averaging strategy applied. [ABSTRACT FROM AUTHOR]

In this paper we study the multifractal analysis and large derivations for singular hyperbolic attractors, including the geometric Lorenz attractors. For each singular hyperbolic homoclinic class whose periodic orbits are all homoclinically related and such that the space of ergodic probability measures is connected, we prove that: (i) level sets associated to continuous observables are dense in the homoclinic class and satisfy a variational principle; (ii) irregular sets are either empty or are Baire generic and carry full topological entropy. The assumptions are satisfied by C 1-generic singular hyperbolic attractors and Cr -generic geometric Lorenz attractors (r ⩾ 2). Finally we prove level-2 large deviations bounds for weak Gibbs measures, which provide a large deviations principle in the special case of Gibbs measures. The main technique we apply is the horseshoe approximation property. [ABSTRACT FROM AUTHOR]

The focusing performances of high-numerical-aperture (NA) Fresnel zone plates (FZP) under different immersion media are investigated by combining the vectorial angular spectrum (VAS) theory and the finite-difference time-domain method. It has been found that as the refractive index deviation increases, the focus approximately linearly shifts along the positive z-axis. Simultaneously, the transverse size of the focusing spot gradually decreases, and super-resolution focusing is realized. However, the peak intensity declines with an increase in the refractive index. In addition, when the deviation of the refractive index of the actual immersion medium from the design value is less than about 30%, VAS theory can correctly estimate the focusing light field distribution, except when the FZP has only one or two transparent annuli. On the contrary, VAS theory cannot achieve an accurate prediction when the deviation is larger. These findings will benefit the practical application of high-NA FZPs. [ABSTRACT FROM AUTHOR]

We study the large deviation behaviors of a stochastic fluid queue with an input being a generalized Riemann–Liouville (R–L) fractional Brownian motion (FBM), referred to as GFBM. The GFBM is a continuous mean-zero Gaussian process with non-stationary increments, extending the standard FBM with stationary increments. We first derive the large deviation principle for the GFBM by using the weak convergence approach. We then obtain the large deviation principle for the stochastic fluid queue with the GFBM as the input process as well as for an associated running maximum process. Finally, we study the long-time behavior of these two processes; in particular, we show that a steady-state distribution exists and derives the exact tail asymptotics using the aforementioned large deviation principle together with some maximal inequality and modulus of continuity estimates for the GFBM. [ABSTRACT FROM AUTHOR]

An algorithm for a three-dimensional fine-grid block encompassing a moving solid body using a multi-relaxation time model of the lattice Boltzmann method is proposed and developed. In this numerical framework, a geometry-conforming fine block shifts a coarse lattice unit as the object translates by same amount. The effective utilization of higher-order spatial interpolation has been demonstrated in place of the commonly used low-order temporal interpolation in traditional grid refinement techniques within the lattice Boltzmann method. The successful application of this method has been showcased through three distinct cases: the settling of a solid sphere in a fluid tank under the influence of gravity, hovering motion of an elliptic airfoil, and the "clap and fling" motion of an insect wing. In this regard, various interpolation schemes based on the location of nodes in the overlapping zones of fine and coarse block are discussed. In addition, two cases were evaluated, case 1 where distributions are interpolated and case 2 where macroscopic variables are directly interpolated. It was observed that both interpolations gave same computational accuracy for low Reynolds number [ ∼ O ( 10 2) ]. However, as Re is increased [ ∼ O ( 10 3) ], direct interpolation of macroscopic variables proved erroneous and resulted in a large deviation in fluid forces and is not recommended. The geometry-conforming dynamic mesh refinement results in a substantial decrease in computation time, approximately 90%, along with a memory reduction of about 80% compared to the fully refined counterpart. [ABSTRACT FROM AUTHOR]

Let λ = (λ1,...,λn) be β-Jacobi ensembles with parameters p1, p2, n and β while β varying with n. Set γ = lim n → ∞ n p 1 and σ = lim n → ∞ p 1 p 2 . In this paper, supposing lim n → ∞ log n β n = 0 , we prove that the empirical measures of different scaled λ converge weakly to a Wachter distribution, a Marchenko–Pastur law and a semicircle law corresponding to σγ > 0, σ = 0 or γ = 0, respectively. We also offer a full large deviation principle with speed βn2 and a good rate function to precise the speed of these convergences. As an application, the strong law of large numbers for the extremal eigenvalues of β-Jacobi ensembles is obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with uniform large deviation principles of fractional stochastic reaction-diffusion equations driven by additive noise defined on unbounded domains where the solution operator is non-compact and hence the result of [32] does not apply. The nonlinear drift is assumed to be locally Lipschitz continnous instead of being globally Lipschitz continuous. We first prove a large deviation principle for a fractional linear stochastic equation by the weak convergence method, and then show a uniform large deviation principle for the fractional nonlinear equation by a uniform contraction principle, despite the Sobolev embeddings are non-compact in unbounded domains. The result of the paper regrading the uniform large deviations can be applied to investigate the exit time and exit place of the solutions of the stochastic reaction-diffusion equations from a given domain in the phase space. [ABSTRACT FROM AUTHOR]

We prove moderate deviations bounds for the lower tail of the number of odd cycles in a 풢(n,m) random graph. We show that the probability of decreasing triangle density by t3, is exp(−Θ(n2t2)) whenever n−3/4≪t3≪1. These complement results of Goldschmidt, Griffiths, and Scott, who showed that for n−3/2≪t3≪n−1, the probability is exp(−Θ(n3t6)). That is, deviations of order smaller than n−1 behave like small deviations, and deviations of order larger than n−3/4 behave like large deviations. We conjecture that a sharp change between the two regimes occurs for deviations of size n−3/4, which we associate with a single large negative eigenvalue of the adjacency matrix becoming responsible for almost all of the cycle deficit. We give analogous results for the k‐cycle density, for all odd k. Our results can be interpreted as finite size effects in phase transitions in constrained random graphs. [ABSTRACT FROM AUTHOR]

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Historically, higher airspace has been used for military exercises and as transit for space vehicles. Riding on commercial space operations' coattails, more and more vehicles are under development that will make use of higher airspace resources. This will lead to increasing interactions with conventional air traffic since these new vehicles will have to transit through lower airspaces. The management of these operations is necessary to ensure the safe and practicable shared usage of these airspaces. This paper outlines an assessment of the impact of higher airspace operations on conventional air traffic in Europe. Initially, a synthesis of possible use cases was performed, and demand scenarios were developed that served as input to a fast-time simulation. The impact on air traffic was measured by means of flight efficiency parameters. The simulation results showed that the impact is dependent on the type of operation. High-altitude platform system flights and orbital launches cause the largest deviations in flight distance, flight duration and fuel consumption. Higher airspace operation parameters, including location, time, and duration, strongly affect the impact on the conventional air traffic. [ABSTRACT FROM AUTHOR]

Although many experiments and analyses have recently been performed to determine the intrinsic mobilities of austenite/ferrite ( γ / α) interfaces, there are large deviations in the temperature dependence characteristics of the measured values. However, in carbon steels, there is another transformation between ferrite and austenite, the δ / γ transformation, near the peritectic temperature. Due to the large temperature gap between the δ / γ and γ / α transformations, evaluating the δ / γ interface mobility at high temperatures is important for guiding the temperature dependence of the γ / α interface mobility. Nishimura et al. (Mater Sci Eng 84:012062, 2015) measured interface velocities by in situ observations of the massive δ → γ transformation. In this study, we analyze their results by applying the sharp and diffuse interface models to extract intrinsic mobilities for the δ / γ interface. The resultant mobilities at high temperatures appear to effectively match the extrapolation from recent mobility data for the γ / α interface at low temperatures. The best fit between the mobilities of the δ / γ interface and γ / α interface yields an activation energy of Q = 265 kJ/mol. This value is nearly twice the activation energy of Q = 147 kJ/mol employed for the γ / α interface. [ABSTRACT FROM AUTHOR]

Multi-source information intelligent sensing and online weld quality evaluation are two challenging problems in complex welding scenes. The difficulty is particularly pronounced in different welding scenes, where the multi-source sensing data exists large system deviations and small welding defect sample data are at large. This paper proposes an improved few-shot image generation model with the Fusing-and-Filling GAN (F2GAN) structure for welding data augmentation. In order to verify the effectiveness of the modified F2GAN, we carried out some experiments with various welding conditions. Two welding quality classification models combining multiple information are designed through our proposed welding dataset augmentation approach. We show that the final classification accuracy of burn-through, incomplete joint penetration, and welding deviation is 96.60%. Our results benefit welding monitoring and quality evaluation in complex welding scenes. [ABSTRACT FROM AUTHOR]

This article aims to investigate the accuracy and dimensional stability of bonded metal and CFRP (Carbon Fibre Reinforced Plastic) adherends. The motivation behind this study was to assess the suitability of CFRP for optical devices through the evaluation of precision bonding technology. A binocular was selected as a reference optical device. A technological sample was designed, with required total runout of key dimensions 0.05 mm. The sample underwent testing according to ISO 9022-1. The total runout was evaluated after production and environmental tests. Eight out of 15 samples were turned after gluing due to insufficient accuracy. None of the turned samples exceeded the total runout deviation of 0.01 mm, and the average value of the maximal deviation was 0.0041 mm. The noncalibrated samples performed significantly worse with the average value of the maximal deviation of 0.0164 mm. The measurements during the climatic tests showed that the largest deviation (on average 77.6% of the maximum achieved deviation) occurs at the first temperature loading. Subsequent temperature cycles caused lower deviations. The results highlight the significance of addressing deformations resulting from adhesive volume shrinkage-induced stress as a crucial factor in precision bonding technology. [ABSTRACT FROM AUTHOR]

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy |$P(X>t) \leq{\text{ e}}^{- I(t)}$|⁠ , where |$I: \mathbb{R} \rightarrow \mathbb{R}$| is an increasing function and |$I(t)/t \rightarrow \alpha \in [0, \infty)$| as |$t \rightarrow \infty $|⁠. Our main theorem can not only recover some of the existing results, such as the concentration of the sum of sub-Weibull random variables, but it can also produce new results for the sum of random variables with heavier tails. We show that the concentration inequalities we obtain are sharp enough to offer large deviation results for the sums of independent random variables as well. Our analyses which are based on standard truncation arguments simplify, unify and generalize the existing results on the concentration and large deviation of heavy-tailed random variables. [ABSTRACT FROM AUTHOR]

Improving the bearing design helps in reducing the negative consequences related to errors in installation, manufacturing, deflections under severe loading conditions, progressive wear of machine elements, and many other aspects. One of the methods of such a design improvement effort is changing the bearing profile along the bearing width to compensate for the reduction in the geometrical gap between the shaft and the bearing inner surface due to the aforementioned causes. Since in all rotating machinery, unbalance usually exists at some level, this paper deals with the response of this modified bearing to unbalanced excitation to evaluate the effectiveness of such geometrical design on the dynamic characteristics of the rotor-bearing system. The numerical solution is performed using the finite difference method by assuming Reynolds boundary conditions to determine the cavitation limits, and the 4th-order Range-Kutta method is used to determine the time responses resulting from the unbalance excitation. The time responses to this type of excitation show that the rotor-bearing with the improved geometrical design is more stable, particularly at high speeds. In addition, this modification leads to an improvement in the lubricant layer thickness and the reduction in the levels of the generated pressure between the surfaces despite the presence of large deviations from the perfectly aligned bearing system. Furthermore, the suggested geometrical design overcomes the problem of asymmetricity in the pressure field resulting from the shaft deviation to a large extent. The results of this work (the enhancement in the level of the film thickness and the improvement in the dynamic response of the system as well as the reduction of the maximum pressure value) extend the range of misalignment in which the rotor bearing systems can operate safely which represents a significant step in designing the rotor-bearing system. [ABSTRACT FROM AUTHOR]

Hawkes process is a continuous-time stochastic model that captures temporal stochastic self-exciting phenomena. In particular, the linear Hawkes process has been well studied and widely used in practice because of its mathematical tractability. However, in some contexts, a Hawkes model is not directly applicable because data is recorded in a discrete-time scheme or an aggregated way. Thus, a discrete-time Hawkes model is appealing for applications. In this paper, we study large and moderate deviations for a discrete-time marked Hawkes process first proposed in Xu, Zhu, and Wang (2020). [ABSTRACT FROM AUTHOR]

M. Loeve wrote that "the fundamental limit theorems of Probability theory may be classified into two groups. One group deals with the problem of limit laws of sequences of some of random variables, the other deals with the problem of limits of random variables, in the sense of almost sure convergence, of such sequences. The list of topics is extensive, and it includes classical models of sums of both independent and various types of dependent random variables, probabilities of large deviations, functional limit theorems, and limit theorems for random processes, in high-dimensional spaces, for spectra of random matrices and random graphs, and more. It is assumed that the covariance structure is one of three covariance structures: (1) an independent covariance structure with the same variance, (2) an independent covariance structure with different variances, and (3) a uniform covariance structure. [Extracted from the article]

We prove a new inequality controlling the large deviations of the empirical measure of a Markov chain. This inequality is based on the martingale used by Donsker and Varadhan and the minimax theorem. It holds for convex sets and it requires to take an infimum over the starting point. In the case of a compact space, this inequality is a partial improvement of the large deviations estimates of Donsker and Varadhan. In the case of a non-compact space, we condition on the event that the process visits n times a compact subset of the space and we still obtain a control on the exponential scale. [ABSTRACT FROM AUTHOR]

We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The long memory makes clusters larger, and the asymptotic behaviour of the size of the cluster turns out to be described by the first hitting time of a randomly shifted fractional Brownian motion with drift. [ABSTRACT FROM AUTHOR]

The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random variables occurring in time interval given by a renewal process. Our result extends the one obtained in Lefevere et al. (2011) in the sense that we impose no specific dependency between the cumulated random variables and the renewal process and the proof uses Mariani and Zambotti (2014). In the companion paper Cattiaux et al. (2022) we apply this principle to Hawkes processes with inhibition. Under some assumptions Hawkes processes are indeed cumulative processes, but they do not enter the framework of Lefevere et al. (2011). [ABSTRACT FROM AUTHOR]

We introduce a nonlinear, nonhierarchical generalization of Derrida's GREM and establish through a Sanov-type large deviation analysis both a Boltzmann–Gibbs principle as well as a Parisi formula for the limiting free energy. In line with the predictions of the Parisi theory, the free energy is given by the minimal value over all Parisi functionals/hierarchical structures in which the original model can be coarse grained. [ABSTRACT FROM AUTHOR]

This paper describes the use of experimentally validated computational fluid dynamics methods to study the similarity performance of various models scaled by the DaI criterion. First, the numerical method is validated by particle image velocimetry and CH* chemiluminescence data under the reaction state. Combustor prototypes and models are then simulated under different equivalence ratios (ERs) and swirl numbers (SWs) with the geometric scaling factor (Q) ranging from 0.1 to 1. When Q < 0.3, the reaction zone is obviously stretched. Changes in Q produce large deviations in the velocity distribution. Increasing either ER or SW increases the deviation in the velocity distribution in the outer shear region in front of the combustor but reduces that in the recirculation zone and jet zone at the back of the combustor. The scaling law changes with ER and SW. To distinguish whether the reaction flow field of a model maintains similarity with respect to the prototype, a novel concept called "degree of similarity" is proposed. The "non-similarity range" for geometric scaling factors under different conditions is further clarified. When ER = 0.55, the range of non-similarity of the combustion flow field is Q ≤ 0.3. As ER increases, the range of non-similar intervals decreases, and when ER reaches 0.95, the non-similarity range is Q ≤ 0.1. When SW = 0.42, the non-similarity range is Q ≤ 0.4, and when SW ≥ 0.42, the non-similarity range is Q ≤ 0.3. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a uniform contraction principle for verifying the uniform large deviation principles of locally Hölder continuous maps in Banach spaces. We then show the local Hölder continuity of the solutions of a class of fractional parabolic equations with polynomial drift of any order defined on ℝ n . We finally establish the large deviation principle of the fractional stochastic equations uniformly with respect to bounded initial data, despite the solution operators are not compact due to the non-compactness of Sobolev embeddings on unbounded domains. [ABSTRACT FROM AUTHOR]

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method for nonautonomous dynamics developed by [D. Dragičević, G. Froyland, C. Gonzàlez-Tokman and S. Vaienti, A spectral approach for quenched limit theorems for random expanding dynamical systems, Commun. Math. Phys.360 (2018) 1121–1187], to deal with the case of random dynamics that exhibits nonuniform decay of correlations, which are ubiquitous in the context of the multiplicative ergodic theory. [ABSTRACT FROM AUTHOR]

Stability of an affine switching system is studied. The system comes to existence when stabilizing a chain of two integrators by means of a feedback in the form of nested saturators. The use of such a feedback allows one to easily take into account boundedness of the control resource, to constrain the maximum velocity of approaching the equilibrium state, which is especially important in the case of large initial deviations, and to ensure desired characteristics of the transient process, such as a given exponential rate of the deviation decrease near the equilibrium state. It is proved that the closed-loop system is globally stable. [ABSTRACT FROM AUTHOR]

We consider the variational problem associated with the Freidlin–Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation (SHE). For a general class of initial-terminal conditions, we show that a minimizer of this variational problem exists, and any minimizer solves a system of imaginary-time Nonlinear Schrödinger equations. This system is integrable. Utilizing the integrability, we prove that the formulas from the physics work (see Alexandre Krajenbrink and Pierre Le Doussal [Phys. Rev. Lett. 127 (2021), p. 8]) hold for every minimizer of the variational problem. As an application, we consider the Freidlin–Wentzell LDP for the SHE with the delta initial condition. Under a technical assumption on the poles of the reflection coefficients, we prove the explicit expression for the one-point rate function that was predicted in the physics works (see Pierre Le Doussal, Satya N. Majumdar, Alberto Rosso, and Grégory Schehr [Phys. Rev. Lett. 117 (2016), p. 070403]; Alexandre Krajenbrink and Pierre Le Doussal [Phys. Rev. Lett. 127 (2021), p. 8]). Under the same assumption, we give detailed pointwise estimates of the most probable shape in the upper-tail limit. [ABSTRACT FROM AUTHOR]

We derive the short-maturity asymptotics for option prices in the local volatility model in a new short-maturity limit T → 0 at fixed ρ = (r − q) T , where r is the interest rate and q is the dividend yield. In the case of practical relevance ρ being small, however, our result holds for any fixed ρ. The result is a generalization of the Berestycki–Busca–Florent formula (Berestycki et al., 2002) [Asymptotics and calibration of local volatility models, Quantitative Finance 2, 61–69] for the short-maturity asymptotics of the implied volatility which includes interest rates and dividend yield effects of O (((r − q) T) n) to all orders in n. We obtain the analytical results for the ATM volatility and skew in this asymptotic limit. Explicit results are derived for the CEV model. The asymptotic result is tested numerically against the exact evaluation in the square-root model σ (S) = σ ∕ S , which demonstrates that the new asymptotic result is in very good agreement with the exact evaluation in a wide range of model parameters relevant for practical applications. [ABSTRACT FROM AUTHOR]

We consider the multiparameter random simplicial complex as a higher dimensional extension of the classical Erdős–Rényi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large deviations. We first study upper tail large deviation probabilities for subcomplex counts, deriving the order of magnitude of such probabilities at the logarithmic scale precision. The obtained results are then applied to analyze large deviations for the number of simplices of the multiparameter simplicial complexes. Finally, these results are also used to deduce large deviation estimates for Betti numbers of the complex in the critical dimension. [ABSTRACT FROM AUTHOR]

Temperature is one important factor which decides the assembly accuracy and reliability of the aircraft. Especially with the development of large-sized aircraft, the small temperature change in the aircraft assembly will result in a large displacement deviation and non-negligible internal stress. Therefore, it's crucial to characterize and predict the temperature during the assembly process of aircraft. Selecting one type of assembly frame for aircraft wing as the study object, temperature in this structure was measured and recorded for one year. Based on the measured data, a model of an optimized BP neural network is proposed to analyze and predict the temperature distribution. The trained temperature model shows a good result with a relative error of 1% and an absolute error of 2 ∘ C. Finally, the displacement of assembly frame is obtained from the temperature distribution. [ABSTRACT FROM AUTHOR]

We present a new implementation of a trust-region augmented Hessian approach (TRAH-SCF) for restricted and unrestricted Hartree–Fock and Kohn–Sham methods. With TRAH-SCF, convergence can always be achieved even with tight convergence thresholds, which requires just a modest number of iterations. Our convergence benchmark study and our illustrative applications focus on open-shell molecules, also antiferromagnetically coupled systems, for which it is notoriously complicated to converge the Roothaan–Hall self-consistent field (SCF) equations. We compare the number of TRAH iterations to reach convergence with those of Pulay's original and Kollmar's (K) variants of the direct inversion of the iterative subspace (DIIS) method and also analyze the obtained SCF solutions. Often, TRAH-SCF finds a symmetry-broken solution with a lower energy than DIIS and KDIIS. For unrestricted calculations, this is accompanied by a larger spin contamination, i.e., larger deviation from the desired spin-restricted ⟨S2⟩ expectation value. However, there are also rare cases in which DIIS finds a solution with a lower energy than KDIIS and TRAH. In rare cases, both TRAH-SCF and KDIIS may also converge to a non-aufbau solution. For those calculations, standard DIIS always diverges. For cases that converge smoothly with either method, TRAH usually needs more iterations to converge than DIIS and KDIIS because for every new set of orbitals, the level-shifted Newton–Raphson equations are solved approximately and iteratively. In such cases, the total runtime of TRAH-SCF is still competitive with the DIIS-based approaches even if extended basis sets are employed, which is illustrated for a large hemocyanin model complex. [ABSTRACT FROM AUTHOR]