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Abstract: In a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than x whose prime factors are less than y are asymptotically equidistributed in arithmetic progressions to modulus q, provided that and that y is neither too large nor too small compared with x. We show that these latter restrictions on y are unnecessary, thereby proving a conjecture of Soundararajan. Our argument uses a simple majorant principle for trigonometric sums to handle a saddle point that is close to 1. [Copyright &y& Elsevier]

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders' shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli's equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research. • Vibration analysis of fluid-filled ring-stiffened conical shells. • Finite element method for hydroelastic stability of conical shell. • The solid model based on Sanders' shell theory. • Fluid pressure is expressed using velocity potential and Bernoulli's equation. • Natural frequency is determined for different boundary conditions and geometries. [ABSTRACT FROM AUTHOR]

• A piezoelectric combined cantilever-asymmetric-pendulum structure is proposed. • Can efficiently harvest vibratory energy from any arbitrary direction. • Numerical analysis presented as well as simulation conducted to validate theory and proposed model. • The improvement of the voltage amplitude and operational bandwidth are 128.5 % and 229.8 % over variable excitation amplitudes, respectively. This paper introduces a novel approach to address the challenges faced by traditional unidirectional cantilever-based energy harvesters in adapting to multi-directional vibration environments. The proposed solution combines a flexible cantilever with an asymmetric-conical-pendulum structure which consists of two different concentrated end masses and a rigid thin rod By investigation of energy interchange relationship between the kinetic feature of the asymmetric pendulum and beam bending vibration under horizontal and vertical excitations respectively from base movements, utilizing the Lagrange's theorem and multiple-scale method, 1:2 internal resonance can be induced for enabling the delivery of multi-directional motion of pendulums to the unidirectional bending of cantilever. On this basis, the advantages of the proposed system are revealed by comparing with traditional piezoelectric cantilever and piezoelectric cantilever-single-pendulum systems. Furthermore, the performance of the voltage amplitude and operational bandwidth was potentially improved up to 128.5 % and 229.8 % under x -direction. In addition, it is confirmed that its maximum voltage RMS value is 57.9 % and 11.4 % higher than that of the piezoelectric cantilever-single-pendulum in the x - and z -directions, owing to its multi-peak energy harvesting over variable excitation amplitudes. Therefore, the feasibility and superiorities of the proposed configuration are demonstrated theoretically and numerically in this paper. [ABSTRACT FROM AUTHOR]

• Novel bidirectional full-duplex transmitting WDM-PON over single SSMF is proposed. • SRS + FWM impact on the proposed system performance is evaluated. • SXR-input power, SXR-channel spacing, SXR-channel length variations are simulated. • Results show a reliable communication with the system under SRS + FWM impact. • Proposed system and analyses are important for 5G and beyond fronthaul networks. Wavelength division multiplexing (WDM) is an important method in modern optical communication systems for both long-haul and access networks. Particularly, after being standardized by Telecommunication Standardization Sector of International Telecommunication Union (ITU-T), WDM passive optical network (WDM-PON) becomes a considerable choice for fronthaul implementations of 5G networks. Stimulated Raman scattering (SRS) and four-wave mixing (FWM) are crucial nonlinear impacts that significantly limit the performance of WDM-based optical fiber communication systems. In this paper, an ultra-dense/dense WDM-PON (UDWDM/DWDM-PON) architecture has been proposed and combined dual impact of SRS and FWM on performances of upstream channels (USCs) and downstream channels (DSCs) of the proposed UDWDM/DWDM-PON has been numerically analyzed. USCs have been assumed to operate in 1310 nm region while operating wavelength region of DSCs has been taken as 1550 nm. Simulations have been performed on both UDWDM-PON architectures with 3.125 GHz and 6.25 GHz channel spacings and DWDM-PON architectures with channel spacings between 12.5 GHz and 100 GHz. 2x15-channel and 2x63-channel system structures have been considered in simulations. Signal-to-crosstalk ratio (SXR) has been chosen as performance parameter and its variation with channel input powers, channel spacings and channel lengths have been simulated for both USCs and DSCs of 2x15- and 2x63-channel UDWDM/DWDM-PONs. Results show that the proposed UDWDM/DWDM-PONs using single G.652 fiber can exhibit a reliable communication with minimum 23 dB SXR performance under combined dual impact of SRS and FWM unless some highlights about input powers and channel lengths mentioned in the paper are neglected. [ABSTRACT FROM AUTHOR]

The paper discusses a choice of minimal model for describing friction induced vibrations in systems with sealings between the moving and non-moving part. Two models, a classical "mass-on-belt" system and a two-mass model are compared. The parameter study shows that the two-mass model has much better agreement with the practical experiences than the mass-on-belt system. The paper includes the description of the models, the results of numerical analysis and some considerations about the restriction of friction-induced vibrations. [ABSTRACT FROM AUTHOR]

[Display omitted] • Simplify and derive the formulae based on TRL theory and computer programs to demonstrate the relation between parameters. • Derived from the relation of ε' and ε'', a criterion is established to decide what parameters have the possibility of absorbing performance. • A new fitting method is utilized to construct the relation between permittivity and content of absorber. Non-magnetic materials show a great potentiality in microwave absorption with the advantages of low-density, wideband, and thin thickness. Even so, it is still difficult to accurately analyze the connection between performance and parameters. To reveal what electromagnetic parameters could lead to excellent absorbing performance, we simplify and derive the formulae based on Transmission-Reflection-Line theory (TRL) and computer programs. Based on the relation of ε' and ε'', a criterion is established to decide what parameters have the possibility of absorbing performance. Using a new fitting method, the relationship between dielectric constant and absorber content is established. Further, an instruction derived from the relation between ε' and p is used to screen thicknesses. The optimum permittivity of ultra-low reflectivity and ultra-wide band is obtained by combining the numerical analysis results. To verify the accuracy and reliability of results and deductions, the permittivity of four prepared materials and fifty published papers are investigated. [ABSTRACT FROM AUTHOR]

• The paper at hand shows how structural damping and stiffness parameters in shrunk joints can be determined by a generic joint experiment. • With thin layer elements these parameters from the joint experiment are coupled to the structures Finite Element Model. • Equivalent modal damping factors can be determined by performing a complex numerical modal analysis, by which the stability of the rotor can be tested. • The two disc rotor is examined as an application sample. • This rotor consists of a shaft with two shrunk-on discs. • With the above mentioned approach, and by considering structural damping added to material damping, the modal damping of the first torsional eigenfrequency is calculated and then compared to the results of an experimental modal analysis. • The paper shows that the presented approach leads to a reliable approximation of the examined structure's dissipation properties. • It serves as a prediction tool for the response behavior of a turbo-generator. The paper at hand shows how structural damping and stiffness parameters in shrunk joints can be determined by a generic joint experiment. With thin layer elements these parameters from the joint experiment are coupled to the structures Finite Element Model. Equivalent modal damping factors can be determined by performing a complex numerical modal analysis, by which the stability of the rotor can be tested. The two disc rotor is examined as an application sample. This rotor consists of a shaft with two shrunk-on discs. With the above mentioned approach, and by considering structural damping added to material damping, the modal damping of the first torsional eigenfrequency is calculated and then compared to the results of an experimental modal analysis. The paper shows that the presented approach leads to a reliable approximation of the examined structure's dissipation properties. It serves as a prediction tool for the response behavior of a turbo-generator. [ABSTRACT FROM AUTHOR]

Abstract A novel 5th-order shock capturing scheme is presented in this paper. The scheme, so-called P 4 T 2 − BVD (polynomial of 4-degree and THINC function of 2-level reconstruction based on BVD algorithm), is formulated as a two-stage spatial reconstruction scheme following the BVD (Boundary Variation Diminishing) principle that minimizes the jumps of the reconstructed values at cell boundaries. In the P 4 T 2 − BVD scheme, polynomial of degree four and THINC (Tangent of Hyperbola for INterface Capturing) functions with two-level steepness are used as the candidate reconstruction functions. The final reconstruction function is selected through the two-stage BVD algorithm so as to effectively control both numerical oscillation and dissipation. Spectral analysis and numerical verifications show that the P 4 T 2 − BVD scheme possesses the following desirable properties: 1) it effectively suppresses spurious numerical oscillation in the presence of strong shock or discontinuity; 2) it substantially reduces numerical dissipation errors; 3) it automatically retrieves the underlying linear 5th-order upwind scheme for smooth solution over all wave numbers; 4) it is able to resolve both smooth and discontinuous flow structures of all scales with substantially improved solution quality in comparison to other existing methods; and 5) it produces accurate solutions in long term computation. P 4 T 2 − BVD , as well as the underlying idea presented in this paper, provides an innovative and practical approach to design high-fidelity numerical schemes for compressible flows involving strong discontinuities and flow structures of wide range scales. Highlights • An innovative fifth-order shock capturing scheme is proposed. • Low-dissipation linear scheme is retrieved for smooth solution over all wave numbers. • Discontinuous and smooth solution of wide-band scales are simultaneously solved with high accuracy. • The free-mode solutions are faithfully maintained in long term computation. [ABSTRACT FROM AUTHOR]

Highlights • Construct special techniques to preserve two bounds without using the maximum-principle-preserving technique. • Treat the time derivative of the pressure as a source of the concentration equation. • Apply the algorithm on unstructured meshes. • In the flux limiter, use the second-order flux as the lower-order one. • Use L2-projection of the porosity and construct special limiters that suitable for multi-component fluid mixtures. Abstract In this paper, we develop high-order bound-preserving (BP) discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacements on triangular meshes. We consider the problem with multi-component fluid mixture and the (volumetric) concentration of the j th component, c j , should be between 0 and 1. There are three main difficulties. Firstly, c j does not satisfy a maximum-principle. Therefore, the numerical techniques introduced in Zhang and Shu (2010) [44] cannot be applied directly. The main idea is to apply the positivity-preserving techniques to all c j ′ s and enforce ∑ j c j = 1 simultaneously to obtain physically relevant approximations. By doing so, we have to treat the time derivative of the pressure d p / d t as a source in the concentration equation and choose suitable fluxes in the pressure and concentration equations. Secondly, it is not easy to construct first-order numerical fluxes for interior penalty DG methods on triangular meshes. One of the key points in the high-order BP technique applied in this paper is the combination of high-order and lower-order numerical fluxes. We will construct second-order BP schemes and use the second-order numerical fluxes as the lower-order one. Finally, the classical slope limiter cannot be applied to c j. To construct the BP technique, we will not approximate c j directly. Therefore, a new limiter will be introduced. Numerical experiments will be given to demonstrate the high-order accuracy and good performance of the numerical technique. [ABSTRACT FROM AUTHOR]

Abstract Spatially distributed networks of large size arise in a variety of science and engineering problems, such as wireless sensor networks and smart power grids. Most of their features can be described by properties of their state-space matrices whose entries have indices in the vertex set of a graph. In this paper, we introduce novel algebras of Beurling type that contain matrices on a connected simple graph having polynomial off-diagonal decay, and we show that they are Banach subalgebras of B (ℓ p) , 1 ≤ p ≤ ∞ , the space of all bounded operators on the space ℓ p of all p -summable sequences. The ℓ p -stability of state-space matrices is an essential hypothesis for the robustness of spatially distributed networks. In this paper, we establish the equivalence among ℓ p -stabilities of matrices in Beurling algebras for different exponents 1 ≤ p ≤ ∞ , with quantitative analysis for the lower stability bounds. Admission of norm-control inversion plays a crucial role in some engineering practice. In this paper, we prove that matrices in Beurling subalgebras of B (ℓ 2) have norm-controlled inversion and we find a norm-controlled polynomial with close to optimal degree. Polynomial estimate to powers of matrices is important for numerical implementation of spatially distributed networks. In this paper, we apply our results on norm-controlled inversion to obtain a polynomial estimate to powers of matrices in Beurling algebras. The polynomial estimate is a noncommutative extension about convolution powers of a complex function and is applicable to estimate the probability of hopping from one agent to another agent in a stationary Markov chain on a spatially distributed network. [ABSTRACT FROM AUTHOR]

Abstract Let k ˜ be a cubic extension of Q. For quadratic fields F , let L = F ⋅ k ˜. In this paper and its companion paper, we prove that with a certain cohomological invariant i (F) , lim X → ∞ ⁡ X − 2 ∑ 0 < ± Δ F < X h L R L (h F R F) − 1 (1 + i (F) − 1) converges to a positive constant which is given by an Euler product. [ABSTRACT FROM AUTHOR]

From spline theory it is well-known that univariate cubic spline interpolation, if carried out in its natural Hilbert space W 2 2 [ a , b ] and on point sets with fill distance h , converges only like O ( h 2 ) in L 2 [ a , b ] if no additional assumptions are made. But superconvergence up to order h 4 occurs if more smoothness is assumed and if certain additional boundary conditions are satisfied. This phenomenon was generalized in 1999 to multivariate interpolation in Reproducing Kernel Hilbert Spaces on domains Ω ⊂ R d for continuous positive definite Fourier-transformable shift-invariant kernels on R d . But the sufficient condition for superconvergence given in 1999 still needs further analysis, because the interplay between smoothness and boundary conditions is not clear at all. Furthermore, if only additional smoothness is assumed, superconvergence is numerically observed in the interior of the domain, but a theoretical foundation still is a challenging open problem. This paper first generalizes the “improved error bounds” of 1999 by an abstract theory that includes the Aubin–Nitsche trick and the known superconvergence results for univariate polynomial splines. Then the paper analyzes what is behind the sufficient conditions for superconvergence. They split into conditions on smoothness and localization , and these are investigated independently. If sufficient smoothness is present, but no additional localization conditions are assumed, it is numerically observed that superconvergence always occurs in the interior of the domain, and some supporting arguments are provided. If smoothness and localization interact in the kernel-based case on R d , weak and strong boundary conditions in terms of pseudodifferential operators occur. A special section on Mercer expansions is added, because Mercer eigenfunctions always satisfy the sufficient conditions for superconvergence. Numerical examples illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

When studying non-symmetric nonlocal operators on R d : L f ( x ) = ∫ R d ( f ( x + z ) − f ( x ) − ∇ f ( x ) ⋅ z 1 { | z | ⩽ 1 } ) κ ( x , z ) | z | d + α d z , where 0 < α < 2 , d ⩾ 1 , and κ ( x , z ) is a function on R d × R d that is bounded between two positive constants, it is customary to assume that κ ( x , z ) is symmetric in z . In this paper, we study heat kernel of L and derive its two-sided sharp bounds without the symmetric assumption κ ( x , z ) = κ ( x , − z ) . In fact, we allow the kernel κ to be time-dependent and x → κ ( t , x , z ) to be only locally β -Hölder continuous with Hölder constant possibly growing at a polynomial rate in | z | . We also derive gradient estimate when β ∈ ( 0 ∨ ( 1 − α ) , 1 ) as well as fractional derivative estimate of order θ ∈ ( 0 , ( α + β ) ∧ 2 ) for the heat kernel. Moreover, when α ∈ ( 1 , 2 ) , drift perturbation of the time-dependent non-local operator L t with drift in Kato's class is also studied in this paper. As an application, when κ ( x , z ) = κ ( z ) does not depend on x , we show the boundedness of nonlocal Riesz's transformation: for any p > 2 d / ( d + α ) , ‖ L 1 / 2 f ‖ p ≍ ‖ Γ ( f ) 1 / 2 ‖ p , where Γ ( f ) : = 1 2 L ( f 2 ) − f L f is the carré du champ operator associated with L , and L 1 / 2 is the square root operator of L defined by using Bochner's subordination. Here ≍ means that both sides are comparable up to a constant multiple. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the global well-posedness and decay rates of strong solutions for the three-dimensional compressible Oldroyd-B model. We prove that this set of equations admits a unique global strong solution provided the initial data are close to the constant equilibrium state in H 2 -framework. Moreover, if the initial data belong to L 1 , the convergence rate of the solutions in L p -norm with 2 ⩽ p ⩽ 6 and convergence rates of their spatial derivatives in L 2 -norm are obtained. It is noteworthy that the smallness restriction on the coupling constant ω is not necessary in this paper. [ABSTRACT FROM AUTHOR]

In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are rational functions). Along with some general results, a thorough analysis of the particular case of two fixed negative charges (“attractors”) is presented; indeed, the main result of the paper deals with this particular case. As for the main tools used, this paper is a natural continuation of [31] , where polynomial external fields were thoroughly studied, and [37] , where rational external fields with a polynomial part were considered. However, the absence of the polynomial part in the external fields analyzed in the current paper adds a considerable difficulty to solve the problem and justifies its separated treatment; moreover, it is noteworthy to point out the simplicity and beauty of the results obtained. [ABSTRACT FROM AUTHOR]

A new definition of entropy fluctuation is provided in this paper, that allows properly separating entropy and mixture composition fluctuations. This decomposition into linearly independent variables prevents from overestimating compositional noise in indirect noise prediction. When considering quasi one-dimensional flow in nozzles, a new resulting system of linearized Euler equations is obtained. Two analytical solutions of this system of equations are investigated in this study, one dedicated to low-frequency perturbations and another one for all frequency perturbations. This new theory is then validated by comparing the model predictions with direct numerical simulation of nozzle flows in which composition fluctuations are pulsed. To do so, new Navier–Stokes characteristics boundary conditions to account for the new properly defined entropy wave are provided. Furthermore, non-reflecting inlet boundary conditions have been newly derived, relaxing on the axial mass-flow rate, static temperature and species mass fractions. Finally, a parametric study based on an air-kerosene (equivalent C 10 H 20 ) mixture and an ideal framework shows that composition noise can reach a maximum of 10% of entropy noise for lean combustion and choked nozzle while for rich combustion, composition noise and entropy noise show comparable levels. [Display omitted] • New entropy noise decomposition that prevents overestimation of the compositional part of indirect combustion noise. • New system of linearized equations that characterize indirect combustion noise. • New non-reflecting Navier–Stokes boundary conditions for pulsing species mass factions fluctuations. [ABSTRACT FROM AUTHOR]

HPL-AI, also known as HPL-MxP, is a new benchmark program used to evaluate the upper-bound performance of AI-related tasks on a specific computing cluster. It solves a large linear equation system in FP64, preconditioned by complete LU factorization in lower precision. In this paper, we propose a new HPL-AI approach that relies on the factorization of the coefficient matrix in mixed precision: FP32 diagonals and FP16 off-diagonals. Without compromising the quality of the resultant LU preconditioner, the proposed approach only utilizes the primitive of dense matrix multiplication in FP16 on the accelerator, maximizing the FP16 throughput. Numerical analysis and experiments validate our approach, ensuring avoidance of numerical underflow or overflow during factorization. We implement the proposed approach on Kunpeng+Ascend clusters, a novel AI-specific platform with exceedingly high FP16 peak performance. By applying various optimization techniques, including 2D lookahead, HCCL-based communication pipeline, and SYCL-based tasks overlapping, we achieve 975 TFlops on a single node and nearly 100 PFlops on a cluster of 128 nodes, with a weak scalability of 79.8%. • First-time adaptation and optimization of HPL-AI on the Kunpeng+Ascend platform. • A novel approach for mixed-precision LU: FP32 diagonals and FP16 off-diagonals. • Over/underflow avoidance: error analysis and magnitude estimation of HPL-AI LU. • On a single node, 8 Ascend 910A Pro AI accelerators achieve 42.3% HPL-AI efficiency. • On a 128-node cluster: 98.9 PFlops HPL-AI performance and 79.8% weak scalability. [ABSTRACT FROM AUTHOR]

This paper deals with the implementation of high order semi-Lagrangian particle methods to handle high dimensional Vlasov–Poisson systems. It is based on recent developments in the numerical analysis of particle methods and the paper focuses on specific algorithmic features to handle large dimensions. The methods are tested with uniform particle distributions in particular against a recent multi-resolution wavelet based method on a 4D plasma instability case and a 6D gravitational case. Conservation properties, accuracy and computational costs are monitored. The excellent accuracy/cost trade-off shown by the method opens new perspective for accurate simulations of high dimensional kinetic equations by particle methods. [ABSTRACT FROM AUTHOR]

Text A set A of nonnegative integers is said to be complete if every sufficiently large natural number is the sum of distinct terms taken from A . In 1959, Birch confirmed a conjecture of Erdős by proving that the set { p n q m : n , m = 0 , 1 , … } is complete, where p and q are two coprime integers greater than 1. In this paper, we study extensively the set P ( S p 1 , … , p r ) of all vectors ( m 1 , … , m r ) with integer coordinates which can be represented as ∑ ( p 1 α 1 , … , p r α r ) , where p 1 , … , p r are integers greater than 1 and α 1 , … , α r are nonnegative integers. We find many regular parts in P ( S p 1 , … , p r ) , for example, discrete rectangles. To study the problem, we find a new matching principle. Video For a video summary of this paper, please visit https://youtu.be/qXUe1E4jlLQ . [ABSTRACT FROM AUTHOR]

Text Let k , l , a , b , c be positive integers such that gcd ⁡ ( k a , l b ) = 1 , min ⁡ { a , b , c } > 1 , a ≠ 3 , b ≠ 3 and 2 ∤ c . In this paper, we prove that there are at most four solutions in positive integers ( x , y , z ) to the equation k a x + l b y = c z and at most two solutions when 2 ∤ ( u ( l / k ) ) , where u ( m ) is the least positive integer t with m t ≡ 1 ( mod c ) . Video For a video summary of this paper, please visit https://youtu.be/Dt3Y7TDMxlg . [ABSTRACT FROM AUTHOR]

The paper revisits the classical problem of evaluating f ( A ) for a real function f and a matrix A with real spectrum. The evaluation is based on expanding f in Chebyshev polynomials, and the focus of the paper is to study the convergence rates of these expansions. In particular, we derive bounds on the convergence rates which reveal the relation between the smoothness of f and the diagonalizability of the matrix A . We present several numerical examples to illustrate our analysis. [ABSTRACT FROM AUTHOR]

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper. [ABSTRACT FROM AUTHOR]

Modal Identification from Frequency Response Functions (FRFs) has been extensively investigated up to the point its research reached a stagnation state. Yet, a new approach to determine the modal damping factors from FRFs was recently proposed, showing that there still is scope for new findings in the field. Contrary to other modal identification methods which are based on the dynamic motion governing equations, the method used the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produced quite accurate results, especially when compared to the well-known method of the inverse. The method used a plot of the sine of the phase of the receptance against its amplitude, whereby damping was determined from the slope of a linear fit to the resulting plot. In this paper, it is shown that this plot has other (perhaps more important) special properties that were not explored before. Near resonant frequencies, its shape is elliptical, whereby the real and imaginary parts of the modal constants can be determined from numerical curve-fitting. This finding allowed developing a new method which formulation is presented in this paper. The method is discussed through numerical and experimental examples. Although the intention is not to present a new modal identification method that is superior to other existing ones (like the method of the inverse or those based on the Nyquist plot), the authors believe that this new representation of the receptance and its properties may bring valuable insights for other researchers in the field. [ABSTRACT FROM AUTHOR]

The paper presents several results that address a fundamental question in low-rank matrix recovery: how many measurements are needed to recover low-rank matrices? We begin by investigating the complex matrices case and show that 4 n r − 4 r 2 generic measurements are both necessary and sufficient for the recovery of rank- r matrices in C n × n . Thus, we confirm a conjecture which is raised by Eldar, Needell and Plan for the complex case. We next consider the real case and prove that the bound 4 n r − 4 r 2 is tight provided n = 2 k + r , k ∈ Z + . Motivated by Vinzant's work [19] , we construct 11 matrices in R 4 × 4 by computer random search and prove they define injective measurements on rank-1 matrices in R 4 × 4 . This disproves the conjecture raised by Eldar, Needell and Plan for the real case. Finally, we use the results in this paper to investigate the phase retrieval by projection and show fewer than 2 n − 1 orthogonal projections are possible for the recovery of x ∈ R n from the norm of them, which gives a negative answer for a question raised in [1] . [ABSTRACT FROM AUTHOR]

An accurate and predictive modelling of slug flows is required by many industries (e.g., oil and gas, nuclear engineering, chemical engineering) to prevent undesired events potentially leading to serious environmental accidents. For example, the hydrodynamic and terrain-induced slugging leads to unwanted unsteady flow conditions. This demands the development of fast and robust numerical techniques for predicting slug flows. The presented in this paper study proposes a multi-fluid model and its implementation method accounting for phase appearance and disappearance. The numerical modelling of phase appearance and disappearance presents a complex numerical challenge for all multi-component and multi-fluid models. Numerical challenges arise from the singular systems of equations when some phases are absent and from the solution discontinuity when some phases appear or disappear. This paper provides a flexible and robust solution to these issues. A fully implicit formulation described in this work enables to efficiently solve governing fluid flow equations. The proposed numerical method provides a modelling capability of phase appearance and disappearance processes, which is based on switching procedure between various sets of governing equations. These sets of equations are constructed using information about the number of phases present in the computational domain. The proposed scheme does not require an explicit truncation of solutions leading to a conservative scheme for mass and linear momentum. A transient two-fluid model is used to verify and validate the proposed algorithm for conditions of hydrodynamic and terrain-induced slug flow regimes. The developed modelling capabilities allow to predict all the major features of the experimental data, and are in a good quantitative agreement with them. [ABSTRACT FROM AUTHOR]

[Display omitted] • We have developed a novel workflow to clean up the cryo-electron microscopy datasets directly at the 3D level. • We introduce a modular framework that emphasizes various facets of encoder design for the amortized inference of hidden variables in cryo-electron microscopy image processing. • Our introduced uncertainty measure offers a method to quantify the confidence level of our estimations. • Utilizing contrastive learning significantly bolsters the robustness of orientation estimation. • Incorporating preprocessing layers and employing curriculum learning bolster neural network performance in orientation estimation. In single-particle cryo-electron microscopy (cryo-EM), efficient determination of orientation parameters for particle images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels in the datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel method using a 10-dimensional feature vector for orientation representation, extracting orientations as unit quaternions with an accompanying uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Notably, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum , designed for easy access by developers. [ABSTRACT FROM AUTHOR]

The paper focuses on the analysis of an industrial ceramic kiln in order to improve the energy efficiency and thus the fuel consumption and the corresponding carbon dioxide emissions. A lumped and distributed parameter model of the entire system is constructed to simulate the performance of the kiln under actual operating conditions. The model is able to predict accurately the temperature distribution along the different modules of the kiln and the operation of the many natural gas burners employed to provide the required thermal power. Furthermore, the temperature of the tiles is also simulated so that the quality of the final product can be addressed by the modelling. Numerical results are validated against experimental measurements carried out on a real ceramic kiln during regular production operations. The developed numerical model demonstrates to be an efficient tool for the investigation of different design solutions for the kiln's components. In addition, a number of control strategies for the system working conditions can be simulated and compared in order to define the best trade off in terms of fuel consumption and product quality. In particular, the paper analyzes the effect of a new burner type characterized by internal heat recovery capability aimed at improving the energy efficiency of the ceramic kiln. The fuel saving and the relating reduction of carbon dioxide emissions resulted in the order of 10% when compared to the standard burner. [ABSTRACT FROM AUTHOR]

Solving acoustic equations in the time domain, possibly coupled with the description of flexible structure dynamics, remains attractive as compared to solving the same in the frequency domain: this allows for better consideration of local non-linearities (acoustics/structure), and the boundary integral formulation (also known as BEM) offers an exact description of the infinite acoustic field based on a simple surface mesh (no need for 3D-volume discretization). Some issues remain however: the required memory space and computation time continue to grow rapidly when the number of elements of the surface mesh increases. In the case of a structure with a regular non-slender shape, the computational cost, measured in terms of required memory space, varies by Helmholtz number to the power of 4. This paper illustrates how the accelerating method called NGTD helps overcome this difficulty. This paper shows the applicability of 2 level NGTD to acoustic and vibroacoustic problems described solely by the hypersingular formulation for surfaces. It goes into more detail on some important aspects of the interpolation process and on the memory saving obtained. Implementation within the MOT (“March-On-Time”) ASTRYD code shows the benefits of this method. The memory requirement shows an estimated trend lower than power 1.35 of the number of surface elements. [ABSTRACT FROM AUTHOR]

This paper constitutes the advantages of using the weighted Sobolev and weighted Lebesgue spaces in optimal control problems defined on an infinite time interval. Based on numerous examples, it demonstrates how the introduction of certain weight or density functions into the problem statement may influence the existence of an optimal solution and the optimality of a chosen candidate. The positive effects of the proper relation between the state and the co-state functional spaces for the necessary optimality conditions as well as for the development of numerical schemes are discussed. This paper is based on over one decade of research in this field and summarizes the main findings concerning the use of weight functions in optimal control problems. [ABSTRACT FROM AUTHOR]

As a generalization of cyclic codes, constacyclic codes is an important and interesting class of codes due to their nice algebraic structures and various applications in engineering. This paper is devoted to the study of the q -polynomial approach to constacyclic codes. Fundamental theory of this approach will be developed, and will be employed to construct some families of optimal and almost optimal codes in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a one-parameter family of economical formulas is identified that does not require second derivatives of the source term. Among the economical formulas, a unique formula is then derived that does not require gradients of the source term at neighbor nodes, thus leading to a significantly smaller discretization stencil for source terms. All the formulas derived in this paper do not require a boundary closure, and therefore can be directly applied at boundary nodes. Numerical results are presented to demonstrate third-order accuracy at interior and boundary nodes for one-dimensional grids and linear triangular/tetrahedral grids over straight and curved geometries. [ABSTRACT FROM AUTHOR]

The dynamic response of disks has been deeply studied in the last years given that their dynamic characteristics present similarities with more complex disk-like structures used in real engineering applications, such as hydraulic turbine runners. Because of disk-like structures could present fatigue damage or critical failures as a result of resonance conditions, it is of paramount importance to determine their natural frequencies. The dynamic response of disk-like structures is heavily affected by the added mass effect when they are surrounded by a heavy fluid. This added mass is greatly affected by the proximity of walls. Furthermore, the surrounding fluid cavity has its own natural frequencies and mode shapes, called acoustic natural frequencies and acoustic mode-shapes. All studies of submerged and confined disks have been carried out considering that the acoustic natural frequencies of the surrounding fluid cavity are much higher than the natural frequencies of the disk, so they do not affect each other. However, in some cases the acoustic natural frequencies are close to the natural frequencies of the submerged structure, which can be affected considerably. This case has not been deeply discussed yet. In this paper, the influence of the acoustic natural frequencies of a cylindrical fluid cavity on the natural frequencies of a disk has been analysed numerically. First, the effect of the added mass of the fluid has been estimated when the acoustic natural frequencies of the fluid cavity are much higher than the natural frequencies of the disk. For this case, different geometrical and material parameters have been considered. Then, the parameters that affect the acoustical natural frequencies of the fluid cavity have been identified. Finally, the case with acoustic natural frequencies close to the structural natural frequencies is studied in detail and the affectation between both is discussed. All the results presented in this paper have been dimensionless in order to be used for a wide range of disk-like structures. Therefore, with this study it is possible to identify for which conditions the dynamic response of a generic disk-like structure will be affected by the acoustic natural frequencies of its surrounding fluid cylindrical cavity. [ABSTRACT FROM AUTHOR]

Because of several successful applications, indefinite kernels have attracted many research interests in recent years. This paper addresses indefinite learning in the framework of least squares support vector machines (LS-SVM). Unlike existing indefinite kernel learning methods, which usually involve non-convex problems, the indefinite LS-SVM is still easy to solve, but the kernel trick and primal-dual relationship for LS-SVM with a Mercer kernel is no longer valid. In this paper, we give a feature space interpretation for indefinite LS-SVM. In the same framework, kernel principal component analysis with an infinite kernel is discussed as well. In numerical experiments, LS-SVM with indefinite kernels for classification and kernel principal component analysis is evaluated. Its good performance together with the feature space interpretation given in this paper imply the potential use of indefinite LS-SVM in real applications. [ABSTRACT FROM AUTHOR]

Most commonly used distributions on the unit hypersphere S k − 1 = { v ∈ R k : v ⊤ v = 1 } , k ≥ 2 , assume that the data are rotationally symmetric about some direction θ ∈ S k − 1 . However, there is empirical evidence that this assumption often fails to describe reality. We study in this paper a new class of skew-rotationally-symmetric distributions on S k − 1 that enjoy numerous good properties. We discuss the Fisher information structure of the model and derive efficient inferential procedures. In particular, we obtain the first semi-parametric test for rotational symmetry about a known direction. We also propose a second test for rotational symmetry, obtained through the definition of a new measure of skewness on the hypersphere. We investigate the finite-sample behavior of the new tests through a Monte Carlo simulation study. We conclude the paper with a discussion about some intriguing open questions related to our new models. [ABSTRACT FROM AUTHOR]

Some recent papers deal with smooth nonparametric estimators for copula functions and copula derivatives. These papers contain results on copula-based Bernstein estimators for conditional distribution functions and related functionals such as regression and quantile functions. The focus in the present paper is on new copula-based smooth Bernstein estimators for the conditional density. Our approach avoids going through separate density estimation of numerator and denominator. Our estimator is defined as a smoother of the copula-based Bernstein estimator of the conditional distribution function. We establish asymptotic properties of bias and variance and discuss the asymptotic mean squared error in terms of the smoothing parameters. We also obtain the asymptotic normality of the new estimator. In a simulation study we show the good performance of the new estimator in comparison with other estimators proposed in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a fast time adaptive numerical method for interface tracking. The method uses an explicit multiresolution description of the interface, which is represented by wavelet vectors that correspond to the details of the interface on different scale levels. The complexity of standard numerical methods for interface tracking, where the interface is described by N marker points, is O ( N / Δ t ) , when a time step Δ t is used. The methods that we propose in this paper have O ( tol − 1 / p log ⁡ N + N log ⁡ N ) computational cost, at least for uniformly smooth problems, where tol is some given tolerance and p is the order of the time stepping method that is used for time advection of the interface. The adaptive method is robust in the sense that it can handle problems with both smooth and piecewise smooth interfaces (e.g. interfaces with corners) while keeping a low computational cost. We show numerical examples that verify these properties. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the wave propagation in a reaction-convection infectious disease model with a spatio-temporal delay. Previous numerical studies have demonstrated the existence of traveling wave fronts for the system and obtained a critical value c ⁎ , which is the minimal wave speed of the traveling waves. In the present paper, we provide a complete and rigorous proof. To overcome the difficulty due to the lack of monotonicity for the system, we construct a pair of upper and lower solutions, and then apply the Schauder fixed point theorem to establish the existence of a nonnegative solution for the wave equation on a bounded interval. Moreover, we use a limiting argument and in turn generate the solution on the unbounded interval R . In particular, by constructing a suitable Lyapunov functional, we further show that the traveling wave solution converges to the epidemic equilibrium point as t = + ∞ . [ABSTRACT FROM AUTHOR]

The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patterns – referred to as viscous fingering – may arise. Their physical and mathematical study has been the object of numerous investigations over the past century. The objective of this paper is to present a review of these contributions with particular emphasis on variational methods. These algorithms are tailored to real field applications thanks to their advanced features: handling of general complex geometries, robustness in the presence of rough tensor coefficients, low sensitivity to mesh orientation in advection dominated scenarios, and provable convergence with fully unstructured grids. This paper is dedicated to the memory of Dr. Jim Douglas Jr., for his seminal contributions to miscible displacement and variational numerical methods. [ABSTRACT FROM AUTHOR]

This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper. [ABSTRACT FROM AUTHOR]

The paper presents an alternative Vold–Kalman filter order tracking (VKF_OT) method, i.e. adaptive angular-velocity VKF_OT technique, to extract and characterize order components in an adaptive manner for the condition monitoring and fault diagnosis of rotary machinery. The order/spectral waveforms to be tracked can be recursively solved by using Kalman filter based on the one-step state prediction. The paper comprises theoretical derivation of computation scheme, numerical implementation, and parameter investigation. Comparisons of the adaptive VKF_OT scheme with two other ones are performed through processing synthetic signals of designated order components. Processing parameters such as the weighting factor and the correlation matrix of process noise, and data conditions like the sampling frequency, which influence tracking behavior, are explored. The merits such as adaptive processing nature and computation efficiency brought by the proposed scheme are addressed although the computation was performed in off-line conditions. The proposed scheme can simultaneously extract multiple spectral components, and effectively decouple close and crossing orders associated with multi-axial reference rotating speeds. [ABSTRACT FROM AUTHOR]

Using a simple one-dimensional shock problem as an example, the present paper investigates numerical properties of the original material point method (MPM), the generalized interpolation material point (GIMP) method, the convected particle domain interpolation (CPDI) method, and the dual domain material point (DDMP) method. For a weak isothermal shock of ideal gas, the MPM cannot be used with accuracy. With a small number of particles per cell, GIMP and CPDI produce reasonable results. However, as the number of particles increases the methods fail to converge and produce pressure spikes. The DDMP method behaves in an opposite way. With a small number of particles per cell, DDMP results are unsatisfactory. As the number of particles increases, the DDMP results converge to correct solutions, but the large number of particles needed for convergence makes the method very expensive to use in these types of shock wave problems in two- or three-dimensional cases. The cause for producing the unsatisfactory DDMP results is identified. A simple improvement to the method is introduced by using sub-points. With this improvement, the DDMP method produces high quality numerical solutions with a very small number of particles. Although in the present paper, the numerical examples are one-dimensional, all derivations are for multidimensional problems. With the technique of approximately tracking particle domains of CPDI, the extension of this sub-point method to multidimensional problems is straightforward. This new method preserves the conservation properties of the DDMP method, which conserves mass and momentum exactly and conserves energy to the second order in both spatial and temporal discretizations. [ABSTRACT FROM AUTHOR]

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy. [ABSTRACT FROM AUTHOR]

In this paper we present a novel method for the numerical solution of linear advection equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that ridgelet systems are well adapted to the structure of linear transport operators, it can be shown that our scheme operates in optimal complexity, even if line singularities are present in the solution. The key to this is showing that the system matrix (with diagonal preconditioning) is uniformly well-conditioned and compressible – the proof for the latter represents the main part of the paper. We conclude with some numerical experiments about N -term approximations and how they are recovered by the solver, as well as localisation of singularities in the ridgelet frame. [ABSTRACT FROM AUTHOR]

This paper presents a new approach, so-called boundary variation diminishing (BVD), for reconstructions that minimize the discontinuities (jumps) at cell interfaces in Godunov type schemes. It is motivated by the observation that diminishing the jump at the cell boundary can effectively reduce the dissipation in numerical flux. Differently from the existing practices which seek high-order polynomials within mesh cells while assuming discontinuities being always at the cell interfaces, the BVD strategy presented in this paper switches between a high-order polynomial and a jump-like reconstruction that allows a discontinuity being partly represented within the mesh cell rather than at the interface. Excellent numerical results have been obtained for both scalar and Euler conservation laws with substantially improved solution quality in comparison with the existing methods. It is shown that new schemes of high fidelity for both continuous and discontinuous solutions can be devised by the BVD guideline with properly-chosen candidate reconstruction schemes. This work provides a simple and accurate alternative of great practical significance to the current high-order Godunov paradigm which overly pursues the smoothness within mesh cells under the questionable premiss that discontinuities only appear at cell interfaces. [ABSTRACT FROM AUTHOR]

Compact difference schemes have been used extensively for solving the incompressible Navier–Stokes equations. However, the earlier formulations of the schemes are of central type (called central compact schemes, CCS), which are dispersive and susceptible to numerical instability. To enhance stability of CCS, the optimal upwind compact schemes (OUCS) are developed recently by adding high order dissipative terms to CCS. In this paper, it is found that OUCS are essentially not of the upwind type because they do not use upwind-biased but central type of stencils. Furthermore, OUCS are not the most optimal since orders of accuracy of OUCS are at least one order lower than the maximum achievable orders. New upwind compact schemes (called standard upwind compact schemes, SUCS) are developed in this paper. In contrast to OUCS, SUCS are constructed based completely on upwind-biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations. Furthermore, SUCS can achieve the maximum achievable orders of accuracy and hence be more compact than OUCS. More importantly, SUCS have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a combined numerical and experimental method, called Extended Load Confluence Algorithm, is presented to accurately predict the dynamic response of non-periodic structures when little or no information about the applied loads is available. This approach, which falls into the category of Shape Sensing methods, inputs limited experimental information acquired from sensors to a mapping algorithm that predicts the response at unmeasured locations. The proposed algorithm consists of three major cores: an experimental core for data acquisition, a numerical core based on Finite Element Method for modeling the structure, and a mapping algorithm that improves the numerical model based on a modal approach in the frequency domain. The robustness and precision of the proposed algorithm are verified through numerical and experimental examples. The results of this paper demonstrate that without a precise knowledge of the loads acting on the structure, the dynamic behavior of the system can be predicted in an effective and precise manner after just a few iterations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new multiscale representation of surfaces using tight wavelet frames. Both triangular and quadrilateral (quad) surfaces are considered. The multiscale representation for triangulated surfaces is generalized from the non-tensor-product tight wavelet frame representation of functions (of two variables) that were introduced in [1] , while the tensor-product tight frames of continuous linear B-spline from [63] are used for quad surfaces representation. As one of many possible applications of such representation, we consider surface denoising as an example at the end of the paper. We propose an analysis based surface denoising model for triangular and quad surfaces. Fast numerical algorithms are also proposed, which is different from the algorithms used in image restoration [50,52] due to the nonlinear nature of the proposed tight wavelet frame transforms on surfaces. [ABSTRACT FROM AUTHOR]

High-fidelity computation of shock-associated noise places stringent requirements on the accuracy, linear and nonlinear spectral properties of shock-capturing scheme. In this paper, a novel weighted nonlinear compact scheme with seventh-order accuracy is developed for the purpose of improving the linear and nonlinear spectral properties of original scheme (Zhang et al., (2008) [1]). The numerical fluxes at cell centers are obtained using upwind-biased weighted nonlinear interpolation based on the new S-type smoothness indicator that be constant for sine and cosine functions (Wu et al., (2020) [2]). Through systematic spectral analysis and numerical experiments, it is demonstrated that the newly proposed scheme has very weak nonlinear effect and reduces the dissipation and dispersion at the medium and high wavenumbers. The resolution for the short waves and the fine-scale structures is improved. It has the potential to become a suitable candidate for the computation of shock-associated noise. • A novel seventh-order weighted compact scheme named WCOM7S is proposed. • WCOM7S reduces the dissipation and dispersion at medium and high wavenumbers. • WCOM7S has good nonlinear spectral properties and weak nonlinear effect. [ABSTRACT FROM AUTHOR]

Periodic structures feature frequency band gaps in which the propagation of certain waves will be attenuated. Therefore, they are widely applied in the vibration control of structures. The premise of this theory is that the structure should be perfectly periodic. However, this must be broken more or less due to inevitable deviations, leading structures to disorder. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Moreover, the disorder pattern plays an important role in such a performance change. In this paper, we study the influence of the disorder patterns and explore a general permutation to retune the disordered periodic structures which means to reduce the deviation of the dynamic characteristics between the nominal and disordered structures. This research is conducted through three stages. In the first stage, a diatomic lumped-mass model is used. We study the implication of the disorder and propose a sorting strategy inspired by global sensitivity analysis (GSA). In the second stage, the sorting strategy is corroborated with numerical simulations by a finite element (FE) model of beam. We use the wave finite element method (WFEM) to calculate the band gaps. A thousand samples are generated randomly to test the sorting strategy and the contrarian strategy. In the third stage, the sorting strategy is verified by an experimental structure of beam. We set up an experimental system and scheme to measure and analyze the effects of the strategy for 5 groups of experiments. We show that vibration suppression may deteriorate statistically due to disorder for periodic structures. Specifically, vibration mitigation is most sensitive to the deviation in the first unit cell from the excitation. Inspired by this finding, a retuning strategy is proposed for the first time, i.e. the unit cell with the smallest deviation should be arranged in the position nearest to the excitation. The results in all stages show that the strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures. [Display omitted] • Vibration suppression may deteriorate statistically due to disorder for periodic structures. • A retuning strategy is proposed for the first time and verified experimentally. • The unit cell with minimum deviation should be arranged near the excitation. • The influence of disorder is reduced by an order of magnitude after retuning. [ABSTRACT FROM AUTHOR]

This paper presents equivalent deflection as a new concept for bridge damage detection. The equivalent deflection is similar to the real deflection and can be inferred from bridge acceleration measurements (accelerometer). While calculating measured acceleration, the method essentially explores the static response of the bridge to load. It is laid on the premise that most of the deflection response is generally static rather than dynamic. By using the equivalent deflection from a group a trains without knowing their bogie weights, the average single bogie equivalent deflection response (ASBED) can be calculated and used as an indicator of structural damage. Initially, the theoretical procedure is described to find the equivalent deflection from an acceleration signal using a moving force identification algorithm. Then, numerical analyses are carried out to validate the algorithm. The results confirm that the equivalent deflection is close to the real deflection and contains only a small dynamic component. Then, a method to find the shape of influence line is developed. Using real acceleration data from a 26.8 m simply supported railway bridge (located over the West Coast Mainline in Staffordshire, UK), the shapes of equivalent influence lines are obtained from different groups of trains with very good repeatability. The ASBED response concept is introduced as the product of the 'inferred bogie weight' and the shape of the influence line. Good repeatability of the ASBED response is obtained from site with variability less than 1.5%. Theoretically, this ASBED response should be able to detect changes in the influence line when the average bogie weight at the site is repeatable. The last section explores the changes in the theoretical influence line due to different bridge damage conditions by using a 2D grillage bridge model. The results show that a 2% overall reduction in material stiffness or 20% local reduction (over 1.5 m) should be detectable using this method. [ABSTRACT FROM AUTHOR]