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Fermionic condensate is investigated in $(D+1)$-dimensional de Sitter spacetime by using the cutoff function regularization. In order to fix the renormalization ambiguity for massive fields an additional condition is imposed, requiring the condensate to vanish in the infinite mass limit. For large values of the field mass the condensate decays exponentially in odd dimensional spacetimes and follows a power law decay in even dimensional spacetimes. For a massless field the fermionic condensate vanishes for odd values of the spatial dimension $D$ and is nonzero for even $D$. Depending on the spatial dimension the fermionic condensate can be either positive or negative. The change in the sign of the condensate may lead to instabilities in interacting field theories., 12 pages, 2 figures, to appear in Astrophysics

Loop diagrams with near-Planck energies create a strong external gravitational field, which slows down local processes for distant observers up to their freezing. Since Planck length is the gravitational radius of the system of quanta, the events of this and smaller scale cannot occur in finite world time t and do not contribute to the S-matrix. Consequently, gravitational time dilation, leading to a strong redshift of local frequencies, provides gravitational self-regularization of the loop diagrams. The loop corrections without gravity effects, cut off at Planck energy, give upper bounds for the corrections with gravity effects and this fact leads to simple rules of gravitational regularization. The corrections with quanta of gauge fields and gravitons are small, and the perturbation theory series converge. At pre-Planck energies, one-loop graviton contributions are sufficient, since the multi-loop ones are damped by high degrees of the relation “energy/Planck energy”. Scalar field with power-law growing corrections should be effective field. Non-linearity of fields enhances gravity and get faster freezing, which suppresses the high energy terms. Nonrenormalizable models are finite, but become consistent only when their loop corrections remain small on Planck scale and this occurs in quantum gravity. Gravitationally regularized Extended Standard Model (ESM), including gravitons and Standard Model with effective scalars, is renormalizable and finite, which simplifies its further generalization.

We present two-loop renormalization of $\phi^3$-model effective action by using the background field method and cutoff momentum regularization. In this paper, we also study a derivation of the quantum equation of motion and its application to the renormalization., Comment: LaTeX, 15 pages, 3 figures; The work has been published three years ago. In this version we have made some corrections and added calculations for the counterterm

The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

If the gauge quantum chiral anomaly predicts chiral effects related to chemical potentials, then the gravitational chiral anomaly is responsible for the effects of temperature. The prediction of the gravitational anomaly for the temperature term in the chiral vortical effect coincides with the prediction of statistical calculations by the Kubo formula for spin 1/2, but two predictions disagree already for spin 1. A solution to this problem related to the features of infrared regularization is described. Also the thermodynamic instability in systems with acceleration, which occurs at temperatures below the Unruh temperature and the transition through the Unruh temperature are discussed.

We consider a diffuse interface model describing flow and phase separation of a binary isothermal mixture of (partially) immiscible viscous incompressible Newtonian fluids having different densities. The model is the nonlocal version of the one derived by Abels, Garcke and Grun and consists in a inhomogeneous Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard equation. This model was already analyzed in a paper by the same author, for the case of singular potential and non-degenerate mobility. Here, we address the physically more relevant situation of degenerate mobility and we prove existence of global weak solutions satisfying an energy inequality. The proof relies on a regularization technique based on a careful approximation of the singular potential. Existence and regularity of the pressure field is also discussed. Moreover, in two dimensions and for slightly more regular solutions, we establish the validity of the energy identity. We point out that in none of the existing contributions dealing with the original (local) Abels, Garcke Grun model, an energy identity in two dimensions is derived (only existence of weak solutions has been proven so far).

We develop a constrained theory for constituent migration in bodies with microstructure described by a scalar phase field. The distinguishing features of the theory stem from a systematic treatment and characterization of the reactions needed to maintain the internal constraint given by the coincidence of the mass fraction and the phase field. We also develop boundary conditions for situations in which the interface between the body and its environment is structureless and cannot support constituent transport. In addition to yielding a new derivation of the Cahn–Hilliard equation, the theory affords an interpretation of that equation as a limiting variant of an Allen–Cahn type diffusion system arising from the unconstrained theory obtained by considering the mass fraction and the phase field as independent quantities. We corroborate that interpretation with three-dimensional numerical simulations of a recently proposed benchmark problem.

Ab initio methods have been the workhorse for the computational investigation of new materials during the past few decades. In spite of the improvements regarding the efficiency and scalability achieved by various implementations, the self-consistent solution of the Konhn-Sham equations remains challenging as the size of the system increases. We propose here machine learning methods based on a feature-free deep ANN approach that are able to predict the ground state charge density by starting from readily accessible free-atom charge densities, thus bypassing the usual Hamiltonian diagonalization. We validate our approach on hybrid C-BN nanoflakes with random atomic configurations by comparing the predicted charge density to that computed by DFT. The ANN architecture is optimized in order to reach the high prediction accuracy required to extract ground state based material properties. In order to correlate the effect of spatial rotations in the input-output mapping, we introduce a novel rotational equivariant network (RE-ANN), by properly symmetrizing the synaptic weights during training. This regularization procedure enhances the prediction accuracy, provides consistent results under rotation operations and also increases the sparsity of the weight matrix. These methods have the potential to speed-up DFT simulations and can be used as high throughput investigation tools.

The time difference of arrival (TDOA) localization method has been widely applied in partial discharge (PD) localization in substations based on an ultra-high-frequency (UHF) antenna array. However, TDOA errors obtained from different UHF antennas can result in poor localization accuracy. In this paper, a novel nonlinear transform localization algorithm based on regularization for PD in substations is proposed. First, to avoid the problem of difficult solutions and heavy calculations caused by solving nonlinear localization equations, the equations are transformed from nonlinear to linear by eliminating the second-order terms. Then, for the ill-conditioned problem of the localization equations caused by the antenna array positions and time difference errors, the equations are optimized by centralization and row balance to reduce their ill-conditioned degree. Finally, the Tikhonov regularization method is used to solve the localization equations with an ill-conditioned problem, and then, the PD position is determined. The experimental results show that the proposed localization algorithm can improve the accuracy of PD localization in substations and that the localization errors are within 2.23 m.

In high-frequency over-the-horizon radar (OTHR), it is a challenging work to detect targets in the nonhomogeneous range-Doppler (RD) map with multitarget interference and sharp/smooth clutter edges. The intensity transition of the clutter edge may be sharp or smooth due to the coexistence of atmospheric noise, sea clutter, and ionospheric clutter in OTHR. The analysis of the RD map shows the spatial correlation among neighboring cell-under-test (CUT) that varies from clutter to clutter. This article proposes an algorithm that uses the spatial relationship to estimate the statistical distribution parameters of every CUT by the adaptive tight frame and the weighted group-sparsity regularization. In the proposed algorithm, the spatial relationship is formulated mathematically by regularization terms and combined with the log-likelihood function of CUTs to construct the objective function. The proposed algorithm is verified by the simulated data and real RD maps collected from both trial sky-wave and surface-wave OTHRs in which it shows robust and improved detection.

A thermodynamically consistent phase field formulation for modeling the interactions between interfacial damage and bulk brittle fracture is presented. A regularization scheme is considered for bot...

Magnetic particle imaging is a new medical imaging modality which is based on the non-linear response of magnetic nanoparticles. The reconstruction task is an inverse problem and ill-posed in nature. To overcome the problem, we propose to use the least absolute shrinkage and selection operator (LASSO) regularization model. In order to reach a good result with a short reconstruction time, we use the truncated system matrix and the truncated measurement based on two threshold setting methods for reconstruction research. In this paper, we study the reconstruction quality of different threshold values and different regularization parameter values. We compare the reconstruction performance of the proposed model with the Tikhonov model from visualization and performance indicators. The conducted study illustrated that the proposed method yields significantly higher reconstruction quality than the state-of-the-art reconstruction method based on Tikhonov model.

Seismic acoustic impedance inversion plays an important role in reservoir prediction. However, single-trace inversion methods often suffer from spatial discontinuities and instability due to poor-quality seismic records with spatially variable signal-to-noise ratios or missing traces. The specified hyperparameters for seismic inversion cannot be suitable to all seismic traces and subsurface structures. In addition, conventional multichannel inversion imposes lateral continuity with a prespecified mathematical model. However, the inversion results constrained with specified lateral regularization are inferior when the subsurface situations violate the hypothesis. A data-driven multichannel acoustic impedance inversion method with patch-ordering regularization is introduced, in which the spatial correlation of seismic reflection is used. The method decomposes the seismic profile into patches and constructs the patch-ordering matrix based on the similarity among seismic patches to record the impedance structural extension. So the patch-ordering matrix can record the spatial extension of the acoustic impedance. Then, a simple regularization with difference operators of varying weights can reduce the random noise presented in the inverted impedance profile, stabilize the inversion result, and enhance the spatial continuity of the layer extension. The objective function for multichannel poststack seismic impedance inversion can be constructed by integrating the observed seismic record and the spatial continuity in the form of patch-ordering regularization, and it can be solved effectively with the limited-memory BFGS algorithm. The synthetic and field data tests illustrate the improvement of accuracy and lateral continuity of inverted results with our method, compared to conventional model-based inversion results.

This work describes a new method for diffusion-weighted (DW) magnetic resonance imaging (MRI) without susceptibility artifacts. The technique combines a DW spin-echo module and a single-shot stimulated echo acquisition mode (STEAM) MRI readout with undersampled radial trajectories and covers a volume by a gapless series of cross-sectional slices. In a first step, optimal coil sensitivities for all slices are obtained from a series of non-DW acquisitions by nonlinear inverse reconstruction with regularization to the image and coil sensitivities of a directly neighboring slice. In a second step, these coil sensitivities are used to compute all series of non-DW and DW images by linear inverse reconstruction with spatial regularization to a neighboring image. Proof-of-principle applications to the brain (51 sections) and prostate (31 sections) of healthy subjects were realized for a protocol with two b-values and 6 gradient directions at 3 T. Including averaging the measuring times for studies of the brain at 1.0×1.0×3.0 mm(3) resolution (b =1,000 s mm(−2)) and prostate at 1.4×1.4×3.0 mm(3) resolution (b =600 s mm(-2)) were 2.5 min and 4.5 min, respectively. All reconstructions were accomplished online with use of a multi-GPU computer integrated into the MRI system. The resulting non-DW images, mean DW images averaged across directions and maps of the apparent diffusion coefficient confirm the absence of geometric distortions or false signal alterations and demonstrate diagnostic image quality. The novel method for DW STEAM MRI of a volume without susceptibility artifacts warrants extended clinical trials.

We study quantum versions of the Shannon capacity of graphs and non-commutative graphs. We introduce the asymptotic spectrum of graphs with respect to quantum and entanglement-assisted homomorphisms, and we introduce the asymptotic spectrum of non-commutative graphs with respect to entanglement-assisted homomorphisms. We apply Strassen's spectral theorem (J. Reine Angew. Math., 1988) in order to obtain dual characterizations of the corresponding Shannon capacities and asymptotic preorders in terms of their asymptotic spectra. This work extends the study of the asymptotic spectrum of graphs initiated by Zuiddam (Combinatorica, 2019) to the quantum domain. We then exhibit spectral points in the new quantum asymptotic spectra and discuss their relations with the asymptotic spectrum of graphs. In particular, we prove that the (fractional) real and complex Haemers bounds upper bound the quantum Shannon capacity, which is defined as the regularization of the quantum independence number (Mančinska and Roberson, J. Combin. Theory Ser. B, 2016), and that the fractional real and complex Haemers bounds are elements in the quantum asymptotic spectrum of graphs. This is in contrast to the Haemers bounds defined over certain finite fields, which can be strictly smaller than the quantum Shannon capacity. Moreover, since the Haemers bound can be strictly smaller than the Lovász theta function (Haemers, IEEE Trans. Inf. Theory, 1979), we find that the quantum Shannon capacity and the Lovász theta function do not coincide. As a consequence, two well-known conjectures in quantum information theory, namely: 1) the entanglement-assisted zero-error capacity of a classical channel is equal to the Lovász theta function and 2) maximally entangled states and projective measurements are sufficient to achieve the entanglement-assisted zero-error capacity, cannot both be true.

We study a rate-independent system with non-convex energy in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized \begin{document}$ BV $\end{document} -solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy Ea, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.

The purpose of this paper is to study the local well-posedness problem on the magnetohydrodynamics (MHD)-structure interaction (MHDSI) systems. The fluid is represented by the incompressible viscous and non-resistive MHD equation in Euler coordinates while the structure is modeled by the elasticity equation with superconductor material in Lagrangian coordinates. The equations are coupled along the moving interface though transmission boundary conditions for velocity, stress and magnetic field. The local existence of at least one strong solution in time to the incompressible viscous and non-resistive MHD-structure interaction model was proved in the sense of one suitable Sobolev's space norm by using the careful energy method and fixed point theory combining with penalization and regularization techniques and by overcoming the coupling difficulties caused by the magnetic field.

A phaseless Gauss-Newton inversion (GNI) algorithm is developed for microwave imaging applications. In contrast to full-data microwave imaging inversion that uses complex (magnitude and phase) scattered field data, the proposed phaseless GNI algorithm inverts phaseless (magnitude-only) total field data. This phaseless Gauss-Newton inversion (PGNI) algorithm is augmented with three different forms of regularization, originally developed for complex GNI. First, we use the standard weighted L2 norm total variation multiplicative regularizer which is appropriate when there is no prior information about the object being imaged. We then use two other forms of regularization operators to incorporate prior information about the object being imaged into the PGNI algorithm. The first one, herein referred to as SL-PGNI, incorporates prior information about the expected relative complex permittivity values of the object of interest. The other, referred to as SP-PGNI, incorporates spatial priors (structural information) about the objects being imaged. The use of prior information aims to compensate for the lack of total field phase data. The PGNI, SL-PGNI, and SP-PGNI inversion algorithms are then tested against synthetic and experimental phaseless total field data.

The problem of real bremsstrahlung calculation is considered using the modern methods of regularization of divergencies. In particular, we calculate soft photon bremsstrahlung in the most general form using the method of dimensional regularization of infrared divergences. The general calculation algorithm of hard photon bremsstrahlung is described. It is shown that the contribution of hard bremsstrahlung can be separated into the finite and divergent parts. The divergent part can be factorized with the contribution of the initial process in the Born approximation. It is shown that a good choice of kinematic variables makes an analytic covariant calculation of the divergent part of the hard bremsstrahlung possible. In a particular case, an algorithm for determining the kinematic constraints on the invariants is described. A numerical analysis of the radiative corrections for gauge bosons production processes in the case of electron-photon collisions is performed. It is discovered that the contribution of the finite part of bremsstrahlung at high collision energies reaches 20 per cent and must be taken into account in calculations of radiative corrections. The results obtained can be used in various calculations, including covariant ones, performed in the context of confirmation of the Standard Model theoretical predictions or searching for manifestations of alternative gauge models.

The inverse source framework, which comprises a subset of electromagnetic inversion, is applied to the noninvasive specific absorption rate (SAR) characterization problem. An algorithm is developed and presented which takes field measurements external to the phantom and provides the electromagnetic sources required to obtain the SAR distribution. The unique aspect of this inverse source algorithm is that it casts the problem as the simultaneous inversion (SI) of two sets of equivalent currents: one for the device under test (DUT), and the other for the phantom. The dependency of these two sets of currents is then incorporated as an explicit regularization term in the resulting algorithm. The method is proposed to be relatively robust in terms of measurement noise. A simplified two-dimensional problem is presented to support this proposition.

In this paper we propose a notion of irreversibility for the evolution of cracks in the presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with damage models, and we investigate its applicability to the construction of a quasi-static evolution in a simple one-dimensional model. The cohesive fracture model arises naturally via $$\Gamma $$ -convergence from a phase-field model of the generalized Ambrosio-Tortorelli type, which may be used as regularization for numerical simulations.

Recently a $D$-dimensional regularization approach leading to the non-trivial $(3+1)$-dimensional Einstein-Gauss-Bonnet (EGB) effective description of gravity was formulated which was claimed to bypass the Lovelock's theorem and avoid Ostrogradsky instability. Later it was shown that the regularization is possible only for some broad, but limited, class of metrics and Aoki, Gorji and Mukohyama [arXiv:2005.03859] formulated a well-defined four-dimensional EGB theory, which breaks the Lorentz invariance in a theoretically consistent and observationally viable way. The black-hole solution of the first naive approach proved out to be also the exact solution of the well-defined theory. Here we calculate quasinormal modes of scalar, electromagnetic and gravitational perturbations and find the radius of shadow for spherically symmetric and asymptotically flat black holes with Gauss-Bonnet corrections. We show that the black hole is gravitationally stable when ($-16 M^2, Comment: RevTex, 12 pages, 8 figures, the version published in the journal, the title is slightly changed

The results of the experiments on the influence of a positive-buoyancy-particle layer on the process of breaking and regularization of the standing gravity Faraday wave on free water surface in a rectangular vessel are discussed. The effect of increase in the particle layer thickness on the limit steepness of the regular wave and its dissipative properties is considered. It is shown that the use of highly concentrated polystyrene particle suspension as the upper layer modifies significantly the barotropic wave mode dynamics and ensures regularization of the waves with total suppression of their breaking mechanisms.

Recently, a novel four-dimensional Einstein-Gauss-Bonnet (EGB) theory was presented to bypass the Lovelock's theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $\alpha\rightarrow\alpha/(D-4)$ and to take the limit $D\rightarrow4$. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem [arXiv:2003.11552, arXiv:2003.12771, arXiv:2004.08362, arXiv:2004.09472, arXiv:2004.10716]. The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss-Bonnet term in four dimensions contributes to the string geometry in the new theory., Comment: 20 pages, 9 figures, published version

The optical three-dimensional (3D) measurement technique based on the laser stripe has become increasingly important in additive manufacturing, which is necessary to extract the laser stripe accurately. In welding, the wrong laser stripe centers due to the high-brightness noise are usually extracted, which causes serious measurement error. In this paper, a laser stripe extraction algorithm based on spatiotemporal noise regularization (SNR) is proposed, which calculates the noise weight of each pixel in time dimension and suppresses the high-brightness noise in space dimension. The proposed algorithm contains four novel steps to achieve accurate and fast laser stripe extraction when the laser stripe is influenced by the high-brightness noise. Meanwhile, an online welding 3D measurement system is constructed based on double-line structured light, which can achieve online 3D measurement in additive manufacturing. Experimental analysis verifies its effectiveness and accurateness.

We propose specification tests for parametric distributions that compare the potentially complex theoretical and empirical characteristic functions using the continuum of moment conditions analogue to an overidentifying restrictions test, which takes into account the correlation between influence functions for different argument values. We derive its asymptotic distribution for fixed regularization parameter and when this vanishes with the sample size. We show its consistency against any deviation from the null, study its local power and compare it with existing tests. An extensive Monte Carlo exercise confirms that our proposed tests display good power in finite samples against a variety of alternatives.

The numerical solutions of boundary integral equations by the Boundary Element Method (BEM) have been applied in several areas of computational engineering and science such as elasticity and fracture mechanics. The BEM formulations often require the evaluation of complex singular and hypersingular integrals. Therefore, BEM requires special integration schemes for singular elements. The Subtraction Singularity Technique (SST) is a general procedure for evaluating such integrals, which allows for the integral over high-order curved boundary elements. The SST regularises these kernels through the Taylor expansion of the integral kernels around the source point. This study presents the expressions from Taylor expansions, which are required for the regularization of singular and hypersingular boundary integral equations of plane linear anisotropic elasticity. These expressions have been implemented into an academic BEM code, which enables the integration over high-order straight and curved boundary elements. The proposed scheme leads to excellent performance. The results obtained by the proposed scheme are in excellent agreement with reference responses available in the literature.

Background Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. Methods A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. Results The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. Conclusions In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

A new analytical wind turbine wake model, based on a super-Gaussian shape function, is presented. The super-Gaussian function evolves from a nearly top-hat shape in the near wake to a Gaussian shape in the far wake, which is consistent with observations and measurements of wind turbine wakes. Using such a shape function allows the recovery of the mass and momentum conservation that is violated when applying a near-wake regularization function to the expression of the maximum velocity deficit of the Gaussian wake model. After a brief introduction of the theoretical aspects, an easy-to-implement model with a limited number of parameters is derived. The super-Gaussian model predictions are compared to wind tunnel measurements, full-scale measurements, and a large-eddy simulation (LES), showing a good agreement and an improvement compared with predictions based on the Gaussian model.

This article presents the plan to design model predictive control (MPC) built load frequency control (LFC) action for a multi-area interconnected control framework. The multi-area control framework comprises of plants with differing sources of vitality. The HVDC tie-lines are considered as an interconnection within the control framework. Further, the most of the past studies in this area was to evaluate the performance of LFC based on step load disturbance and these strategies does not speak to the genuine time circumstances of the control framework operation which may cause the over regulation of the control framework. To improve the execution of LFC, a short term load forecasting (STLF) founded LFC using artificial neural network (ANN) is proposed in this paper. Assist, the real load pattern data is collected on hourly basis and process with the help of ANN for LFC studies. The predicted hourly load is utilized to supply future load to the LFC framework by means of look-ahead control calculation on the premise of 10 miniature interim and MPC based LFC are design to alter the set point to zero in order to match the generation with real load pattern in a best possible manner. The comparison between real and forecasted load utilizing MPC is given through computer reenactments for LFC and the application results of real scenario is presented to show efficacy of the proposed work.

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich., This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively., Strain gradient continuum damage modelling has been applied to quasistatic brittle fracture within an approach based on a maximum energy-release rate principle. The model was implemented numerically, making use of the FEniCS open-source library. The considered model introduces non-locality by taking into account the strain gradient in the deformation energy. This allows for stable computations of crack propagation in differently notched samples. The model can take wedges into account, so that fracture onset can occur at wedges. Owing to the absence of a damage gradient term in the dissipated energy, the normal part of the damage gradient is not constrained on boundaries. Thus, non-orthogonal and non-parallel intersections between cracks and boundaries can be observed.

International audience; In this study, a practical numerical method is proposed to estimate losses of high specific power density electric motors, using few simulated temperature data. In such electric motors, these losses generate high heat fluxes inside the motor components that can be critically sensitive to temperature. Electromagnetic and mechanical friction phenomena are behind the occurring of these thermal dissipations. For both phenomena, losses could be difficult to compute with electrical or mechanical approaches. However, thermal management of electric motors requires a precise knowledge of those losses, in particular for high-performance motors such as those considered in future hybrid planes. To determine electric motor losses in a Permanent Magnet Synchronous Motor (PMSM) in real time, an inverse method using a Lumped Parameter Thermal Model (LPTM) is elaborated. In the first step, the dynamic profile of losses is determined through the inverse method, based on temperature data at easy-access points of the motor. In a second step, the identified losses are used to find temperatures at critical non-accessible hot spot points of the motor through forward LPTM. The method is applied for three useful cases, from the simplest case scenario, where only one type of losses has to be identified, to the most complicated case where all losses are simultaneously estimated. A global strategy for the choice of the number of future time steps used for regularization of the ill-posed problem is also proposed. Results show that this method enables adequate real-time supervision of the critical motor temperatures, mainly rotor and winding core.

An efficient pseudo-3D Occam’s inversion scheme is proposed here to stabilize the traditional 1D inversion for the frequency-domain helicopter-borne electromagnetic (FHEM) data. In this scheme, multiple flight lines are inverted simultaneously for layered 1D models minimizing a common objective function with lateral, vertical, and cross-line in the model regularization function. Applying the lateral, vertical, and cross-line weighting factors into the regularization matrix yields a more stable solution and produces geologically more realistic results. In addition, we investigate how the errors of height measurements obscure the FHEM response and affect recovered resistivity models. In this inversion, attempt is made to recover a correct altitude that deals with distortions caused by the presence of measurement height errors in the reconstructed resistivity models. The comparison among 1D, pseudo-2D, and pseudo-3D Occam’s inversions is made through the analysis of data from two different 3D synthetic models and one field dataset acquired from the north of Iran. The results indicate that pseudo-3D Occam’s inversion provides fewer inversion artifacts, better model recognition, and smoother and more continuous models, while, reduces the effects of data noise in an effective manner.

We study the solvability of certain linear nonhomogeneous elliptic equations and establish that, under some technical assumptions, the L2-convergence of the right-hand sides yields the existence and convergence of solutions in an appropriate Sobolev space. The problems involve differential operators with or without Fredholm property, in particular, the one-dimensional negative Laplacian in a fractional power, on the whole real line or on a finite interval with periodic boundary conditions. We prove that the presence of the transport term in these equations provides regularization of the solutions.

Resident space object population in highly elliptical high perigee altitude (> 600 km) orbits is significantly affected by luni-solar gravity. Using regularization, an analytical orbit theory with luni-solar gravity effects as third-body perturbations in terms of Kustaanheimo-Stiefel regular elements is developed. Numerical tests with different cases resulted in good accuracy for both short- and long-term orbit propagations. It is observed that the luni-solar perturbations affect the accuracy of the analytical solution seasonally. The analytical theory is tested with the observed orbital parameters of the few objects in highly elliptical orbits. The analytical evolution of osculating perigee altitude is found to be concurrent with observed data. Solar perturbation, when compared with lunar perturbation, is established to be dominant over such orbits.

In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our approach allows us to study in a uniform way open and closed Koba-Nielsen amplitudes over arbitrary local fields of characteristic zero. In the regularization process we use techniques of local zeta functions and embedded resolution of singularities. As an application we present the regularization of p-adic open string amplitudes with Chan-Paton factors and constant B-field. Finally, all the local zeta functions studied here are partition functions of certain 1D log-Coulomb gases, which shows an interesting connection between Koba-Nielsen amplitudes and statistical mechanics., Some additional comments were added

This case study aims to determine the effect of five-dimensional regularization and interpolation on seismic subsurface imaging, particularly focusing on impacts to noise attenuation, velocity analysis, and migration. Advanced seismic processing requires high fold coverage and regular cross-spread data to attain good noise attenuation and common offset vectors for appropriate migration. Complex geological scenarios pose substantial challenges for subsurface imagers and interpreters. Stratton Field, USA, contains a major fault, Agua Dulce, along with many smaller faults and thus requires dense acquisition for high-resolution subsurface imaging to reduce migration smiles. Data were processed twice, the first migration without 5D regularization and interpolation and the second with 5D regularization and interpolation. The migration without 5D regularization and interpolation was found to suffer from acquisition footprints, migration smiles and a lack of amplitude versus offset (AVO) behavior, whereas the subsurface image was enhanced with 5D regularization and interpolation and improved in terms of AVO behavior.

This work is devoted to the modeling of brittle and ductile fracture under the use of the level-set method. Within the proposed model a level-set function is taken as a smooth function that represents brittle damage in an implicit manner, that is the zero level-set of the continuous function coincides with the boundaries of the damage. Under the utilization of a regularization parameter that can be interpreted as a material’s internal length, crack faces of zero width are replaced by interfaces of finite width scaled by the length parameter. An energy functional is adopted and after following a variational field approach the equations of damage nucleation and propagation are revealed. Simple numerical examples indicate that the proposed level-set model is in good agreement with other successful models for brittle fracture. Moreover, ductile fracture is successfully captured by introducing an additional level set function so as to describe three distinct phases within the body: the damaged area, the rigid-perfectly plastic region and the elastic region. A simple example of damage propagation provides the behavior of a ductile material.

We have used least-squares migration to emphasize edge diffractions. The inverted forward-modeling operator is the chain of three operators: Kirchhoff modeling, azimuthal plane-wave destruction, and the path-summation integral filter. Azimuthal plane-wave destruction removes reflected energy without damaging edge-diffraction signatures. The path-summation integral guides the inversion toward probable diffraction locations. We combine sparsity constraints and anisotropic smoothing in the form of shaping regularization to highlight edge diffractions. Anisotropic smoothing enforces continuity along edges. Sparsity constraints emphasize diffractions perpendicular to edges and have a denoising effect. Synthetic and field data examples illustrate the effectiveness of the proposed approach in denoising and highlighting edge diffractions, such as channel edges and faults.

A system to process data from a 2D network of magnetic stations is proposed for the identification of eddy currents in the ionosphere and the estimation of their parameters. The methodology is applied to an analysis of the structure of daytime traveling convection vortices (TCVs) based on data from Arctic. The problem is solved with optimization methods for various functions obtained via spatial interpolation and subsequent data regularization. The developed approach makes it possible not only to find eddy structures automatically but also to determine the current values of their characteristic parameters: the spatial structure of the field aligned currents (FACs), and the group velocity of the horizontal propagation of the vortex along the ionosphere.

In this article, different standard and nonstandard continualization techniques are applied to a one-dimensional solid consisting in a chain of masses interacting with nearest and next-nearest neighbors through linear springs. The study focuses on the reliability of the different continua in capturing the dispersive behavior of the discrete, on the order of the continuous governing equation because of its effect on the need for including nonclassical boundary conditions, as well as on the physical inconsistencies that appear for short wavelengths. The Regularization method, used by Bacigalupo and Gambarotta for a lattice with nearest interactions, presents advantages over the others. The authors wish to acknowledge the Ministerio de Economía y Competitividad de España for the financial support [Grant no. PGC2018-098218-B-I00].

We present a same-level comparison of the most prominent inversion methods for the reconstruction of the matter density field in the quasi-linear regime from the Ly$\alpha$ forest flux. Moreover, we present a pathway for refining the reconstruction in the framework of numerical optimization. We apply this approach to construct a novel hybrid method. The methods which are used so far for matter reconstructions are the Richardson-Lucy algorithm, an iterative Gauss-Newton method and a statistical approach assuming a one-to-one correspondence between matter and flux. We study these methods for high spectral resolutions such that thermal broadening becomes relevant. The inversion methods are compared on synthetic data (generated with the lognormal approach) with respect to their performance, accuracy, their stability against noise, and their robustness against systematic uncertainties. We conclude that the iterative Gauss-Newton method offers the most accurate reconstruction, in particular at small S/N, but has also the largest numerical complexity and requires the strongest assumptions. The other two algorithms are faster, comparably precise at small noise-levels, and, in the case of the statistical approach, more robust against inaccurate assumptions on the thermal history of the intergalactic medium (IGM). We use these results to refine the statistical approach using regularization. Our new approach has low numerical complexity and makes few assumptions about the history of the IGM, and is shown to be the most accurate reconstruction at small S/N, even if the thermal history of the IGM is not known. Our code will be made publicly available under https://github.com/hmuellergoe/reglyman., Comment: 21 pages, 13 figures, 3 tables, submitted to MNRAS, a python toolkit containing our implementations will be made publicly available under https://github.com/hmuellergoe/reglyman

A model describing the dynamics of a set of quantum states generated by a nonlinear Schrodinger equation is studied. The relationship between the blow-up of a solution with self-focusing and the transition from pure to mixed states of a quantum system was investigated in [1]. In this context, a natural question is concerned with the dynamics generated by the nonlinear Schrodinger equation in the set of mixed quantum states. The dynamics of mixed quantum states is described by the Liouville–von Neumann equation corresponding to the nonlinear Schrodinger equation. For the former equation, conditions for the global existence of a unique solution of the Cauchy problem and blow-up conditions are obtained.

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and ${\cal N}=(1,0)$ supersymmetric way. We exploit the regularization by dimensional reduction in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant $\beta$-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed {\it a priori}. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations., Comment: 18 pages, 1 figure, final version accepted for publication in JHEP

In this paper, we prove the existence of global and exponential attractors of optimal regularity of a regularization for the three-dimensional Navier–Stokes equations with damping, which is called the three-dimensional velocity–vorticity–Voigt (VVV) system proposed by Larios, Pei and Rebholz (Larios et al., 2019). Differently, there is no “Voigt term”- α 2 A w t in the second equation of system (1.1) below. The proof is based on some energy estimates in Sobolev spaces and the semigroup decomposition.

The subject of this paper is a generalized Camassa-Holm equation under random perturbation. We first establish local existence and uniqueness results as well as blow-up criteria for pathwise solutions in the Sobolev spaces Hs with s>3/2. Then we analyze how noise affects the dependence of solutions on initial data. Even though the noise has some already known regularization effects, much less is known concerning the dependence on initial data. As a new concept we introduce the notion of stability of exiting times and construct an example showing that multiplicative noise (in Itô sense) cannot improve the stability of the exiting time, and simultaneously improve the continuity of the dependence on initial data. Finally, we obtain global existence theorems and estimate associated probabilities., Deutsche Forschungsgemeinschaft, Projekt DEAL, Alexander von Humboldt Foundation

In this paper, we investigate a class of differential linear stochastic complementarity system consisting of an ordinary differential equation and a stochastic complementarity problem. The existence of solutions for such system is obtained under two cases of the coefficient matrix of the linear stochastic complementarity problem: P-matrix and positive semi-definite matrix. As for the first case, the sample average approximate method and time-stepping method are adopted to get the numerical solutions. Furthermore, a regularization approximation is introduced to the second case to ensure the uniqueness of solutions. The corresponding convergence analysis is conducted, and numerical examples are presented to illustrate the convergence results we derived. Finally, we provide numerical results which come from applications involving dynamic traffic flow problems to support our theorems.

We consider the one-constant Landau-de Gennes model for nematic liquid crystals. The order parameter is a traceless tensor field $$\mathbf{Q}$$ , which is constrained to be uniaxial: $$\mathbf{Q}= s (\mathbf{n}\otimes \mathbf{n}- d^{-1}\mathbf{I})$$ where $$\mathbf{n}$$ is a director field, $$s\in \mathbb {R}$$ is the degree of orientation, and $$d\ge 2$$ is the dimension. Building on similarities with the one-constant Ericksen energy, we propose a structure-preserving finite element method for the computation of equilibrium configurations. We prove stability and consistency of the method without regularization, and $$\Gamma $$ -convergence of the discrete energies towards the continuous one as the mesh size goes to zero. We design an alternating direction gradient flow algorithm for the solution of the discrete problems, and we show that such a scheme decreases the energy monotonically. Finally, we illustrate the method’s capabilities by presenting some numerical simulations in two and three dimensions including non-orientable line fields.