Critical Embedding Research Articles

A physics-informed neural network approach for predicting fatigue life of SLM 316L stainless steel based on defect features

Defects in additively manufactured materials severely limit the performance of parts in practical applications, often exposing them to the risk of fatigue failure. In order to improve the reliability and performance of additively manufactured parts, it becomes crucial to accurately predict the fatigue life of the material. Although traditional semi-empirical formulas can assess the effect of defects on the fatigue performance of parts, they still lack detailed research and consideration of defect morphology features. Therefore, this study proposes a method based on Physics-Informed Neural Networks (PINN). This method improves the predictive capability of the model and enhances its interpretability by extracting the sensitive features of critical defects and embedding known physical knowledge or fracture mechanics methods as loss functions into the training process of the neural network. Additionally, the method effectively captures the complex relationship between defect features and fatigue life, providing a deeper understanding of the model prediction results. The results show that the PINN model considering feature-related knowledge has higher prediction accuracy and reliability, and all predicted fatigue life are narrowed within 2-factor bands, enabling more accurate prediction of fatigue life for SLM 316L stainless steel under different processing conditions.

Effect of fiber characteristic parameters on the synergistic action and mechanism of basalt fiber asphalt mortar

Basalt fiber has been shown to significantly improve the performance of asphalt mixtures and extend the lifespan of roads. However, more research is needed to investigate the characteristic parameters of basalt fiber when used in asphalt mortar and asphalt mixture. In order to enhance the reinforcing effect of basalt fiber on asphalt mixture and understand how it works, this study examines the properties of asphalt mortar mixed with basalt fiber with different characteristic parameters. Nine types of basalt fibers with varying characteristic parameters were selected for this work, including three lengths (3 mm, 6 mm, 12 mm) and three diameters (7 μm, 16 μm, 25 μm). The properties of asphalt mortar mixed with basalt fiber with different characteristic parameters were tested. High-temperature properties were characterized using the ZSV and MSCR tests; medium-temperature properties were characterized using the LAS test; low-temperature properties were characterized using the BBR and direct tensile tests. In addition, the effects of fiber characteristics on the viscosity, structural integrity and interfacial properties of asphalt mortar were analyzed through the bond strength test, Rigden porosity test and fiber monofilament drawing test. The results demonstrate that basalt fiber can improve high-temperature properties significantly in asphalt mortar while being greatly influenced by its characteristic parameters. Specifically, fibers with a length of 6 mm and a diameter of 7 μm exhibit superior reinforcement effects. Fatigue life results indicate that basalt fiber enhances fatigue resistance in asphalt mortar as well; furthermore, the influence exerted by fiber characteristic parameters aligns consistently with that observed for high-temperature performance. Although the BBR test results indicate that fiber incorporation has minimal impact on its enhancement, the direct tensile test results demonstrate a significant improvement in the toughness of asphalt mortar due to fiber reinforcement. The addition of basalt fiber enhances the bond strength of asphalt mortar. According to Einstein viscosity formula, the viscosity of asphalt mortar decreases with shorter fiber lengths and larger diameters. Incorporating basalt fiber can enhance the proportion and strength of structural asphalt in asphalt mortar. When comparing fibers with equal diameter or length, an increase in either parameter initially improves the strength of structural asphalt but eventually leads to a decline. Results from monofilament fiber drawing tests and theoretical critical embedding length confirm that a 6 mm fiber length is most beneficial for enhancing the performance of asphalt mortar. Basalt fiber exhibits significant potential for improving various properties of asphalt mortar and provides a favorable reference for optimizing the selection of basalt fiber.

Processing map of the in-situ micro-forging (MF) assisted cold spray for additive manufacturing of fully dense metals without MF particle inclusion

The newly developed in-situ micro-forging assisted cold spraying (MFCS) is an economical and convenient way to deposit dense metals with porosity lower than 0.1%. During this process, forging effect induced by impact of large-size hard micro-forging particles to in-situ densification of the deposited materials. Therefore, a fully dense metallic deposit could be produced at moderate gas temperature and pressure without using expensive helium gas. However, it is found that the porosity is highly dependent on the type of depositing materials, shot-penning particle size, and spraying parameters. Shot-peening particle deposition-induced inclusion is frequently observed for soft depositing materials. This makes the application challenging and a universal processing map is in great demand. In this study, pure Al, pure Ti, pure Ni, 2219 Al, 6061 Al, 7055 Al, and TC4 with different hardness values are used as examples to explore a universal spraying processing map for MFCS. The influence of impact velocity and volume fraction of the shot-peening particle, types of the depositing materials, and spraying parameter on densification and shot-peening particle deposition is investigated. Adding 30vol.% of 410 stainless steel MF particles into the depositing powders decreases the porosity of all deposits and particle deposition-induced inclusion is observed in pure Al, all three Al alloys, and pure Ti deposits. The single particle deposition experiment and the numerical simulation reveal that mechanical interlocking is the prime mechanism for MF particle deposition. A critical embedding MF particle size (dcr,e), above which MF particle inclusion can be avoided, is defined. A new concept of MF intensity (IMF) is proposed to comprehensively consider all main factors influencing the densification of the deposit. Finally, optimized processing maps for depositing fully dense metals without MF particle inclusion are established by plotting the critical embedding velocity and IMF against the hardness of the depositing materials.

The Road (Trip) Home? Migration, Borders and Belonging in Contemporary Bosnian Cultural Production

In the last decade, post-Yugoslav (diasporic) cultural production has experienced an upswing in the emergence of (female-authored, feminist) literature and film that critically engage with the aftermath of displacement, exile and migration following the wars of the 1990s. For this article, I will focus on three recent cultural artefacts that belong to this category: two books – the acclaimed Uhvati Zeca (Catch the Rabbit) by Lana Bastašić (2018) and Deset Šljiva za Fašiste (Ten Plums for Fascists) by Elvira Mujčić (2020) – and one film, Take Me Somewhere Nice, by Ena Sendijarević (2019). I will explore how in these itinerant narratives, Bosnia and the Balkans emerge as a stylistic vehicle, linking the past and present, East and West, as well as questions of belonging and exile. Working at the intersection of postcolonial and postsocialist critique, as well as of border studies and feminist theory, I will analyze how a certain Balkanist discourse is recuperated in the three proposed works. I will argue that this is not a simple reproduction but rather a mimetic engagement with Balkanism by way of the protagonist’s (and by extension – the author’s) critical embedding within its workings.

Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise

The asymptotically autonomous dynamics in $$H^s(\mathbb R^n)$$ for any $$s\in (0,1)$$ and $$n\in \mathbb {N}$$ are discussed for a class of highly nonlinear nonclassical diffusion equations perturbed by colored noise. The main feature of this model is that the time-dependent drift and diffusion terms have subcritical and superlinear polynomial growth of orders p and q, respectively, satisfying $$\begin{aligned} 2\le 2q<p<\infty \text { if }n=1\text { and }s\in [\frac{1}{2},1);\text { otherwise, }\, 2\le 2q<p<\frac{2n}{n-2s}. \end{aligned}$$ The number $$\frac{2n}{n-2s}$$ is called the fractional critical Sobolev embedding exponent. Under this setting, we prove the existence, time-dependent uniform compactness and asymptotically autonomous convergence of pathwise random attractors of the equations in $$H^s(\mathbb R^n)$$ when the time-dependent nonlinearities satisfy some new conditions. The time-dependent uniform pullback asymptotical compactness of the solution operators in $$H^s(\mathbb R^n)$$ is proved by virtue of a cut-off technique [38], a spectral decomposition approach and uniform estimates in a time-uniformly tempered attracting universe in order to overcome several difficulties caused by the lack of compact Sobolev embeddings on unbounded domains, the weak dissipativeness of the systems and the unknown measurability of attractors.

Theoretical Assessment of the Role of Bond Material during Grinding of Superhard Materials with Diamond Wheels

The grinding of superhard materials poses an important challenge to manufacturing industry, due to the increased wear and the high possibility of fracture of both the wheel and workpiece material. Various strategies have been proposed for effective grinding of these materials, but further research is still required, especially in cases in which the hardness of the wheel and the workpiece are almost equal. In this study, the role of the bond of a diamond grinding wheel during the processing of superhard materials, such as synthetic diamond, is investigated using theoretical models and FE simulation. Six different types of bonds are studied and the effect of their properties on the stress distribution of workpiece material is determined. Results indicate that even a slight increase in elastic modulus can affect considerably the stress state of the workpiece, directly affecting the critical embedding value of grains into the bond, something that can alter considerably the efficiency of grinding superhard materials. Thus, grinding wheels with bonds of high elastic modulus should be selected in order to increase grain retention, increase processing efficiency, and reduce specific consumption even at higher cross feeds and wheel speeds.

Critical meter identification and network embedding based attack detection for power systems against false data injection attacks

Modern power systems are becoming vulnerable to false data injection attacks (FDIAs) due to the high penetration of communication devices. To deal with such threats and challenges, this research develops a multi-task framework for power system operations against FDIAs, which aims to: (1) investigate the mechanism for the grid response model to FDIAs; (2) identify and protect critical meter measurements to reduce the loss of grids to such attacks; (3) detect attacks which may lead to severe consequences. To this end, a quantitative critical meter index (CMI) and a severe attack detection method based on network embeddings are proposed. The performance of the proposed method is evaluated by FDIAs simulations in the Institute of Electrical and Electronic Engineers (IEEE) 30- and 118-bus systems. Results show that protecting the identified meters can reduce the load shedding of 118-bus system greatly, and the accuracy rate of the proposed method to detect severe attacks reaches 96.62% and 98.91% for 30- and 118-bus systems against FDIAs, respectively.

Embedding Principle: A Hierarchical Structure of Loss Landscape of Deep Neural Networks

We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i.e., loss landscape of an NN contains all critical points of all the narrower NNs. This result is obtained by constructing a class of critical embeddings which map any critical point of a narrower NN to a critical point of the target NN with the same output function. By discovering a wide class of general compatible critical embeddings, we provide a gross estimate of the dimension of critical submanifolds embedded from critical points of narrower NNs. We further prove an irreversiblility property of any critical embedding that the number of negative/zero/positive eigenvalues of the Hessian matrix of a critical point may increase but never decrease as an NN becomes wider through the embedding. Using a special realization of general compatible critical embedding, we prove a stringent necessary condition for being a "truly-bad" critical point that never becomes a strict-saddle point through any critical embedding. This result implies the commonplace of strict-saddle points in wide NNs, which may be an important reason underlying the easy optimization of wide NNs widely observed in practice.

Study on Rock Damage Mechanism for Lateral Blasting under High In Situ Stresses

A 3D numerical model was presented to investigate the blast-induced damage characteristics of highly stressed rock mass. The RHT (Riedel, Hiermaier, and Thoma) model in LS-DYNA was used to simulate the blast-induced damage and its parameters were calibrated by a physical model test. Based on the calibrated numerical model, the influences of confining pressure and free surface span on the blast-induced damage characteristics were investigated. The results show that under uniaxial loading, the crater volume increases with confining pressure increases. The uniaxial static load can change the optimal burden and the critical embedding depth of charge. In stressed rock, the variation law of the crater shape affected by radial tensile fractures is opposite to that affected by reflected tensile fractures. Under the biaxial static load, the crater volume of the borehole placed on the side of the max static load is greater than the other side. The explosion crater can be improved by increasing the free surface span on the same side. Finally, it is suggested that the blasting efficiency can be improved by preferentially detonating the charge on the side of the max static load, and then the charge on the other side can be detonated with a wider free surface span.

Spatio-temporal connections in streamflow: a complex networks-based approach

This study introduces a new complex networks-based method to examine the spatio-temporal connections in streamflow. The method involves reconstruction of two (or more) time series jointly in a multi-dimensional phase space using a nonlinear phase space embedding procedure and construction of the spatio-temporal streamflow network of nodes and links based on the reconstructed vectors. After this spatio-temporal network construction, the clustering property of the network is measured using the clustering coefficient, which quantifies the tendency of a network to cluster. The approach is applied to monthly streamflow time series observed at each of 639 streamflow stations in the United States. Different distance threshold values are used to identify the presence/absence of links in the streamflow network and, hence, to calculate the clustering coefficient. The clustering coefficient results help to identify the critical distance threshold and optimal embedding dimension of each streamflow time series using different distance threshold values. The optimal embedding dimensions and the clustering coefficient values of the 639 streamflow time series are also discussed in terms of the role of catchment and flow properties (drainage area, elevation, flow mean, and flow coefficient of variation). The dimensions for the 639 streamflow time series are generally found to range from 2 to 18 (but even up to 30 for a few stations), indicating a wide range of complexity in the spatio-temporal connections in streamflow across the United States. The clustering coefficient values for the 639 stations are found to be in the range of 0.53–0.99, which suggest generally strong connections. The outcomes of this study clearly indicate the usefulness of the networks-based approach for examining the spatio-temporal connections in streamflow.

More insights into the Trudinger–Moser inequality with monomial weight

In this paper we present a detailed study of critical embeddings of weighted Sobolev spaces into weighted Orlicz spaces of exponential type for weights of monomial type. More precisely, we give an alternative proof of a recent result by N. Lam [NoDEA 24(4), 2017] showing the optimality of the constant in the Trudinger–Moser inequality. We prove a Poincare inequality for this class of weights. We show that the critical embedding is optimal within the class of Orlicz target spaces. Moreover, we prove that it is not compact, and derive a corresponding version of P.-L. Lions’ principle of concentrated compactness.

Approximation of Smoothness Classes by Deep Rectifier Networks

We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces $B^\alpha_{q}(L^p)$ in arbitrary dimension $d$, on general domains. We show that \alert{deep rectifier} networks with a fixed activation function attain optimal or near to optimal approximation rates for functions in the Besov space $B^\alpha_{\tau}(L^\tau)$ on the critical embedding line $1/\tau=\alpha/d+1/p$ for \emph{arbitrary} smoothness order $\alpha>0$. Using interpolation theory, this implies that the entire range of smoothness classes at or above the critical line is (near to) optimally approximated by deep ReLU/RePU networks.

Multiple peak solutions for polyharmonic equation with critical growth

AbstractThis paper is concerned with the following elliptic problem: where is the polyharmonic operator, is the critical Sobolev embedding exponent. B1 is the unit ball in , s1 and are parameters, is the eigenfunction of corresponding to the first eigenvalue λ1 with , . By using the Lyapunov–Schimit reduction method combining with the minimax argument, we construct the solutions to (P) with many peaks near the boundary but not on the boundary of the domain. Moreover, we prove that the number of solutions for the problem (P) is unbounded as the parameter tends to infinity, therefore proving the Lazer–McKenna conjecture for the higher order case with critical growth.

Polyharmonic k-Hessian equations in [formula omitted

This work is focused on the study of the nonlinear elliptic higher order equation(−Δ)mu=Sk[−u]+λf,x∈RN, where the k-Hessian Sk[u] is the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix of the solution and the datum f belongs to a suitable functional space. This problem is posed in RN and we prove the existence of at least one solution by means of topological fixed point methods for suitable values of m∈N. Questions related to the regularity of the solutions and extensions of these results to the nonlocal setting are also addressed. On the way to construct these proofs, some technical results such as a fixed point theorem and a refinement of the critical Sobolev embedding, which could be of independent interest, are introduced.

Teamwork situated in multiteam systems: Key lessons learned and future opportunities.

Many important contexts requiring teamwork, including health care, space exploration, national defense, and scientific discovery, present important challenges that cannot be addressed by a single team working independently. Instead, the complex goals these contexts present often require effectively coordinated efforts of multiple specialized teams working together as a multiteam system (MTS). For almost 2 decades, researchers have endeavored to understand the novelties and nuances for teamwork and collaboration that ensue when teams operate together as "component teams" in these interdependent systems. In this special issue on the settings of teamwork, we aim to synthesize what is known thus far regarding teamwork situated in MTS contexts and offer new directions and considerations for developing, maintaining, and sustaining effective collaboration in MTSs. Our review of extant research on MTSs reveals 7 key lessons learned regarding teamwork situated in MTSs, but also reveals that much is left to learn about the science and practice of ensuring effective multiteam functioning. We elaborate these lessons and delineate 4 major opportunities for advancing the science of MTSs as a critical embedding context for collaboration and teamwork, now and in the future. (PsycINFO Database Record

Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity

In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose–Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |ψ|2ψ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H12(R2,C2)↪L4(R2,C4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments.

Bourgain–Brezis inequalities on symmetric spaces of non-compact type

Let M be a global Riemannian symmetric space of non-compact type. We prove a duality estimate, for pairings of divergence-free L1 vector fields, with vector fields in a critical Sobolev space on M:|∫M〈f,ϕ〉dV|≤C‖f‖L1(dV)‖∇ϕ‖Lm(dV). This estimate provides a remedy for the failure of a critical Sobolev embedding on such symmetric spaces.

Critical Nonlocal Systems with Concave-Convex Powers

Abstract By using the fibering method jointly with Nehari manifold techniques, we obtain the existence of multiple solutions to a fractional p-Laplacian system involving critical concave-convex nonlinearities, provided that a suitable smallness condition on the parameters involved is assumed. The result is obtained although there is no general classification for the optimizers of the critical fractional Sobolev embedding.

Dynamic embedding of workflow requests for bandwidth efficiency in data centers

In this paper, we address the problem of embedding dynamically-arriving workflow requests in data centers. Workflows pose challenges due to data precedence and time disjointness among tasks, thus driving the need for intelligent methods to embed workflows in data centers while improving the bandwidth efficiency as well as guaranteeing the application performance. We first formulate an integer programming optimization model for the embedding problem that minimizes the amount of bandwidth required for workflow execution. We then develop two algorithms namely Critical Path Workflow Embedding (CPWE) and Edge Priority Workflow Embedding (EPWE) to solve this problem. We consider two data center network architectures: packet switching electrical networks and circuit switching optical wavelength division multiplexed (WDM) networks. While WDM-based optical networks have much larger bandwidth capacity to meet the ever-growing traffic demand in data centers, they pose challenges due to wavelength continuity constraint and the nature of circuit switching. We thus additionally propose methods for selecting appropriate Top-of-the-Rack (ToR) switches and wavelengths during the embedding process so as to increase the chance of accommodating many requests that span over multiple ToRs. We evaluate CPWE and EPWE through comprehensive simulations. The results show that CPWE and EPWE significantly reduce the bandwidth required for a workflow request by up to 66% for random workflows and 80% for realistic-application workflows compared to baseline algorithms. The results also show that the proposed methods for ToR selection and wavelength selection in optical data centers outperform other methods by reducing the rejection ratio by up to 47% with dynamic reconfiguration of lightpaths and 40% with incremental configuration of lightpaths.

Optimal decay of extremals for the fractional Sobolev inequality

We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.