Singular Terms Research Articles

Improved soil–structure interaction model considering time-lag effect

An important aspect of soil– structure interaction analysis is establishing a high-precision conversion relationship between the dynamic impedance in the frequency domain and impulse response function in the time domain. Accordingly, an improved Nakamura model was developed in this study to convert dynamic impedance to an impulse response function. The causes and distribution rules of repeated phase angles were investigated based on the traveling time-lag effect, rendering the improved method more robust. In addition, the impulse response function and interaction force can achieve high fitting accuracy by stripping the singular term from the conventional term. In this study, the time-domain impulse response function and interaction force were derived based on the force–displacement relationship. Further, the accuracy and stability of the improved method were verified using a semi-infinite bar on an elastic foundation. Then, the effects of frequency interval, maximum frequency, and shape of the coefficient matrix on the impulse response function and interaction force were studied by considering the analytical solution of a spherical cavity embedded in full space as an example. Finally, two interaction systems were used to verify the applicability of the improved method in analyzing the soil–structure dynamic interaction.

On the applicability of digital image correlation method in extracting the higher order terms in stress field around blunt notches

Accurate and deep understanding of the stress field has a key role in designing and optimizing the engineering structures. The main objective of the present article is to experimentally investigate the stress field around various blunt notches by means of the digital image correlation (DIC) method. First, several mode I tests were conducted using two types of specimens, namely single edge notch tension (SENT) and single edge notch bending (SENB), each consisting of three different notches (U, VO, and Keyhole). Then, the optical method of DIC was used to determine the stress field around the notch tip by calculating the coefficients of singular and higher-order terms (HOTs) for each notch type. To do so, the output displacement field of the DIC measurements was considered as input data for a computer program, and the coefficients of the stress field were calculated by the least square method (LSM) and an over-deterministic approach. Moreover, the effects of several geometry parameters like notch opening angle and notch tip shape on the stress distribution around the notch were discussed in detail. Finally, the precision of the calculated notch stress intensity factors (NSIFs) and the coefficients of HOTs were studied by comparing the DIC results with those obtained from the finite element (FE) analysis. It is also shown that HOTs of stress field have considerable contribution in more precise determination of the stress field around notches.

A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms

By a probabilistic method, we prove the existence and uniqueness of weak solutions to Neumann problems for a class of semi-linear elliptic partial differential equations with nonlinear singular divergence terms, which can only be understood in distributional sense. This leads to the further study on a new class of infinite horizon backward stochastic differential equations, which involves integrals with respect to a forward–backward martingale and a singular continuous increasing process.

A regularized fast multipole method of moments for rapid calculation of three-dimensional time-harmonic electromagnetic scattering from complex targets

The article applies the recent research results of the singular boundary method to rapidly calculate time-harmonic electromagnetic scattering from complex targets. The study focuses on how to efficiently solve the large-scale and completely dense linear equations obtained by the regularized method of moments. The core innovation point is to propose a regularized fast multipole method of moments by combining the regularized method of moments and the fast multipole method. Several key mechanical issues encountered in simulation of electromagnetic scattering are discussed. The Rao-Wilton-Glisson vector basis function is used as the basis function. A modified fundamental solution is employed in place of the fundamental solution of the Helmholtz equation to avoid non-uniqueness at interior resonances. The fast multipole method is used to expedite the solution process. A fast near-field approximation preconditioner is introduced to greatly reduce excessive iterations. The origin intensity factor is applied to calculate the singular terms of interpolation matrix. The radar cross section of the NASA almond and a scaled stealth fighter has been accurately calculated by the proposed method.

On the existence of weak solutions for a class of singular reaction diffusion systems

We study the existence of weak solutions for a parabolic reaction diffusion model applied in Quenching endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The techniques used are based on energy estimates to approach nonsingular problems and uniform control on the set where singularities are localizing.

Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format

Abstract The Poisson–Boltzmann equation (PBE) is a fundamental implicit solvent continuum model for calculating the electrostatic potential of large ionic solvated biomolecules. However, its numerical solution encounters severe challenges arising from its strong singularity and nonlinearity. In (P. Benner, V. Khoromskaia, B. Khoromskij, C. Kweyu, and M. Stein, “Regularization of Poisson-Boltzmann type equations with singular source terms using the range-separated tensor format,” SIAM J. Sci. Comput., vol. 43, no. 1, pp. A415–A445, 2021; C. Kweyu, V. Khoromskaia, B. Khoromskij, M. Stein, and P. Benner, “Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format,” arXiv:2109.14073, 2021), the effect of strong singularities was eliminated by applying the range-separated (RS) canonical tensor format (P. Benner, V. Khoromskaia, and B. N. Khoromskij, “Range-separated tensor format for many-particle modeling,” SIAM J. Sci. Comput., vol. 40, no. 2, pp. A1034–A1062, 2018; B. N. Khoromskij, “Range-separated tensor representation of the discretized multidimensional Dirac delta and elliptic operator inverse,” J. Comput. Phys., vol. 401, p. 108998, 2020) to construct a solution decomposition scheme for the PBE. The RS tensor format allows deriving a smooth approximation to the Dirac delta distribution in order to obtain a regularized PBE (RPBE) model. However, solving the RPBE is still computationally demanding due to its high dimension N $\mathcal{N}$ , where N $\mathcal{N}$ is always in the millions. In this study, we propose to apply the reduced basis method (RBM) and the (discrete) empirical interpolation method ((D)EIM) to the RPBE in order to construct a reduced order model (ROM) of low dimension N ≪ N $N\ll \mathcal{N}$ , whose solution accurately approximates the nonlinear RPBE. The long-range potential can be obtained by lifting the ROM solution back to the N $\mathcal{N}$ -space while the short-range potential is directly precomputed analytically, thanks to the RS tensor format. The sum of both provides the total electrostatic potential. The main computational benefit is the avoidance of computing the numerical approximation of the singular electrostatic potential. We demonstrate in the numerical experiments, the accuracy and efficacy of the reduced basis (RB) approximation to the nonlinear RPBE (NRPBE) solution and the corresponding computational savings over the classical nonlinear PBE (NPBE) as well as over the RBM being applied to the classical NPBE.

Holographic S-fold theories at one loop

A common feature of tree-level holography is that a correlator in one theory can serve as a generating function for correlators in another theory with less continuous symmetry. This is the case for a family of 4d CFTs with eight supercharges which have protected operators dual to gluons in the bulk. The most recent additions to this family were defined using S-folds which combine a spatial identification with an action of the S-duality group in type IIB string theory. Differences between these CFTs which have a dynamical origin first become manifest at one loop. To explore this phenomenon at the level of anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop double discontinuity. Compared to previous studies, the subsequent analysis is performed without any assumption about which special functions are allowed. Instead, the Casimir singular and Casimir regular terms are extracted iteratively in order to move from one Regge trajectory to the next. Our results show that anomalous dimensions in the presence of an S-fold are no longer rational functions of the spin.

An optimal design problem with non-standard growth and no concentration effects

We obtain an integral representation for certain functionals arising in the context of optimal design and damage evolution problems under non-standard growth conditions and perimeter penalisation. Under our hypotheses, the integral representation includes a term which is absolutely continuous with respect to the Lebesgue measure and a perimeter term, but no additional singular term. We also study some dimension reduction problems providing results for the optimal design of thin films.

The incapacity to work as moving target. Exploring the possibilities of praxiography for analysing realities of disability in history

While acknowledging the discursive meaning of bodies, both gender and disability scholars try to overcome a strict nature–culture or medical model–social model divide. This article explores the possibilities of praxiography for disability history to overcome this divide. Praxiography, as introduced by Annemarie Mol, approaches the body and gender as something that is made up in encounters between people, objects, and practices. Mol has shown that, although a singular term may suggest there is coherence, this coherence is managed in practice. This article provides a practice-focused analysis of appeal cases in which incapacity to work was contested in the context of the first disability benefit act in the Netherlands (1901–1921) and shows how incapacity to work was made up as incapacity to earn a living and shifted to meticulous descriptions of the functioning of individual body parts. Although the topic of power remains to be explored, by looking at incapacity to work as a site of interaction, we can challenge perceptions of disability and gender as a biological or a cultural truth and incorporate matter into the historical analysis of the making of social categories.

Relation between Phenomenological Features of Perception and Semantics of Singular Terms in the Context of Taste and Desire Attitudes

Introduction. The study of the semantics of singular terms, that is, such expressions of language that are used to designate a single concrete object, which, first of all, can be sensibly perceived and be a component of our practice in the physical sense, has been going on for several decades. But, according to the author, the essence of singular terms still needs to be clarified in many ways. Does analysis require the meaning of singular terms for tools outside the semantics? If so, what tools should be used? We would like to outline some considerations that may help in answering these questions.Methodology and sources. A considerable number of works by famous researchers of the language are devoted to the disclosure and description of possible approaches to the problems of using singular terms (see, for example, the works of B. Russell, M. Cresswell, Z. Vendler, D. Ninan, M. Schwager, etc.). This article attempts to expand the methodology with phenomenological analysis and description, what explain the citation of M. Merleau-Ponty, A. Schutz, E. Husserl, N.V. Motroshilova, and others.Results and discussion. On the one hand, we classify various linguistic units as singular terms, distinguished according to the specificity that their use has. On the other hand, endowing singular terms with a special status, we are forced to ask ourselves about the prerequisites for the «genesis» of such terms. The work demonstrated the necessity and effectiveness of the phenomenological method, which performs the propaedeutic and explanatory functions in relation to the semantic analysis of singular terms itself. The reason for this is the close connection between the natural language and the sensory world as a given, which, as the research has shown, cannot be ignored.Conclusion. The closedness of semantics in itself limits the possibilities of analyzing a natural language, in connection with which it seems to us quite clear the actual need to turn to phenomenology. We tried to illustrate the importance of considering the genetic aspects of the use of singular terms and the relationship of their pre-linguistic genesis with the uniqueness of the status of these linguistic units. Therefore, we have good reasons to turn to the phenomenological description of perception and to assert its conceptual connection with the semantics of singular terms.

The semantics of fiction

The paper reviews proposals by Abell, Predelli, and others on the semantics of fiction, focusing on the discourse through which fictions are created. Predelli develops the radical fictionalism of former writers like Kripke and van Inwagen, according to which that discourse is contentless and does not express propositions. This paper offers reasons to doubt these claims. It then explores realist proposals like Abell's in which singular terms in fictions refer to fictional characters, understood as socially created representational artifacts, and irrealist alternatives in which the discourse is fully meaningful even though those terms fail to refer.

Substitutional Accounting for Singular Terms: Some Problems and a Slightly More Kantian Solution for Brandom

Abstract This article grapples with Robert Brandom’s account of singular terms. I argue that neither Brandom’s answer to the question “What are singular terms?” nor his answer to the question “Why are there any singular terms?” works as they currently stand. Brandom’s substitution-inferential semantic account of what singular terms are fails to distinguish between the semantic role of singular terms and indefinite descriptions, and Brandom’s “expressive transcendental deduction” for why there are any singular terms fails to deciseively show that singular terms are expressively necessary for the use of logical vocabulary. Still, I then characterize how Brandom does have resources within his substitution-inferential semantics to give a better, revised answer to the question “What are singular terms?” that both fits programmatically within his framework and has a curious Kantian parallel. I leave the matter offering a Brandom-friendly replacement account for why there are any singular terms thus conceived for another occasion.

Convergence Analysis of the Variational Operator Splitting Scheme for a Reaction-Diffusion System with Detailed Balance

We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of the reaction trajectory, and both the reaction and diffusion parts dissipate the same free energy. The scheme is energy stable and positivity-preserving. In this paper, the detailed convergence analysis and error estimate are performed for the operator splitting scheme. The nonlinearity in the reaction trajectory equation, as well as the implicit treatment of nonlinear and singular logarithmic terms, impose challenges in numerical analysis. To overcome these difficulties, we make use of the convex nature of the logarithmic nonlinear terms, which are treated implicitly in the chemical reaction stage. In addition, a combination of a rough error estimate and a refined error estimate leads to a desired bound of the numerical error in the reaction stage, in the discrete maximum norm. Furthermore, a discrete maximum principle yields the evolution bound of the numerical error function at the diffusion stage. As a direct consequence, a combination of the numerical error analysis at different stages and the consistency estimate for the operator splitting results in the convergence estimate of the numerical scheme for the full reaction-diffusion system.

Modal Collapse and Modal Fallacies: No Easy Defense of Simplicity

Abstract I critically examine the claim that modal collapse arguments against the traditional doctrine of divine simplicity (DDS) are in general fallacious. In a recent paper, Christopher Tomaszewski alleges that modal collapse arguments against DDS are invalid, owing to illicit substitutions of nonrigid singular terms into intensional contexts. I show that this is not, in general, the case. I show, further, that where existing modal collapse arguments are vulnerable to this charge the arguments can be repaired without any apparent dialectical impropriety. I conclude that the genuine debate over modal collapse and divine simplicity and modal collapse is substantially a controversy over the metaphysics of divine action, and that this constitutes a fruitful direction in which to take future discussions of the subject.

Theoretical and Experimental Study considering the Influence of T-Stress on the Fracture Behavior of Compression-Shear Crack

The influence of the nonsingular stress term (T-stress), existing in the Williams expansion of the crack tip stress field, on the fracture behavior of the compressive-shear crack is comprehensively considered in this paper. According to the stress boundary conditions on the crack surfaces, the theoretical solution of the stress field around the closed crack tip is established using the complex potential theory, which includes not only the singular term containing the stress intensity factor KII but also three nonsingular terms (T-stress: Tx, Ty, and Txy) without KII. Then, the differences between tangential stresses and shear stresses at the crack tip obtained in the cases with and without T-stress are compared, respectively. Outcome indicates that there are tangential tensile stress and compressive stress zones at the crack tip when considering T-stress, while only the former exists when ignoring T-stress. In the case of considering T-stress, an improved crack initiation criterion is proposed, where the maximum tangential tensile stress and maximum shear stress are utilized simultaneously to predict the crack initiation and failure mode under the multiaxial compression stress state. Besides, the triaxial compression tests were carried out on the prismatic rock-like material samples with a central crack, and the effectiveness and validity of the proposed criterion are verified by comparing the experimental results and theoretical predictions. It reveals that the proposed criterion can reliably predict the crack initiation angles and failure modes with higher accuracy than traditional fracture criterion.

An extended Flaherty-Keller formula for an elastic composite with densely packed convex inclusions

In this paper, we are concerned with the effective elastic property of a two-phase high-contrast periodic composite with densely packed inclusions. The equations of linear elasticity are assumed. We first give a novel proof of the Flaherty-Keller formula for elliptic inclusions, which improves a recent result of Kang and Yu (Calc Var Partial Differ Equ 59(1):3, 2020). We construct a family of auxiliary functions consisting of the Keller-type functions and additional correctors which depend on the coefficients of Lamé system and the geometry of inclusions, to capture the full singular term of the gradient. On the other hand, this method allows us to deal with the inclusions of arbitrary shape, even with zero curvature. An extended Flaherty-Keller formula is proved for m-convex inclusions, $$m>2$$ , curvilinear squares with round off angles, which minimize the elastic energy under the same volume fraction of hard inclusions.

Some Nonlinear Parabolic Problems with Singular Natural Growth Term

Some Nonlinear Parabolic Problems with Singular Natural Growth Term

Conviviality and its others: for a plural politics of living with difference

ABSTRACT Over the past 15 years, a range of scholarship exploring how people live with difference in their everyday lives has come to mark a multi-disciplinary ‘convivial turn’. This article suggests that while such work has been generative, there has been a prevalent tendency to imagine the capacity to live with difference in relatively singular terms. This article begins by unpacking two ‘major’ themes within the convivial turn: the negotiated deconstruction of bounded identities, and the cultivation of public civilities. It suggests that despite important differences, both approaches imagine the capacity to live with difference in terms of general orientations towards a generic other. The article draws out the limits of these approaches by interweaving an ethnographic exploration of relations at a community café in the London neighbourhood of Kilburn with a review of various ‘minor’ themes within the convivial turn: boundedness, care and joint commitment, opacity, and interweaving. The article argues that each of these themes, major and minor, characterises a distinctive mode of relating, each marked by its own possibilities and limits. In doing so it argues for a more plural understanding of difference and forms of togetherness, connected to a more expansive politics.

Existence of Solutions for p-Kirchhoff Problem of Brézis-Nirenberg Type with Singular Terms

In this paper, we prove the existence of positive solution for a p-Kirchhoff problem of Brézis-Nirenberg type with singular terms, nonlocal term, and the Caffarelli-Kohn-Nirenberg exponent by using variational methods, concentration compactness, and maximum principle.

Positive Solutions for Anisotropic Singular Dirichlet Problems

We consider a Dirichlet problem driven by a (p(z), q(z))-Laplacian and a reaction involving the sum of a parametric singular term plus a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter lambda >0 varies. Also we show that for every admissible parameter the problem has a smallest positive solution and obtain the monotonicity and continuity properties of the minimal solution map.