Singular Model Research Articles

Clustering Phenomenon of the Singular Cucker-Smale Model with Finite Communication Weight and Variable Coupling Strength

Clustering Phenomenon of the Singular Cucker-Smale Model with Finite Communication Weight and Variable Coupling Strength

Singular Cotangent Models and Complexity in Fluids with Dissipation

Singular Cotangent Models and Complexity in Fluids with Dissipation

Numerical Aspects of Isogeometric Boundary Element Methods: (Nearly) Singular Quadrature, Trimmed NURBS and Surface Crack Modeling

This work presents some numerical aspects of isogeometric boundary element methods (IGABEM). The behavior of hyper-singular and nearly-singular integration is first explored on the distorted NURBS surface. Several numerical treatments are proposed to enhance the quadrature in the framework of isogeometric analysis. Then a numerical implementation of IGABEM on the trimmed NURBS is detailed. Based on this idea, the surface crack problem is modeled incorporation with the phantom element method. The proposed method allows the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.

State and fault estimation based on fuzzy observer for a class of Takagi-Sugeno singular models

Singular nonlinear systems have received wide attention in recent years, and can be found in various applications of engineering practice. On the basis of the Takagi-Sugeno (T-S) formalism, which represents a powerful tool allowing the study and the treatment of nonlinear systems, many control and diagnostic problems have been treated in the literature. In this work, we aim to present a new approach making it possible to estimate simultaneously both non-measurable states and unknown faults in the actuators and sensors for a class of continuous-time Takagi-Sugeno singular model (CTSSM). Firstly, the considered class of CTSSM is represented in the case of premise variables which are non-measurable, and is subjected to actuator and sensor faults. Secondly, the suggested observer is synthesized based on the decomposition approach. Next, the observer’s gain matrices are determined using the Lyapunov theory and the constraints are defined as linear matrix inequalities (LMIs). Finally, a numerical simulation on an application example is given to demonstrate the usefulness and the good performance of the proposed dynamic system.

HOMO-LUMO photosensitization analyses of coronene-cytosine complexes

Photosensitization analyses of models of (–HC = CH–)n assisted coronene-cytosine complexes assigned by Cor-n-Cyt; n varying by 0, 1, 2, and 3, were investigated in this work by performing density functional theory (DFT) calculations. The investigated models were optimized and chemical descriptors were evaluated. To achieve the goal of this work, energy levels of the highest occupied and the lowest unoccupied molecular orbitals (HOMO and LUMO) were evaluated to reach the absorption energy requirement for innovating photosensitizer (PS) compounds. The models indicated that the complex formations could help the structures to participate in interactions easier than the singular models, in which HOMO-LUMO descriptors indicated lower required absorption energy for them to increase their safety for human health level. The required absorption energies of complexes with n = 0, 1, and 2, were in ultraviolet (UV) region whereas that of complex with n = 3 was moved to visible region. In this regard, the idea of new PS compounds innovation was examined here to introduce Cor-n-Cyt complexes for possible applications in photodynamic therapy (PDT).

Structural analysis of an iron-assisted carbon monolayer for delivery of 2-thiouracil

An idea of employing an iron-assisted carbon (FeC) monolayer for delivery of 2-thiouracil (2TU) was examined in this work by analyzing structural features for singular and bimolecular models. Density functional theory (DFT) calculations were performed for optimizing the structures and evaluating molecular and atomic descriptors for analyzing the models systems. Two bimolecular models were obtained assigning by S-FeC and O-FeC models, in which each of S and O atom of 2TU was relaxed towards the Fe region of FeC surface in the mentioned models, respectively. The results indicated that both models were achievable with slightly more favorability for formation of S-FeC model. The obtained molecular orbital properties revealed the dominant role of FeC monolayer for managing future interactions of attached 2TU, which is indeed a major role for employing nanomaterials for targeted drug delivery purposes. In addition to energies and molecular orbital features, atomic quadrupole coupling constants indicated the benefit of employing FeC monolayer for drug delivery of 2TU.

Evolutionary heuristic with Gudermannian neural networks for the nonlinear singular models of third kind

The presented research work articulates a new design of heuristic computing platform with artificial intelligence algorithm by exploitation of modeling with feed-forward Gudermannian neural networks (FFGNN) trained with global search viability of genetic algorithms (GA) hybrid with speedy local convergence ability of sequential quadratic programing (SQP) approach, i.e., FFGNN-GASQP for solving the singular nonlinear third order Emden-Fowler (SNEF) models. The proposed FFGNN-GASQP intelligent computing solver Gudermannian kernel unified in the hidden layer structure of FFGNN systems of differential operators based on the SNEF that are arbitrary connected to represent the error-based merit function. The optimization objective function is performed with hybrid heuristics of GASQP. Three problems of the third order SNEF are used to evaluate the correctness, robustness and effectiveness of the designed FFGNN-GASQP scheme. Statistical assessments of the performance of FFGNN-GASQP are used to validate the consistent accuracy, convergence and stability.

Extended virtual element method for two-dimensional linear elastic fracture

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes. For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis functions by suitable enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The design of the X-VEM requires an extended projector that maps functions lying in the extended virtual element space onto a set spanned by linear polynomials and the enrichment fields. An efficient scheme to compute the mixed-mode stress intensity factors using the domain form of the interaction integral is described. The formulation permits integration of weakly singular functions to be performed over the boundary edges of the element. Numerical experiments are conducted on benchmark mixed-mode linear elastic fracture problems that demonstrate the sound accuracy and optimal convergence in energy of the proposed formulation.

The 2021 Bitcoin Bubbles and Crashes—Detection and Classification

In this study, the Log-Periodic Power Law Singularity (LPPLS) model is adopted for real-time identification and monitoring of Bitcoin bubbles and crashes using different time scale data, and the modified Lagrange regularization method is proposed to alleviate the impact of potential LPPLS model over-fitting to better estimate bubble start time and market regime change. The goal here is to determine the nature of the bubbles and crashes (i.e., whether they are endogenous due to their own price evolution or exogenous due to external market and/or policy influences). A systematic market event analysis is performed and correlated to the Bitcoin bubbles detected. Based on the daily LPPLS confidence indictor from 1 December 2019 to 24 June 2021, this analysis has disclosed that the Bitcoin boom from November 2020 to mid-January 2021 is an endogenous bubble, stemming from the self-reinforcement of cooperative herding and imitative behaviors of market players, while the price spike from mid-January 2021 to mid-April 2021 is likely an exogenous bubble driven by extrinsic events including a series of large-scale acquisitions and adoptions by well-known institutions such as Visa and Tesla. Finally, the utilities of multi-resolution LPPLS analysis in revealing both short-term changes and long-term states have also been demonstrated in this study.

Globalizing racial triangulation: including the people and nations of color on which White supremacy depends

ABSTRACT Racial triangulation theory brilliantly conjoins, at once, two different types of racialized hierarchies, thereby allowing more than the metrics of standard anti-African American racism (“the color line”) to be theorized. This is one of the hallmarks of the pathbreaking model. At the same time, this essay chronicles how racial triangulation falls prey to the common social science tendency of US centrism, nation-state singularity, and catch-all models, omitting the influence of (neo)imperialism, (neo/post)colonialism, neoliberalism, and other foundational projects of global and American racism. For instance, U.S. empire – i.e., militarist, capitalist, cultural dominance – means that most Asian ethnic groups experienced racial injustice and a version of racial triangulation in their sending countries before migration; in turn, the pre-migrant context profoundly shapes how the US racializes/positions these groups (often vis-a-vis one another) and how the margins respond. In addition, racial triangulation privileges eastern-descent ethnics, overlooks anti-South Asian American racism in the post-1980s and post-911 era, underappreciates Asian/Asian American resistance, and neglects to theorize those positioned at the intersection of “inferior” and “foreigner” (of which former President Barack Obama is emblematic). In spite of the (constructive) criticism, in this era of Covid-19 racism, the Atlanta Massacre, widespread state murder of Black Americans, anti-Latinx/-Mexican nativist racism, and Muslim Bans, we need to expand racial triangulation theory, not dismiss it.

Community banks versus non‐community banks: Post the Great Recession

AbstractCommunity banks (CBs), despite holding a fairly small share of US banking assets, provide vital financial services to key segments of the economy and fill a void untapped by larger non‐community banks (Non‐CBs). They face challenges brought on by a fast‐changing banking landscape, evolving technology, and ever‐increasing regulatory burden. To remain competitive and to gain scale‐related efficiencies, CBs have been seeking mergers even as greater institutional size causes a departure from the classical relationship‐based business model. This study examines performance of US CBs and Non‐CBs post the Great Recession to reveal how size of these institutions may affect their business operations. Empirical findings show that CBs, compared with their larger counterparts, tend to maintain higher levels of liquidity and lower levels of capital, and demonstrate a greater dependence on core deposits, confirming that CBs focus on deposit taking and soft information‐based lending strategies. Furthermore, this study suggests that CBs should not be considered a homogenous group operating under a singular business model and cautions that regulatory dialectics aimed at the banking industry should not employ a one‐size‐fits‐all approach.

Event-triggered output quantized control of discrete Markovian singular systems

This paper is concerned with the event-triggered H∞ admissible analysis and controller synthesis for discrete delayed singular Markovian jump network systems with output quantizations. Based on event-triggered communication mechanism and quantized control strategy, a singular network system model with network-induced delays is firstly established, and sufficient criteria are then given to guarantee that the singular stochastic network systems are stochastically H∞ admissible. Furthermore, according to variable separation and matrix decomposition techniques, output quantized controllers and event-triggered matrices are tactfully co-designed for the stochastic H∞ admissibility of the singular network model. An example is also provided to illustrate the effectiveness of the proposed approach.

Youth Athlete Development Models: A Narrative Review.

Physical activity has shown to be beneficial for the overall physical and mental health of youth. There has been an increasing focus on youth sports moving from a recreational activity to becoming a launching pad for participation at elite levels. Several models of athlete development have emerged to guide specialized and nonspecialized athletes at an age-appropriate level, taking into consideration their physical and mental development. The purpose of this review is to summarize the current evidence and theoretical models regarding youth athlete development and discuss broader initiatives for sports participation and future directions for the field. An electronic databases search, including PubMed, Google Scholar, ScienceDirect, National Institutes of Health, UpToDate, and Springer was conducted. Articles from 1993 to 2021 were included. The search terms long term athlete development, LTAD model, youth physical development, youth athlete development, sports specialization, and pediatric athlete, among others, were used. Narrative review. Levels 4 and 5. Several models of youth athlete development are discussed in this article. More recent models have built on previous models to incorporate more age- and development-specific recommendations; however, no singular model could be identified as the gold standard for youth athlete development, especially given the lack of empirical data to support these models. Youth athlete development currently consists of several theoretical models, each with their own strengths and weaknesses, that can guide the training of young athletes to maximize their performance. Those involved in this process-physicians, athletic trainers, coaches, physical educators, and parents-should understand these various models and trial their various features to see what works best for their individual athlete with consideration given to factors such as their stage of development. Ultimately, more empirical data are required to definitively state which is the optimal approach.

Uniqueness of asymptotically conical tangent flows

Singularities of the mean curvature flow of an embedded surface in R^3 are expected to be modelled on self-shrinkers that are compact, cylindrical, or asymptotically conical. In order to understand the flow before and after the singular time, it is crucial to know the uniqueness of tangent flows at the singularity. In all dimensions, assuming the singularity is multiplicity one, uniqueness in the compact case has been established by the second-named author, and in the cylindrical case by Colding-Minicozzi. We show here the uniqueness of multiplicity-one asymptotically conical tangent flows for mean curvature flow of hypersurfaces. In particular, this implies that when a mean curvature flow has a multiplicity-one conical singularity model, the evolving surface at the singular time has an (isolated) regular conical singularity at the singular point. This should lead to a complete understanding of how to "flow through" such a singularity.

The surface tension effect revealed via the indentation scaling index

The axisymmetric frictionless indentation problem for an isotropic elastic half-space with the uniform surface tension is considered. The first-order regular and singular asymptotic models are constructed for the limit situations of relatively small (in the membrane limit) or large (in the Hertzian limit) values of the contact radius. By using the method of collocation, a two-parameter analytical approximate solution is developed with coefficients evaluated in triple quadratures. The accuracy of the obtained analytical models is investigated in the case of a paraboloidal indenter by comparison with numerical solutions available in the literature. Based on the asymptotic behavior of the solution in the limit situations, the so-called indentation scaling index is introduced for the analysis of the depth-sensing indentation data. By making use of the novel contact parameter it is possible to extract the surface tension effect independently of determining the reduced elastic modulus of a tested semi-infinite sample. It is shown that by employing an appropriate normalization, the contact problem can be reduced to that parameterized by only one parameter (relative contact radius), which implies that irrespectively of the combination of the material parameters, the force–displacement curve drawn in the normalized variables will be universal.

An Efficient Stochastic Numerical Computing Framework for the Nonlinear Higher Order Singular Models

The focus of the present study is to present a stochastic numerical computing framework based on Gudermannian neural networks (GNNs) together with the global and local search genetic algorithm (GA) and active-set approach (ASA), i.e., GNNs-GA-ASA. The designed computing framework GNNs-GA-ASA is tested for the higher order nonlinear singular differential model (HO-NSDM). Three different nonlinear singular variants based on the (HO-NSDM) have been solved by using the GNNs-GA-ASA and numerical solutions have been compared with the exact solutions to check the exactness of the designed scheme. The absolute errors have been performed to check the precision of the designed GNNs-GA-ASA scheme. Moreover, the aptitude of GNNs-GA-ASA is verified on precision, stability and convergence analysis, which are enhanced through efficiency, implication and dependability procedures with statistical data to solve the HO-NSDM.

Artificial Neural Networks to Solve the Singular Model with Neumann-Robin, Dirichlet and Neumann Boundary Conditions.

The aim of this work is to solve the case study singular model involving the Neumann–Robin, Dirichlet, and Neumann boundary conditions using a novel computing framework that is based on the artificial neural network (ANN), global search genetic algorithm (GA), and local search sequential quadratic programming method (SQPM), i.e., ANN-GA-SQPM. The inspiration to present this numerical framework comes through the objective of introducing a reliable structure that associates the operative ANNs features using the optimization procedures of soft computing to deal with such stimulating systems. Four different problems that are based on the singular equations involving Neumann–Robin, Dirichlet, and Neumann boundary conditions have been occupied to scrutinize the robustness, stability, and proficiency of the designed ANN-GA-SQPM. The proposed results through ANN-GA-SQPM have been compared with the exact results to check the efficiency of the scheme through the statistical performances for taking fifty independent trials. Moreover, the study of the neuron analysis based on three and 15 neurons is also performed to check the authenticity of the proposed ANN-GA-SQPM.

Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results.

Weyl point immersed in a continuous spectrum: An example from superconducting nanostructures

A Weyl point in a superconducting nanostructure is a generic minimum model of a topological singularity at low energies. We connect the nanostructure to normal leads thereby immersing the topological singularity in the continuous spectrum of the electron states in the leads. This sets another simple and generic model useful to comprehend the modification of low-energy singularity in the presence of a continuous spectrum. The tunnel coupling to the leads gives rise to new low-energy scale $\mathrm{\ensuremath{\Gamma}}$ at which all topological features are smoothed. We investigate superconducting and normal currents in the nanostructure at this scale. We show how the tunnel currents can be used for detection of the Weyl point. Importantly, we find that the topological charge is not concentrated in a point but rather is spread over the parameter space in the vicinity of the point. We introduce and compute the resulting topological charge density. We also reveal that the pumping to the normal leads helps to detect and investigate the topological effects in the vicinity of the point.

Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model

The aim of this study is to design a singular fractional order pantograph differential model by using the typical form of the Lane-Emden model. The necessary details of the singular-point, fractional order and shape factor of the designed model are also provided. The numerical solutions of the designed model have been presented using the combination of the fractional Meyer wavelet (FMW) neural networks (NNs) modeling and optimization of global search with genetic algorithm (GA) supported with local search of sequential quadratic programming (SQP), i.e., FMWNN-GASQP. The strength of FMWNN is employed to design an objective function using the differential model along with its initial conditions of the singular fractional order pantograph model. The optimization of this objective function is performed using the integrated competence of GA-SQP. The verification, perfection and authentication of the singular fractional order pantograph model using fractional Meyer computing solver is observed for different cases through comparative studies from the available exact solutions which endorsed its robustness, convergence and stability. Moreover, the statistics observation with necessary explanations further authenticate the performance of the FMWNN-GASQP in terms of accuracy and reliability.