Order Terms Research Articles

Spectral structure of the Neumann–Poincaré operator on axially symmetric functions

We consider the Neumann–Poincaré operator on a three-dimensional axially symmetric domain which is generated by rotating a planar domain around an axis which does not intersect the planar domain. We investigate its spectral structure when it is restricted to axially symmetric functions. If the boundary of the domain is smooth, we show that there are infinitely many axially symmetric eigenfunctions and derive Weyl-type asymptotics of the corresponding eigenvalues. We also derive the leading order terms of the asymptotic limits of positive and negative eigenvalues. The coefficients of the leading order terms are related to the convexity and concavity of the domain. If the boundary of the domain is less regular, we derive decay estimates of the eigenvalues. The decay rate depends on the regularity of the boundary. We also consider the domains with corners and prove that the essential spectrum of the Neumann–Poincaré operator on the axially symmetric three-dimensional domain is non-trivial and contains that of the planar domain.

Existence and uniqueness results for an elliptic equation with blowing-up coefficient and lower order term

Existence and uniqueness results for an elliptic equation with blowing-up coefficient and lower order term

Mixed Boundary Value Problem for a Monotone Equation with a Lower Order Term and Point Sources on the Right Side

Mixed Boundary Value Problem for a Monotone Equation with a Lower Order Term and Point Sources on the Right Side

Revisiting flat rotation curves in Chern-Simons modified gravity

We revisit slow rotating black hole (BH) solutions in Chern-Simons modified gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In particular, the case when nondynamical CSMG with noncanonical CS scalar is considered. We provide a new solution different from the previously obtained one [1] which we refer to as KMT model. The present solution accounts for frame dragging effect which includes not only radial dependence as in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that the tidal gravitational force (Kretschmann invariant) associated to the present solution contains a term of order 1/r3 additional to Schwarzschild but absent from directional divergence, unlike KMT model which diverges along the axis of symmetry. We derive the corresponding circular velocity of a massive test particle in which the KMT velocity is recovered in addition to an extra term ∝r. We investigate possible constraints on KMT and the present solutions from the observed rotation curve of UGC11455 galaxy as an example. We show that perturbation solutions cannot physically explain the flattening of galactic rotation curves.

Westerfit: A new program for spin–torsion–rotation spectra

A new program, westerfit, has been developed to treat Cs molecules with internal rotation and spin angular momentum. It implements a single diagonalization Rho Axis Method approach for the torsion–rotation alongside a complete treatment of nuclear quadrupole interaction and spin–rotation coupling. Unlike other programs designed for internal rotation with spin effects, westerfit includes matrix elements off-diagonal in the rotational angular momentum quantum number, N, rather than the perturbative treatment of the spin–rotation and quadrupole interactions. This full combined approach allows fitting of all symmetrically allowed terms in both the spin–rotation and the quadrupole tensors as well as inclusion of higher order terms coupling the large amplitude motion to the spin angular momentum. The program was benchmarked against other published programs to test molecular cases of torsion–rotation, spin–rotation, and spin–torsion-rotation. All three tests produced a lower RMS. westerfit paves a way forward for complete treatment of spin–torsion–rotation problems regardless of barrier height or quadrupole moment.

On global symmetries and Fayet–Iliopoulos terms

We revisit the genuine Fayet–Iliopoulos terms of 4D N=1 supergravity. Such terms are commonly believed to preserve a global symmetry, and therefore they are in conflict with the principles of quantum gravity. However, we find that generically there do exist supersymmetric terms that break explicitly the specific global symmetry, while preserving gauge invariance. We illustrate this, by providing a series of examples, including superpotentials and superspace higher order terms, along with a general prescription for their construction.

Existence and regularity results of parabolic problems with convection term and singular nonlinearity

In this work, we investigate the influence of the convection term and the singular lower order term on the existence and regularity of solutions to the following parabolic problem: \begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}(M(x,t)\nabla u) =-\operatorname{div}(uE(x,t))+\frac{f}{u^{\theta}}&\text{in }\Omega\times(0,T),\\ u(x,t)=0&\text{on }\partial \Omega\times (0,T),\\ u(x,0)=u_{0}(x)&\text{in }\Omega,\end{cases} where \theta>0 , \Omega\subset \mathbb{R}^{N}\ (N>2) is a bounded smooth domain with 0\in \Omega , and f\in L^{m}(\Omega\times (0,T)) with m\geq 1 is a non-negative function. The function u_{0} is a non-negative function that belongs to the space L^{\infty}(\Omega) such that \forall \omega\subset\subset \Omega,\ \exists c_{\omega}>0,\quad u_{0}\geq c_{\omega}\text{ in }\omega. The main idea of this research explains the combined impact of the convection term and the singular lower order term on the existence and regularity of a solution to the above problem.

Multitone Upconverted Phase-Modulated Signal RoF Link for 6G & Next-Generation Networks

The Next-Generation Networks offer a green environment with demanded data rates with ultra-low latency. Future efforts will be oriented in more degrees of freedom and system complexity with incorporating global optimization in terms of non-linearities, cost-effective, and reduced environmental impacts. The multitone upconverted radio over fibre (RoF) link with an optical modulator as phase modulator as desired alternatives with respect to optimization features and quantum photonic integration. In this paper, a framework has been developed to characterise the upconverted phase modulated signal model based on next-generation networks, in which an analytical model is investigated for single-tone upconverted, two-tone upconverted, and three-tone upconverted. Numerical simulations have been carried out to verify the novel outcomes using OptSIM software. The developed analytical models have a major contribution to the implementation of next-generation networks such as 5G, 6G, WiMAX, Quantum Communication, etc. The fundamentals of harmonics and the intermodulation product terms of third and fifth order via optical link are also evaluated for multitone Phase modulated RoF link with upconversion method. As per the finding outcomes, the proposed link is adaptable with frequency upconversion and long fibre distances.

Long‐time asymptotics of solution for the fifth‐order modified KdV equation in the presence of discrete spectrum

AbstractWe investigate the Cauchy problem of an integrable focusing fifth‐order modified Korteweg–de Vries (KdV) equation, which contains the fifth‐order dispersion and relevant higher order nonlinear terms. The long‐time asymptotics of solution is established in the case of initial conditions that lie in some low regularity weighted Sobolev spaces and allow for the presence of discrete spectrum. Our method is based on a generalization of the nonlinear steepest descent method of Deift and Zhou. We show that the solution decomposes in the long time into three main regions: (i) an expanding oscillatory region where solitons and breathers travel with positive velocities, the leading order term has the form of a multisoliton/breather and soliton/breather–radiation interactions; (ii) a Painlevé region, which does not have traveling solitons and breathers, the asymptotics can be characterized with the solution of a fourth‐order Painlevé II equation; (iii) a region of breathers traveling with negative velocities. Employing a global approximation via PDE techniques, the asymptotic behavior of solution is extended to lower regularity spaces with weights.

Effects of squared four-fermion operators of the standard model effective field theory on meson mixing

The standard model effective field theory (SMEFT) is a universal way of parametrizing new physics (NP) manifesting as new, heavy particle interactions with the Standard Model (SM) degrees of freedom, that respect the SM gauged symmetries. Higher order terms in the NP interactions possibly lead to sizable effects, mandatory for meaningful phenomenological studies, such as contributions to neutral meson mixing, which typically pushes the scale of NP to energy scales much beyond the reach of direct searches in colliders. I discuss the leading-order renormalization of double-insertions of dimension-6 four-fermion operators that change quark flavor by one unit (i.e., |ΔF|=1, F=strange-, charm-, or bottom-flavor), by dimension-8 operators relevant to meson mixing (i.e., |ΔF|=2) in SMEFT. Then, I consider the phenomenological implications of contributions proportional to large Yukawas, setting bounds on the Wilson coefficients of operators of dimension-6 via the leading logarithmic contributions. Given the underlying interest of SMEFT to encode full-fledged models at low energies, this work stresses the need to consider dimension-8 operators in phenomenological applications of dimension-6 operators of SMEFT. Published by the American Physical Society 2024

Robust stability and H∞$$ {H}_{\infty } $$ performance evaluation for time‐varying‐delayed uncertain linear systems based on variable‐augmented‐based free‐weighting matrices

AbstractThe problem of the robust stability and performance evaluation of time‐varying‐delayed uncertain linear systems (TVDULSs) is studied in this article. At first, to obtain a modified robust delay‐dependent condition of TVDULSs, a novel augmented Lyapunov‐Krasovskii functional (LKF) is established, and a variable‐augmented‐based free‐weighting matrices (VAFWMs) technique is tailored to evaluate the functional derivative. Compared with the existing robust stability methods, the constructed functional takes fully time delay information of the system into consideration and provides more delay‐cross terms, where the corresponding matrices are used to relax the constraints of linear matrix inequalities in the stability condition. Also, the VAFWMs method fully considers the linear relation of some delayed integral terms in the functional derivative, which avoids the usage of a quadratic order or higher order terms of the time delay. Then, an improved performance analysis criterion of TVDULSs is obtained against the disturbance on the basis of the proposed robust stability condition. The admissible maximal delay upper bounds that the uncertain linear system can tolerate are provided by proposed criterion under a given performance level. At last, two numerical examples are presented to verify the effectiveness and the superiority of the methods obtained.

Effective Storm Water Management in The Urban Area – A Case Study

Urbanization and climate change have negative effects on the changes of natural precipitation and runoff regime, which results with more frequent floods and landslides. Besides of the increased quantity of the stormwater that drainage channels have to collect, neg- ative consequences of urbanization are also evident through increased pollution of runoff stormwater. Stormwater has immense impacts on urban flooding and water quality, leaving the marginalized and the impoverished disproportionately impacted by and vulnerable to stormwater hazards. However, the environmental health concerns of socially and econom- ically marginalized individuals are largely underestimated. Therefore stormwater manage- ment should be adapted to these changes so that the negative effects of new hydrological conditions of precipitation and runoff and stormwater pollution in the urban areas are mitigated. By 2050 the world population will grow to about 9 billion contributing to deep changes in urban areas structure. This would increase the effect of water deficiency and along with projected climate changes the impact of urban flooding, urban heat islands or drought. Stormwater threats can be mitigated with the application of stormwater management meth- ods named differently such as ‘Sustainable (Urban) Drainage Systems’ (SUDS), ‘Low Impact Development’ (LID) or ‘Best Management Practices’ (BMPs). This method includes differ- ent techniques such as Green roof, Rain barrels and cisterns, Infiltration basin, Detention Ponds, Retention Ponds, Green walls, Porous pavements, Bioretention basins, Bioswales. The aim of the research includes a study of the effectiveness of urban stormwater manage- ment techniques for the case study area. The concept of urban stormwater management techniques refers to the ability to provide and manage this primary resource in quantitative and qualitative terms in order to satisfy the future needs of population. The storm wa- ter management techniques provides several benefits: mitigation of the urban heat island effects, reduction of air pollution, additionally, It induces important hydraulic advantages acting as an effective tool for reducing flood risk in urban area with runoff reduction, attenuation and delay of the peak flow. The results confirm that bioretention basin, Permeable pavement, Grassed swale, Infiltration basin are effective techniques for the reduction of total runoff volume of rainwater falling on their area.

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Abstract The p-Laplacian problem - ∇ ⋅ ( ( μ + | ∇ ⁡ u | p - 2 ) ⁢ ∇ ⁡ u ) = f {-\nabla\cdot((\mu+|\nabla u|^{p-2})\nabla u)=f} is considered, where μ is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher order terms, to the error in a quasi-norm. The involved constants being independent of μ, the solution, the mesh size and aspect ratio. An adaptive algorithm is proposed and numerical results are presented when p = 3 {p=3} . From this model problem, we propose a simplified error estimator and use it in the framework of an industrial application, namely a nonlinear Navier–Stokes problem arising from aluminium electrolysis.

II. In Civitate: Captivity and Inheritance in Tannaitic Halakha in Light of Roman Law

Summary The question of the influence of Roman law on tannaitic legal literature, composed in Roman Palestine from the first to the third centuries CE, is currently the focus of an intense scholarly debate. While some argue for a deep link between rabbinic and Roman legal discourse, others regard the impact of Roman law on the rabbis as merely superficial. The current article aims to contribute to this debate by presenting a case study that demonstrates a high level of engagement, by some rabbis, with Roman legal discourse, one that goes well beyond superficial borrowing. In this case study, a rabbinic ruling regarding the inheritance of captives is shown to depend heavily on Roman juristic discourse over the ramifications of the Lex Cornelia de captivis. In a sophisticated process of reworking, the rabbis adapt Roman legal materials and principles into a rabbinic framework. Most importantly, we show that this reworking includes the reappropriation of a native tannaitic term (‘in the medina’) in order to translate a Roman technical legal term (in civitate), infusing the Hebrew term with new legal meanings. The details of this case study reveal what is normally concealed: the self-awareness of the rabbis who handle a Roman legal literary source, most probably derived from a concrete juristic discourse, deliberately reworking it to accord with rabbinic terminology, style, and form. This was probably not a one-time process, and it could well have been standard practice among some of the rabbis. Thus, this case study suggests that the evidence for a dramatic impact of Roman legal discourse on tannaitic halakha might be hiding in plain sight.

Elliptic problems with superlinear convection terms

In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type−div(M(x)∇u)=−div(h(u)E(x))+f(x), where M is a bounded elliptic matrix, the vector field E and the function f belong to suitable Lebesgue spaces, and the function s→h(s) features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle.

Dynamics for wave equations connected in parallel with nonlinear localized damping

Abstract This study investigates the properties of solutions about one-dimensional wave equations connected in parallel under the effect of two nonlinear localized frictional damping mechanisms. First, under various growth conditions about the nonlinear dissipative effect, we try to establish the decay rate estimates by imposing minimal amount of support on the damping and provide some examples of exponential decay and polynomial decay. To achieve this, a proper observability inequality has been proposed and constructed based on some refined microlocal analysis. Then, the existence of a global attractor is proved when the damping terms are linearly bounded at infinity, a special weighting function has been used in this part, which eliminates undesirable terms of the higher order while contributing lower-order terms. Finally, we establish that the long-time behavior of solutions of the nonlinear system is completely determined by the dynamics of large finite number of functionals.

Symmetry resolution in non-Lorentzian field theories

Starting from the computation of Symmetry Resolved Entanglement Entropy (SREE) for boosted intervals in a two dimensional Conformal Field Theory, we compute the same in various non-Lorentzian limits, viz, Galilean and Carrollian Conformal Field Theory in same number of dimensions. We approach the problem both from a limiting perspective and by using intrinsic symmetries of respective non-Lorentzian conformal algebras. In particular, we calculate the leading order terms, logarithmic terms, and the O1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}(1) $$\\end{document} terms and explicitly show exact compliance with equipartition of entanglement, even in the non-Lorentzian system. Keeping in mind the holographic origin of SREE for the Carrollian limit, we further compute SREE for BMS3-Kac-Moody, which couples a U(1) × U(1) theory with bulk gravity.

Crack-tip constraint analysis of bending specimens for considering higher order terms in asymptotic solution

In this research, a higher-order asymptotic J-A2-A4 solution was introduced for studying the effect of the bending moment on the crack-tip constraint of a specimen. The solution was applied to TPB and SENB specimens with varying bending moment loads, and compared to other methods such as FEA, HRR solution, J-A2 solution and J-A2-M solution. The results were analyzed and compared with the FEA, J-A2 theory and J-A2-M theory solutions obtained from references. The impact of global bending on the calculation of crack-tip opening stress was also investigated. The findings showed that the J-A2-A4 solution closely matched the FEA numerical results, and better accounted for the influence of global bending compared to the J-A2 method. Therefore, there is no need to modify the J-A2 method by adding a bending moment term, as suggested in the J-A2-M theory.

A Revisit of Electromagnetic Wave Scattering by a Metal Isotropic Body in a Lossless Environment with Magnetic Sensor Excitation.

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace's or Poisson's interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation.

Transient resonance of sloshing liquid with time-varying mass

This study examines the sloshing of liquid with time-varying mass in a tank. A set of innovative experiments is carried out involving a shaking table supporting a water tank equipped with a drain pipe. Physical evidence of transient resonance is observed for the first time. Transient resonance occurs under specific excitation conditions when the instantaneous average water level (AWL) approaches a critical depth. During transient resonance, the oscillatory amplitude of the free-surface elevation increases sharply and then decreases in an envelope pattern. A bifurcation of the frequency band is first found in the Morlet-wavelet time–frequency spectrum, coinciding with the appearance of the maximum oscillatory amplitude. How the excitation conditions, drainage rate, and initial water depth affect transient resonance is recognized. Two mathematical models—one based on linear modal theory and the other based on nonlinear asymptotic theory and the Bateman–Luke variational principle—are derived to replicate the physical observations, by which application scopes of both models have been greatly broadened. The linear solution fails to predict the key feature of transient resonance, namely, the asymmetric envelopes of the oscillatory component about the AWL. By contrast, the nonlinear asymptotic solution captures this asymmetric feature accurately, and predicts both the steady and maximum oscillatory amplitudes well. The nonlinear solution is decomposed into terms of order 1/3, 2/3, and 1 using an asymptotic series for component analyses. A special nonlinear jump behavior is observed. The effects of draining and filling on transient resonance are compared.