Perturbative Stability Research Articles

Stable perturbations of matrices over rings with respect to pseudo core inverses

Abstract We introduce the stable perturbation of matrices over an arbitrary ∗ {\ast} -ring with respect to pseudo core inverses, which extends the stable perturbation of square complex matrices with respect to core-EP inverses. Let A and B be pseudo core invertible matrices over a unital ∗ {\ast} -ring. Then B is called a stable perturbation of A with respect to pseudo core inverses if ℛ ⁢ ( A k ) ∩ 𝒩 ⁢ ( ( B s ) ∗ ) = { 0 } {\mathcal{R}(A^{k})\cap\mathcal{N}((B^{s})^{\ast})=\{0\}} and ℛ ⁢ ( B s ) ∩ 𝒩 ⁢ ( ( A k ) ∗ ) = { 0 } {\mathcal{R}(B^{s})\cap\mathcal{N}((A^{k})^{\ast})=\{0\}} , where k and s are pseudo core indices of A and B, respectively. It is shown that if R is a right FP-injective ring, then B is a stable perturbation of A if and only if I - ( B π - A π ) 2 {I-(B^{\pi}-A^{\pi})^{2}} is invertible, where A π = I - A ⁢ A \⃝raisebox{0.569055pt}{$\scriptstyle{D}$} {A^{\pi}=I-AA^{\text{\textcircled{\raisebox{0.2mm}{$\scriptstyle{D}$}}}}} and B π = I - B ⁢ B \⃝raisebox{0.569055pt}{$\scriptstyle{D}$} {B^{\pi}=I-BB^{\text{\textcircled{\raisebox{0.2mm}{$\scriptstyle{D}$}}}}} are spectral projectors of A and B, respectively. Necessary and sufficient conditions are given for B to be a stable perturbation of A in terms of the invertibility of certain matrices involving pseudo core inverses of A and B.

Rayleigh-Taylor instability in inhomogeneous relativistic classical and degenerate electron-ion magnetoplasmas

Abstract We study the Rayleigh-Taylor instability (RTI) of electrostatic plane wave perturbations in compressible relativistic magnetoplasma fluids with thermal ions under gravity in three different cases of when (i) electrons are in isothermal equilibrium, i.e., classical or nondegenerate, (ii) electrons are fully degenerate (with $T_e=0$), and (iii) electrons are partially degenerate or have finite temperature degeneracy (with $T_e\neq0$). While in the cases of (i) and (iii), we focus on the regimes where the particle's thermal energy is more or less than the rest mass energy, i.e., $\beta_e \equiv k_{\mathrm B}T_e/{m_ec^2}<1~\rm{or}~>1$, the case (ii) considers from weakly to ultra-relativistic degenerate regimes. A general expression of the growth rate of instability is obtained and analyzed in the three different cases relevant to laboratory and astrophysical plasmas, which generalize and advance the previous theory on RTI.

Stability of axion-saxion wormholes

We reconsider the perturbative stability of Euclidean axion wormholes. The quadratic action that governs linear perturbations is derived directly in Euclidean gravity. We demonstrate explicitly that a stability analysis in which one treats the axion as a normal two-form gauge field is equivalent to one performed in the Hodge-dual formulation, where one considers the axion as a scalar with a wrong-sign kinetic term. Both analyses indicate that axion wormholes are perturbatively stable, even in the presence of a massless dilaton, or saxion, field that couples to the axion.

Nonperturbative phase boundaries in the Gross-Neveu model from a stability analysis

Two out of three phase boundaries of the 1+1-dimensional Gross-Neveu model in the chiral limit can be obtained from a standard, perturbative stability analysis of the homogeneous phases. The third one separating the massive homogeneous phase from the kink crystal is nonperturbative and could so far only be inferred from the full solution of the model. We show that this phase boundary can also be obtained via a modified stability analysis, based on the thermodynamic potential of a single kink or baryon. The same method works for the massive Gross-Neveu model, so that all phase boundaries of the Gross-Neveu model could have been predicted quantitatively without prior knowledge of the full crystal solution. Published by the American Physical Society 2024

Exclusive vector-quarkonium photoproduction at NLO in αs in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation

We perform the first complete one-loop study of exclusive photoproduction of vector quarkonia off protons in Collinear Factorisation (CF) including the scale evolution of the Generalised Parton Distributions (GPDs). We confirm the perturbative instability of the cross section at high photon-proton-collision energies (Wγp) at Next-to-Leading Order (NLO) in αs and solve this issue by resumming higher-order QCD corrections, which are enhanced by a logarithm of the parton energies, using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA) matched to CF. Our NLO CF ⊕ DLA HEF results are in agreement with the latest HERA data and show a smaller sensitivity to the factorisation and renormalisation scales compared to Born-order results. Quark-induced channels via interference with gluon ones are found to contribute at most 20% of the cross section for Wγp>100 GeV. Our results also show that such exclusive cross sections cannot be accurately obtained from the square of usual Parton Distribution Functions (PDFs) and clearly illustrate the importance of quarkonium exclusive photoproduction to advance our understanding of the 3D content of the nucleon in terms of gluons. Our work provides an important step towards a correct interpretation of present and future experimental data collected at HERA, the EIC, the LHC and future experiments.

Next-to-Next-to-Leading Order Global Analysis of Polarized Parton Distribution Functions.

We present a next-to-next-to-leading order (NNLO) global QCD analysis of the proton's helicity parton distribution functions, the first of its kind. To obtain the distributions, we use data for longitudinal spin asymmetries in inclusive and semi-inclusive lepton-nucleon scattering as well as in weak-boson and hadron or jet production in proton-proton scattering. We analyze the data using QCD perturbation theory at NNLO accuracy, employing approximations provided by the threshold resummation formalism in cases where full NNLO results for partonic hard-scattering functions are not readily available. Our numerical results suggest a remarkable perturbative stability of the extracted helicity parton distribution functions.

Dark energy with a shift-symmetric scalar field: Obstacles, loophole hunting and dead ends

We discuss the possibility of a scalar field being the fundamental description of dark energy. We focus on shift-symmetric scalar-tensor theories since this symmetry potentially avoids some fine-tuning problems. We also restrict attention to theories satisfying that the propagation speed of gravitational waves is equal to the speed of light. These considerations lead us to investigate shift-symmetric Kinetic Gravity Braiding theories. Analysing the stability of scalar linear perturbations, we discuss the conditions that seems to be necessary to describe (super) accelerated cosmic expansion without introducing instabilities. However, it has been previously established that the linearised analysis does not guarantee the stability of this non-canonical scalar theory, as potentially dangerous interactions between dark energy fluctuations and tensor perturbations (essentially gravitational waves) appear at a higher order in perturbation theory. Indeed, although we shall point out that the standard proof of absence of dark energy stable braiding models due to this interaction has a possible way-out, we find general arguments suggesting that there are no dark energy stable solutions that can exploit this loophole. Thus, we discuss future research directions for finding viable fundamental descriptions of dark energy. We also provide a dictionary between the covariant version of the theory and that of the Effective Field Theory approach, explicitly computing the parameters in the latter formalism in terms of the functions appearing in the covariant version, and its derivatives. To the best of our knowledge, this is the first time these expressions are explicitly obtained up-to arbitrary order in perturbation theory.

Key roles of surface Cr in the NiFe layered double hydroxides for an efficient oxygen evolution reaction via adaptive reconfiguration

Cr doping is a new strategy to enhance the OER (Oxygen Evolution Reaction) performance of NiFe-LDH (NiFe-Layered Double Hydroxides) by optimizing surface states and offering a scalable production process. However, as an additive element, Cr itself has weak OER performance, so its promotion on the Ni- and Fe-active site by electron perturbation and structural stabilization in NiFeCr-LDH has been the focus. Herein, a one-step hydrothermal method is used to incorporate Cr into NiFe-LDH, systematically investigating the relationship between Cr content and the material's microstructure. The results of physical characterization show that Cr ion plays a leading role in the electron perturbation Ni/Fe-active center, which causes the increasing of Fe3+ and Ni3+ content. Furthermore, variations in Cr content resulted in the lattice stretching and morphology evolving synchronously. The optimized NiFeCr-LDH exhibited significantly enhanced OER activity and durability compared to undoped NiFe-LDH and outperformed commercial RuO2 catalysts. Additionally, a microstructure comparison was made between the initial- and long-term used-NiFeCr-LDH. The findings reveal that the material's distinctive structural evolution behavior confers it with exceptional self-adaptability to the OER reaction, which results in a consistent enhancement of activity lasting up to 12 h during long-term I-t test showing a new idea for the design of high performance NiFeCr-LDH.

Baryon junction and string interactions

We study junctions between confining strings. We show that the effective theory of such junctions is very predictive, with only one new parameter, the junction’s mass, controlling the first couple of terms in the expansion in the system size. By open-closed string duality, these considerations about the baryon junction map to interaction vertices of closed strings. Therefore, we calculate the interaction vertices of closed strings in theories such as Yang-Mills theory. We find some surprising selection rules for string interactions in 3+1 dimensions. Requiring perturbative stability and that the string coupling is weak, we suggest constraints on the junction’s mass. Published by the American Physical Society 2024

The core-EP inverse: a numerical approach for its acute perturbation

This paper studies the concept of stable perturbation B ∈ C n × n for the core-EP inverse of a matrix A ∈ C n × n with index k. For a given stable perturbation B of A, explicit expressions of its core-EP inverse B ◯ $ † $ and its projection at zero B π are presented. Then, the perturbation bounds of ∥ B ◯ $ † $ − A ◯ $ † $ ∥ / ∥ A ◯ $ † $ ∥ and ∥ B π − A π ∥ are given provided that B is a stable perturbation of A. In addition, we investigate the concept of acute perturbation of A. We give a perturbation analysis with respect to core-EP inverses. We provide a condition under which the acute perturbation coincides with the stable perturbation for core-EP inverses.

Comparative Effects of Fatiguing Exercise on Anticipatory and Compensatory Postural Adjustments between Trained and Untrained Individuals.

This study evaluates the effects of general fatiguing exercises on anticipatory postural adjustments (APAs), compensatory postural adjustments (CPAs), and standing stability between 18 individuals with comprehensive training experience (TR) and 18 untrained individuals (UT). Assessments were conducted before and after a 20-min fatiguing exercise using surface electromyography and a force platform during self-initiated perturbation and postural stability tests. Key findings include that, irrespective of fatigue, the APAs onsets in the TrA/IO (p = 0.004), LMF (PRE p = 0.003, POST p < 0.001), and ST (PRE p = 0.001, POST p = 0.006) muscles activated earlier in the TR group than in the UT group. Additionally, the APA co-contraction indices of the TrA/IO-LMF (PRE p = 0.011, POST p = 0.029), TrA/IO-ST (p = 0.014), and LMF-ST (PRE p = 0.002, POST p = 0.005) muscle pairs were higher in the TR group. After fatigue, the UT group significantly increased CPA co-contraction indices for the TrA/IO-LMF (p = 0.035) and LMF-ST (p = 0.005) muscle pairs. This research highlights the importance of comprehensive training in facilitating feedforward control strategies, particularly for individuals facing challenging postural conditions, such as fatigue or disturbances.

Inhibition of human epidermal growth factor receptor-2 protein by some alkaloid inhibitors

BackgroundHuman Epidermal Growth Factor Receptor-2 (HER2), a transmembrane tyrosine kinase receptor, has been associated with several types of cancer, including breast, lung, ovarian, etc. Therefore, this receptor is targeted by a variety of therapeutic approaches for cancer treatments. The alkaloid and lead compounds are among the selective and potent HER2 inhibitors that have been reported so far. MethodsThe present work involves molecular docking, molecular dynamics (MD) simulations, and density functional theory (DFT) calculations on alkaloid and lead compounds as HER2 inhibitors. Significant findingsThe docking results expressed that the alkaloids mainly interacted with Cys805, Val734, and Ala751 residues of HER2 protein. The MD simulation outcomes represented that all the complexes have adequate dynamic stability and flexibility based on the root mean square deviation, root mean square fluctuation, and radius of gyration. Furthermore, it is found that the strongest HER2 − ligand interaction belongs to the nocamycin I (NOI, ΔGbind = -12.84 kcal mol−1) molecule. The DFT calculations showed that electron density and the second − order perturbation stabilization energy values for HER2 − NOI interactions are higher than the other complexes. The molecular docking, MD simulation, and DFT calculation results are all in agreement and complementary. It is expected that the results obtained here can present very helpful information for the design of efficacious inhibitors for the treatment of HER2 − related cancer disease.

Stability and optimal decay for the 3D anisotropic magnetohydrodynamic equations

AbstractThis paper investigates the stability problem and large time behavior of solutions to the three‐dimensional magnetohydrodynamic equations with horizontal velocity dissipation and magnetic diffusion only in the direction. By applying the structure of the system, time‐weighted methods, and the method of bootstrapping argument, we prove that any perturbation near the background magnetic field (1, 0, 0) is globally stable in the Sobolev space . Furthermore, explicit decay rates in are obtained. Motivated by the stability of the three‐dimensional Navier–Stokes equations with horizontal dissipation, this paper aims to understand the stability of perturbations near a magnetic background field and reveal the mechanism of how the magnetic field generates enhanced dissipation and helps stabilize the fluid.

The path to N3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {N}^3\\hbox {LO}$$\\end{document} parton distributions

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document}). We construct an approximation to the N3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {N}^3\\hbox {LO}$$\\end{document} splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {N}^3\\hbox {LO}$$\\end{document} corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to Oαs3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}\\left( \\alpha _s^3\\right) $$\\end{document} accuracy. We determine a set of aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document} PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {N}^3\\hbox {LO}$$\\end{document} terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document} PDFs from the MSHT group. We examine the phenomenological impact of aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document} corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document} PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the aN3LO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {aN}^3\\hbox {LO}$$\\end{document} NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

Instabilities of perturbations in some homogeneous color-electric and -magnetic backgrounds in SU(2) gauge theory

We consider the instabilities of field perturbations around a homogeneous background color-electric and/or -magnetic field in SU(2) pure gauge theory. We investigate a number of distinct cases of background magnetic and electric fields, and we compute the dispersion relations in the linearized theory, identifying stable and unstable momentum modes. In the case of a net homogenous non-Abelian B field, we compute the nonlinear (quadratic and cubic) corrections to the equation of motion and quantify to what extent the instabilities are tempered by these nonlinearities. Published by the American Physical Society 2024

The oblique parameters in the 2HDM with vector-like quarks: confronting M W CDF-II anomaly

The CDF collaboration has released a new measurement of the W boson mass using their complete data set with 8.8 fb−1 in pp¯ collisions. This result deviates from the Standard Model prediction by around 7σ. We explain how the two Higgs doublet model (2HDM) with vector-like quarks (VLQs) is affected by the recently discovered W boson mass. In our study, we include both theoretical constraints such as perturbative unitarity and vacuum stability as well as a number of experimental constraints. We also look into how the effective mixing angle, measured by the SLD collaboration in addition to the CDF W-boson mass, is used to determine the S and T parameters. In the alignment limit, we investigate the case where the lighter CP-even neutral Higgs boson of the 2HDM is the one found at the LHC and demonstrate how the parameter space of the 2HDM type II in the presence of VLQs is constrained. It is found that in most cases, there is a cancellation between the 2HDM and VLQs contributions, which enlarges the parameter space of both models.

A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

A Stable High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation Method for the Numerical Solution of Grating Scattering Problems

Scalar perturbations in nonsingular universes from interacting vacuum

In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.

Asymptotic analysis for the homogeneous model of wind‐driven oceanic circulation in the small viscosity limit

In this paper, we study the asymptotic expansion for the homogeneous model of wind‐driven oceanic circulation with the nonslip boundary condition when both of the beta‐plane parameter and the Reynolds number go to infinity. By asymptotic analysis under certain constraints on wind tensor, we derive a formal expansion including the geophysical boundary layer in the large beta‐plane parameter and high Reynolds number limit, from which one sees that the external force, wind tensor, has an important effect on the behavior of the boundary layers. Moreover, when the external force and initial data satisfy certain constraints, to exclude the appearance of strong boundary layers, we construct approximate solutions with steady boundary layers to the homogeneous model of wind‐driven oceanic circulation in the large beta‐plane parameter and high Reynolds number limit. By using an energy method, we obtain the ‐stability of small perturbation around this approximate solutions, which verifies the validity of the asymptotic expansion of weak boundary layers in the large beta‐plane parameter and high Reynolds number limit.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.