Critical Perturbation Research Articles

A critical perturbation result in prescribing scalar curvature under boundary conditions

A critical perturbation result in prescribing scalar curvature under boundary conditions

Analytically separating the source of the Teukolsky equation

Recent gravitational wave detections from black hole mergers have underscored the critical role black hole perturbation theory and the Teukolsky equation play in understanding the behavior of black holes. The separable nature of the Teukolsky equation has long been leveraged to study the vacuum linear Teukolsky equation; however, as theory and measurements advance, solving the sourced Teukolsky equation is becoming a frontier of research. In particular, second-order calculations, such as in quasinormal mode and self-force problems, have extended sources. This paper presents a novel method for analytically separating the Teukolsky equation’s source, aimed to improve efficiency. Separating the source is a nontrivial problem due to the angular and radial mixing of generic quantities in Kerr spacetime. We provide a proof-of-concept demonstration of our method and show that it is accurate, separating the Teukolsky source produced by the stress-energy tensor of an ideal gas cloud surrounding a Kerr black hole. The detailed application of our method is provided in an accompanying notebook. Our approach opens up a new avenue for accurate black hole perturbation theory calculations with sources in both the time and frequency domain. Published by the American Physical Society 2024

On the time scales of spectral evolution of nonlinear waves

As presented in Annenkov & Shrira (Phys. Rev. Lett., vol. 102, 2009, 024502), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ‘fast’ dynamic time scale of $O(\varepsilon ^{-2})$ , with $\varepsilon$ a measure of wave steepness. This observation poses a challenge to wave turbulence theory that predicts an evolution with a kinetic time scale of $O(\varepsilon ^{-4})$ . We revisit this unresolved problem by studying the same situation in the context of a one-dimensional Majda–McLaughlin–Tabak equation with gravity wave dispersion relation. Our results show that the kinetic and dynamic time scales can both be realised, with the former and latter occurring for weaker and stronger forcing perturbations, respectively. The transition between the two regimes corresponds to a critical forcing perturbation, with which the spectral evolution time scale drops to the same order as the linear wave period (of some representative mode). Such fast spectral evolution is mainly induced by a far-from-stationary state after a sufficiently strong forcing perturbation is applied. We further develop a set-based interaction analysis to show that the inertial-range modal evolution in the studied cases is dominated by their (mostly non-local) interactions with the low-wavenumber ‘condensate’ induced by the forcing perturbation. The results obtained in this work should be considered to provide significant insight into the original gravity wave problem.

Global existence, blow-up and stability of standing waves for the Schrödinger-Choquard equation with harmonic potential

<abstract><p>In this article, we conduct a comprehensive investigation into the global existence, blow-up and stability of standing waves for a $ L^{2} $-critical Schrödinger-Choquard equation with harmonic potential. First, by taking advantage of the ground-state solutions and scaling techniques, we obtain some criteria for the global existence and blow-up of the solutions. Second, in terms of the refined compactness argument, scaling techniques and the variational characterization of the ground state solution to the Choquard equation with $ p_{2} = 1+\frac{2+\alpha}{N} $, we explore the limiting dynamics of blow-up solutions to the $ L^{2} $-critical Choquard equation with $ L^{2} $-subcritical perturbation, including the $ L^{2} $-mass concentration and blow-up rate. Finally, the orbital stability of standing waves is investigated in the presence of $ L^{2} $-subcritical perturbation, focusing $ L^{2} $-critical perturbation and defocusing $ L^{2} $-supercritical perturbation by using variational methods. Our results supplement the conclusions of some known works.</p></abstract>

Effects of ablation velocity on ablative Rayleigh–Taylor instability

The influence of the ablation velocity Va on the evolution of single-mode ablative Rayleigh–Taylor instability from the linear to the deeply nonlinear phases is investigated via two-dimensional numerical simulations. Linear growth rates from simulations agree well with the asymptotic theory except for larger discrepancies in the intermediate Froude number regime. The weakly nonlinear growth behavior of the bubble amplitude is found dependent on a critical perturbation wavenumber in a broad Froude number regime. For a linearly stable mode, its nonlinear excitation threshold is higher for larger Va and thus harder to be exceeded. For short-wavelength modes taking significant ablation effects, the bubble penetration velocity is found to reaccelerate after the first saturation and eventually saturate at a larger value with larger Va, due to stronger vortex-acceleration effects and more significant increase in g.

Fast-ion transport in quasisymmetric equilibria in the presence of a resonant Alfvénic perturbation

Significant progress has been made in designing magnetic fields that provide excellent confinement of the guiding-centre trajectories of alpha particles using quasisymmetry (QS). Given the reduction in this transport channel, we assess the impact of resonant Alfvén eigenmodes (AEs) on the guiding-centre motion. The AE amplitudes are chosen to be consistent with experimental measurements and large-scale simulations. We evaluate the drift resonance condition, phase-space island width and island overlap criterion for quasisymmetric configurations. Kinetic Poincaré plots elucidate features of the transport, including stiff transport above a critical perturbation amplitude. Our analysis highlights key departures from the AE-driven transport in tokamaks, such as the avoidance of phase-space island overlap in quasihelical configurations and the enhanced transport due to wide phase-space islands in low magnetic shear configurations. In configurations that are closer to QS, with QS deviations $\delta B/B_0 \lesssim 10^{-3}$ , the transport is primarily driven by the AE, while configurations that are further from QS, $\delta B/B_0 \sim 10^{-2}$ , experience significant transport due to the QS-breaking fields in addition to the AE.

Primordial black holes in loop quantum cosmology: the effect on the threshold

Primordial black holes form in the early Universe and constitute one of the most viable candidates for dark matter. The study of their formation process requires the determination of a critical energy density perturbation threshold , which in general depends on the underlying gravity theory. Up to now, the majority of analytic and numerical techniques calculate within the framework of general relativity. In this work, using simple physical arguments we estimate semi-analytically the PBH formation threshold within the framework of quantum gravity, working for concreteness within loop quantum cosmology (LQC). In particular, for low mass PBHs formed close to the quantum bounce, we find a reduction in the value of up to compared to the general relativistic regime quantifying for the first time to the best of our knowledge how quantum effects can influence PBH formation within a quantum gravity framework. Finally, by varying the Barbero–Immirzi parameter γ of loop quantum gravity (LQG) we show its effect on the value of while using the observational/phenomenological signatures associated to ultra-light PBHs, namely the ones affected by LQG effects, we propose the PBH portal as a novel probe to constrain the potential quantum nature of gravity.

Positive solutions for Kirchhoff equation in exterior domains with small Sobolev critical perturbation

ABSTRACT The paper concerns with the existence of positive solutions for the following Kirchhoff problem { − ( a + b ∫ Ω | ∇u | 2 d x ) Δu + u = | u | p − 2 u + ε | u | 4 u in Ω , u ∈ H 0 1 ( Ω ) , where a, b>0, 4<p<6, 0 $ ]]> ε > 0 is a parameter and Ω ⊂ R 3 is an exterior domain, that is, Ω is an unbounded domain with R 3 ∖Ω nonempty and bounded. After showing the nonexistence of ground state solutions, we prove the existence of one positive solution with higher energy when R 3 ∖Ω is contained in a small ball and 0 $ ]]> ε > 0 is sufficiently small. The novelty of this paper is that we extend the result obtained in Alves and de Freitas [Existence of a positive solution for a class of elliptic problems in exterior domains involving critical growth. Milan J Math. 2017;85:309–330] to nonlocal case and generalize the subcritical nonlinearity discussed in Chen and Liu [Positive solutions for Kirchhoff equation in exterior domains. J Math Phys. 2021;62:Article ID 041510] to small critical perturbation.

Imposing a constraint on the discrete Reynolds–Orr equation demonstrated in shear flows

The Reynolds–Orr equation predicts the unconditional stability limit of a flow. Although this seems to be a desirable aim in engineering applications, the predicted critical Reynolds numbers are one magnitude below the experimental observations. In this paper, an attempt is made to reduce this gap for incompressible shear flows. It is known that the Navier–Stokes equation has no regular solution at the initial time if the initial velocity field does not fulfill the compatibility condition. However, the original solution of the Reynolds–Orr equation, the critical perturbation, does not necessarily fulfill this condition. Therefore, the condition is added to the original problem as a non-linear constraint. This requires the use of a discrete functional, introduced in the paper. Two different formulations are implemented and discussed. The solution is assumed in a waveform. The augmented problem is solved in the cases of planar Poiseuille and the Couette flow. The result shows that adding the constraint increases the critical Reynolds number significantly in the case of a streamwise perturbation but only slightly in the case of a spanwise one. It was demonstrated using numerical simulations that the single waveform assumption was unreasonably strict. The usage of the compatibility condition without assuming the single waveform has a negligible effect on the critical Reynolds number. However, the presented methods can be used for adding other reasonable and complicated constraints to the variational problem.

Centring Civilisation: Now and After the Apocalypse

AbstractThe intersection of cities, bodies and politics and their material flows creates an interdisciplinary platform for new radical urbanisms. Alberto de Salvatierra, founder and director of the Center for Civilization and assistant professor of urbanism and data in architecture at the University of Calgary in Alberta, Canada, believes we are at a critical perturbation in human society, that all that has been stable for some time is now changing, more voices are being heard, and one dominant point of view is no longer predicated.

Toward the primordial black hole formation threshold in a time-dependent equation-of-state background

The study of the primordial black hole (PBH) gravitational collapse process requires the determination of a critical energy density perturbation threshold ${\ensuremath{\delta}}_{\mathrm{c}}$, which depends on the equation of state of the universe at the time of PBH formation. Up to now, the majority of analytical and numerical techniques calculate ${\ensuremath{\delta}}_{\mathrm{c}}$ by assuming a constant equation-of-state (EoS) parameter $w$ at the time of PBH formation. In this work, after generalizing the constant $w$ prescription of [T. Harada et al., Phys. Rev. D 88, 084051 (2013); T. Harada et al.Phys. Rev. D89, 029903(E) (2014).] for the computation of ${\ensuremath{\delta}}_{\mathrm{c}}$ and commenting its limitations we give a first estimate for the PBH threshold in the case of a time-dependent $w$ background. In particular, we apply our formalism in the case of the QCD phase transition, where the EoS parameter varies significantly with time and one expects an enhanced PBH production due to the abrupt softening of $w$. At the end, we compare our results with analytic and numerical approaches for the determination of ${\ensuremath{\delta}}_{\mathrm{c}}$ assuming a constant EoS parameter.

Normalized Solutions for Lower Critical Choquard Equations with Critical Sobolev Perturbation

We study normalized solutions for the following Choquard equations with lower critical exponent and a local perturbation $ -\Delta u+\lambda u=\gamma (I_{\alpha }\ast |u|^{\frac{\alpha }{N}+1})|u|^{\frac{\alpha }{N}-1}u+\mu |u|^{q-2}u \quad \text{in}\quad \mathbb{R}^{N}, \int_{\mathbb{R}^{N}}$ $|u|^{2}dx=c^{2},$ where $\gamma ,\,\mu,\,c$ are given positive numbers and $2<q\leq \frac{2N}{N-2}$. The frequency $\lambda $ appears as a real Lagrange parameter and is part of the unknowns. By introducing new arguments and under different assumptions on $q,\,c,\,\gamma $, and $\mu ,$ we prove several nonexistence and existence results. In particular, we consider the case $q=\frac{2N}{N-2},$ which corresponds to equations involving double critical exponents. We also describe some qualitative properties of the solutions with prescribed mass and of the associated Lagrange multipliers $\lambda$.

Using system equalization principle to study the effects of multiple factors to the development of bee colony

In recent years, frequent outbreaks of bee colony collapse have seriously threatened food production and ecological balance. Many scholars have studied different factors and formed a consensus that multiple factors jointly cause the colony collapse. However, it is still a challenge to understand the effects of multiple factors on bee colony development due to the complex microcosmic mechanism of each factor. Based on the principle of system equilibrium, this paper models the macroscopic dynamics of bee colony with three core states: the stocks of food, the population of adult bees and the population of larval bees, and the internal and external factors have been abstracted as the model parameters. The mathematical criteria for the benign development of bee colonies are presented from the idea of system stability, and the effects of multiple factors are studied by critical parameter perturbation and Monte Carlo simulation. The results show that the population of adults is most likely to be influenced by multiple factors, that is to say, the observations related to adults, such as the total number of adults and the number/frequency of adults entering and leaving the nest, can more quickly reflect the health status of bee colony, which provides a theoretical basis for experimental studies. Meanwhile, this study reveals the effects of multiple factors on the development of bee colonies from the level of system equilibrium, which is of great significance for understanding the collapse of bee colonies in recent years. Further, according to monitoring the three core states, the trend changes of them could be used to diagnose the healthy problems of actual bee colonies.

On Solving Semilinear Singularly Perturbed Neumann Problems for Multiple Solutions

Based on the analysis of bifurcation points and Morse indices of trivial solutions at any perturbation value for a general semilinear singularly perturbed Neumann boundary value problem, in this paper, the exact critical perturbation value $\varepsilon_c$ which determines the existence or nonexistence of nontrivial positive solutions is obtained. As a result, the generating process of nontrivial positive solutions is studied and further used to guide algorithm design and numerical computation. An improved local minimax method is then proposed accordingly to compute both M-type and W-type saddle points by using an adaptive local refinement strategy and a Newton method to overcome singularity difficulty and accelerate local convergence. Extensive numerical results are reported to justify the critical perturbation value $\varepsilon_c$ and investigate some interesting solution properties of different types of problems.

Ground state solution for a kind of Choquard equations with doubly critical exponents and local perturbation

At present, many achievements have been made in the research of Choquard equation. In this paper, some new conclusions about the Choqaurd type problems are obtained through the variational method. It is different from the other Choqaurd equations with critical exponent, in this study, we consider a kind of Choqaurd equations with doubly critical exponents and local perturbation at the same time. The key point of this paper is that Sobolev embedding from workspace to Lebesgue space is not compact. Therefore, it is almost impossible to use conventional methods to obtain the convergence of (PS)c sequences. In order to eliminate the difficulty, We use the Pohoˇzaev manifold to complete the proof of the existence of solutions for a class of Choquard equations. We also take some new tricks in this equation

Distinct states of proinsulin misfolding in MIDY

A precondition for efficient proinsulin export from the endoplasmic reticulum (ER) is that proinsulin meets ER quality control folding requirements, including formation of the Cys(B19)–Cys(A20) “interchain” disulfide bond, facilitating formation of the Cys(B7)–Cys(A7) bridge. The third proinsulin disulfide, Cys(A6)–Cys(A11), is not required for anterograde trafficking, i.e., a “lose-A6/A11” mutant [Cys(A6), Cys(A11) both converted to Ser] is well secreted. Nevertheless, an unpaired Cys(A11) can participate in disulfide mispairings, causing ER retention of proinsulin. Among the many missense mutations causing the syndrome of Mutant INS gene-induced Diabetes of Youth (MIDY), all seem to exhibit perturbed proinsulin disulfide bond formation. Here, we have examined a series of seven MIDY mutants [including G(B8)V, Y(B26)C, L(A16)P, H(B5)D, V(B18)A, R(Cpep + 2)C, E(A4)K], six of which are essentially completely blocked in export from the ER in pancreatic β-cells. Three of these mutants, however, must disrupt the Cys(A6)–Cys(A11) pairing to expose a critical unpaired cysteine thiol perturbation of proinsulin folding and ER export, because when introduced into the proinsulin lose-A6/A11 background, these mutants exhibit native-like disulfide bonding and improved trafficking. This maneuver also ameliorates dominant-negative blockade of export of co-expressed wild-type proinsulin. A growing molecular understanding of proinsulin misfolding may permit allele-specific pharmacological targeting for some MIDY mutants.

Decoherence scaling transition in the dynamics of quantum information scrambling

Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-body systems. This is a highly challenging task because the fragility of quantum states to external perturbations increases with the system size. Here, we report on a series of experimental quantum simulations that quantify the sensitivity of a controlled Hamiltonian evolution to perturbations that drive the system away from the targeted evolution. Based on out-of-time ordered correlations, we demonstrate that the decay rate of the process fidelity increases with the effective number $K$ of correlated qubits as ${K}^{\ensuremath{\alpha}}$. As a function of the perturbation strength, we observe a decoherence scaling transition of the exponent $\ensuremath{\alpha}$ between two distinct dynamical regimes. In the limiting case below the critical perturbation strength, the exponent $\ensuremath{\alpha}$ drops sharply below 1, and there is no inherent limit to the number of qubits that can be controlled. This resilient quantum feature of the controlled dynamics of quantum information is promising for reliable control of large quantum systems.

Cholesterol metabolism is a potential therapeutic target in Duchenne muscular dystrophy.

BackgroundDuchenne muscular dystrophy (DMD) is a lethal muscle disease detected in approximately 1:5000 male births. DMD is caused by mutations in the DMD gene, encoding a critical protein that links the cytoskeleton and the extracellular matrix in skeletal and cardiac muscles. The primary consequence of the disrupted link between the extracellular matrix and the myofibre actin cytoskeleton is thought to involve sarcolemma destabilization, perturbation of Ca2+ homeostasis, activation of proteases, mitochondrial damage, and tissue degeneration. A recently emphasized secondary aspect of the dystrophic process is a progressive metabolic change of the dystrophic tissue; however, the mechanism and nature of the metabolic dysregulation are yet poorly understood. In this study, we characterized a molecular mechanism of metabolic perturbation in DMD.MethodsWe sequenced plasma miRNA in a DMD cohort, comprising 54 DMD patients treated or not by glucocorticoid, compared with 27 healthy controls, in three groups of the ages of 4–8, 8–12, and 12–20 years. We developed an original approach for the biological interpretation of miRNA dysregulation and produced a novel hypothesis concerning metabolic perturbation in DMD. We used the mdx mouse model for DMD for the investigation of this hypothesis.ResultsWe identified 96 dysregulated miRNAs (adjusted P‐value <0.1), of which 74 were up‐regulated and 22 were down‐regulated in DMD. We confirmed the dysregulation in DMD of Dystro‐miRs, Cardio‐miRs, and a large number of the DLK1‐DIO3 miRNAs. We also identified numerous dysregulated miRNAs yet unreported in DMD. Bioinformatics analysis of both target and host genes for dysregulated miRNAs predicted that lipid metabolism might be a critical metabolic perturbation in DMD. Investigation of skeletal muscles of the mdx mouse uncovered dysregulation of transcription factors of cholesterol and fatty acid metabolism (SREBP‐1 and SREBP‐2), perturbation of the mevalonate pathway, and the accumulation of cholesterol in the dystrophic muscles. Elevated cholesterol level was also found in muscle biopsies of DMD patients. Treatment of mdx mice with Simvastatin, a cholesterol‐reducing agent, normalized these perturbations and partially restored the dystrophic parameters.ConclusionsThis investigation supports that cholesterol metabolism and the mevalonate pathway are potential therapeutic targets in DMD.

Mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids

The liquid-like property of solvent-free nanofluids under room temperature can be harnessed to achieve various advanced functions with significant applications. However, the determination of the critical flow conditions of solvent-free nanofluid is yet an unsolved issue. In this paper, we establish a mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids on the basis of microscopic mechanisms. The microscopic mechanisms of the transverse vibration of corona branches, the rotation of silica nanoparticles and the effects of the external electric field are included in this model. A structure-preserving approach, which combines the multi-symplectic method with the symplectic precise integration, is proposed to simulate the dynamics of ionic-type solvent-free nanofluids. By using this novel model, the critical initial perturbation intensity that results in the flow of an ionic-type solvent-free nanofluid is obtained, and the existence of an upper limit for the flow velocity is demonstrated, which provides a guidance for the preparation and dynamic control of ionic-type solvent-free nanofluids.

No way home: collapse in northern gannet survival rates point to critical marine ecosystem perturbation

Seabirds are one of the most threatened of all bird groups, with a marked community-wide decline across the last decades. Yet, some seabird species are more resilient than others, and it is essential to study under which conditions even these highly resilient organisms are affected by global changes. Here, we report such a case in northern gannets (Morus bassanus). Using global location sensors (GLS), demographic and stable isotope analyses, we performed a long-term study of the migration biology and inter-annual survival of gannets breeding on Rouzic Island in Brittany, France. Across 2006–2015, our analyses showed that the birds spent the inter-breeding period off Western Europe, in the Mediterranean or off West Africa. There were no inter-annual trends in the use of these different areas, but isotopic analyses suggested food competition between gannets and industrial-scale fisheries. Crucially, we found a precipitous decline in the return rates of birds equipped with GLS, from 100% in 2006–2007 to less than 30% after 2015. This decline was consistent with a marked decrease in inter-annual survival probabilities for ringed adult gannets, from > 90% in 2014–2015 to < 60% in 2018–2019, and with a population decline of the Rouzic gannet breeding colony in recent years. Strong ecological signals provided by northern gannets point to critical marine ecosystem perturbation in the Eastern Atlantic, and the decline of this resilient and emblematic species should lead to the urgently needed transformation of marine policies.