Time-dependent Perturbations Research Articles

Orbit-following simulations of fast-ion transport and losses due to the Alfvén eigenmode burst in the Large Helical Device

Orbit-following simulations of fast-ion transport and losses with time-dependent electromagnetic perturbations are performed to clarify the roles of Alfvén eigenmodes (AEs) and the low-frequency magnetohydrodynamic (MHD) mode observed in the kinetic-MHD hybrid simulation of AE bursts in the Large Helical Device. Fast-ion pressure profile flattening in the kinetic-MHD hybrid simulation can be reproduced by an orbit-following simulation with only the primary single AE of the time-dependent amplitude following the kinetic-MHD hybrid simulation result, while orbit-following simulations with constant AE amplitude of average level during AE burst cannot reproduce the fast-ion pressure profile flattening observed. The effects of other modes are negligible on the fast-ion pressure profile flattening. The fast-ion losses in kinetic-MHD hybrid simulation can be reproduced by an orbit-following simulation with time-dependent amplitude when the low-frequency MHD mode is considered in addition to multiple AEs. This indicates the synergetic effect of multiple AEs and the low-frequency MHD mode on fast-ion losses.

Global existence and Blow-up for the 1D damped compressible Euler equations with time and space dependent perturbation

In this paper, we consider the 1D Euler equation with time and space dependent damping term −a(t,x)v. It has long been known that when a(t,x) is a positive constant or 0, the solution exists globally in time or blows up in finite time, respectively. In this paper, we prove that those results are invariant with respect to time and space dependent perturbations. We suppose that the coefficient a satisfies the following condition |a(t,x)−μ0|≤a1(t)+a2(x),where μ0≥0 and a1 and a2 are integrable functions with t and x. Under this condition, we show the global existence and the blow-up with small initial data, when μ0>0 and μ0=0 respectively. The key of the proof is to divide space into time-dependent regions, using characteristic curves.

Metatranscriptomic response of deep ocean microbial populations to infusions of oil and/or synthetic chemical dispersant.

Oil spills are a frequent perturbation to the marine environment that has rapid and significant impacts on the local microbiome. Previous studies have shown that exposure to synthetic dispersant alone did not enhance heterotrophic microbial activity or oxidation rates of specific hydrocarbon components but increased the abundance of some taxa (e.g., Colwellia). In contrast, exposure to oil, but not dispersants, increased the abundance of other taxa (e.g., Marinobacter) and stimulated hydrocarbon oxidation rates. Here, we advance these findings by interpreting metatranscriptomic data from this experiment to explore how and why specific components of the microbial community responded to distinct organic carbon exposure regimes. Dispersant alone was selected for a unique community and for dominant organisms that reflected treatment- and time-dependent responses. Dispersant amendment also led to diverging functional profiles among the different treatments. Similarly, oil alone was selected for a community that was distinct from treatments amended with dispersants. The presence of oil and dispersants with added nutrients led to substantial differences in microbial responses, likely suggesting increased fitness driven by the presence of additional inorganic nutrients. The oil-only additions led to a marked increase in the expression of phages, prophages, transposable elements, and plasmids (PPTEPs), suggesting that aspects of microbial community response to oil are driven by the "mobilome," potentially through viral-associated regulation of metabolic pathways in ciliates and flagellates that would otherwise throttle the microbial community through grazing.IMPORTANCEMicrocosm experiments simulated the April 2010 Deepwater Horizon oil spill by applying oil and synthetic dispersants (Corexit EC9500A and EC9527A) to deep ocean water samples. The exposure regime revealed severe negative alterations in the treatments' heterotrophic microbial activity and hydrocarbon oxidation rates. We expanded these findings by exploring metatranscriptomic signatures of the microbial communities during the chemical amendments in the microcosm experiments. Here we report how dominant organisms were uniquely associated with treatment- and time-dependent trajectories during the exposure regimes; nutrient availability was a significant factor in driving changes in metatranscriptomic responses. Remarkable signals associated with PPTEPs showed the potential role of mobilome and viral-associated survival responses. These insights underscore the time-dependent environmental perturbations of fragile marine environments under oil and anthropogenic stress.

Bounds on the growth of energy for particles on the torus with unbounded time dependent perturbations

We prove a C∞ version of Nekhoroshev theorem for time dependent Hamiltonians in Rd×Td. Precisely, we prove a result showing that for all times the energy of the system is bounded by a constant times ⟨t⟩ɛ. We apply the result to the dynamics of a charged particle in Td subject to a time dependent electromagnetic field.

Perturbations of non-autonomous second-order abstract Cauchy problems

In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application we provide a perturbed non-autonomous wave equation.

Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations

We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, in which the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} is included in the LTB formalism, with inhomogeneous cosmological models based on fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} gravity. While radial perturbations follow a power-law in the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, Yukawa-like contributions appear in the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.

Equilibrium analysis in game theory using nonlinear functional analysis techniques

Game theory provides a mathematical framework for analyzing the tactical choices of rational decision makers. The idea of equilibrium, which states that no player has a motivation to change their existing approach given the strategies of other players, is one of the core ideas of game theory. This study examines a type of undirected graph-based distributed quadratic game. The problem of communication topology constraints is presented and nonlinear dynamics with uncertain time-dependent perturbations are present in the participant's dynamics. Based on a high-gain observer approach, a distributed Nash equilibrium (NE) finding technique is given, and the Lyapunov stability theory is used to study the convergence. It represents that every player approximates the positions of their rival players and that there are differences between the NE and the placements of the minor limitation that finally restricts the players. In addition, chattering problems are eliminated since the offered theory's formulation employs the hyperbolic tangent function to control the perturbation rather than the signum function. In an imitation of the oligopoly match, five enterprises manufacture identical materials in a duopoly market framework; this is done to confirm the effectiveness of the recommended strategy. Our results provide novel perspectives and methods for understanding complicated strategic situations, helping to close the gap between mathematical theory and real-world applications.

Investigation of VVER-1000 fuel assembly bowing effect on power distribution during cycle using neutron noise adiabatic approximation

Thermomechanical and radiation loads in the reactor core cause lateral changes in the shape of Fuel Assemblies (FAs). This phenomenon, known as FA bowing, has significant implications for reactor safety and operation. Bowing results in alterations to the spacing between FAs, which in turn leads to neutron flux perturbations affecting power distribution. These perturbations are time-dependent due to variations in boric acid concentration during the cycle. Neutron noise theory is employed to analyze these time-dependent neutron perturbations. In this research, it is investigated the bowing effect during the cycle in a VVER-1000 reactor using the neutron noise adiabatic approximation. It was initially considered a VVER-1000 reactor core to verify the calculations algorithm without bowed FAs. Results had acceptable accuracy in power, initial boric acid, and cycle length. Subsequently, it was explored various modes of FA bowing as neutron noise sources the results revealed that the power noise caused by bowing varies throughout the cycle, as expected. The noise amplitude during the cycle depends on changes in boric acid concentration, burnup, size, and the direction of bowing.

On the reconstruction of unknown driving forces from low-mode observations in the 2D Navier–Stokes equations

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is proposed for accomplishing this, which makes use of a nonlinear property of the equations of motions to asymptotically enslave small scales to large scales. In particular, an algorithm is introduced that systematically produces approximations of the flow field on the unobserved scales in order to generate an approximation to the unknown force; the process is then repeated to generate an improved approximation of the unobserved scales, and so on. A mathematical proof of convergence of this algorithm is established in the context of the two-dimensional Navier–Stokes equations with periodic boundary conditions under the assumption that the force belongs to the observational subspace of phase space; at each stage in the algorithm, it is shown that the model error, represented as the difference between the approximating and true force, asymptotically decreases to zero in a geometric fashion provided that sufficiently many scales are observed and certain parameters of the algorithm are appropriately tuned.

Temporal changes of gene expression in health, schizophrenia, bipolar disorder, and major depressive disorder

The molecular events underlying the development, manifestation, and course of schizophrenia, bipolar disorder, and major depressive disorder span from embryonic life to advanced age. However, little is known about the early dynamics of gene expression in these disorders due to their relatively late manifestation. To address this, we conducted a secondary analysis of post-mortem prefrontal cortex datasets using bioinformatics and machine learning techniques to identify differentially expressed gene modules associated with aging and the diseases, determine their time-perturbation points, and assess enrichment with expression quantitative trait loci (eQTL) genes. Our findings revealed early, mid, and late deregulation of expression of functional gene modules involved in neurodevelopment, plasticity, homeostasis, and immune response. This supports the hypothesis that multiple hits throughout life contribute to disease manifestation rather than a single early-life event. Moreover, the time-perturbed functional gene modules were associated with genetic loci affecting gene expression, highlighting the role of genetic factors in gene expression dynamics and the development of disease phenotypes. Our findings emphasize the importance of investigating time-dependent perturbations in gene expression before the age of onset in elucidating the molecular mechanisms of psychiatric disorders.

Augmenting Robot-Assisted Pattern Cutting with Periodic Perturbations-Can We Make Dry Lab Training More Realistic?

Teleoperated robot-assisted minimally-invasive surgery (RAMIS) offers many advantages over open surgery, but RAMIS training still requires optimization. Existing motor learning theories could improve RAMIS training. However, there is a gap between current knowledge based on simple movements and training approaches required for the more complicated work of RAMIS surgeons. Here, we studied how surgeons cope with time-dependent perturbations. We used the da Vinci Research Kit and investigated the effect of time-dependent force and motion perturbations on learning a circular pattern-cutting surgical task. Fifty-four participants were assigned to two experiments, with two groups for each: a control group trained without perturbations and an experimental group trained with 1Hz perturbations. In the first experiment, force perturbations alternatingly pushed participants' hands inwards and outwards in the radial direction. In the second experiment, the perturbation constituted a periodic up-and-down motion of the task platform. Participants trained with perturbations learned how to overcome them and improve their performances during training without impairing them after the perturbations were removed. Moreover, training with motion perturbations provided participants with an advantage when encountering the same or other perturbations after training, compared to training without perturbations. Periodic perturbations can enhance RAMIS training without impeding the learning of the perturbed task. Our results demonstrate that using challenging training tasks that include perturbations can better prepare surgical trainees for the dynamic environment they will face with patients in the operating room.

On multiplicative time-dependent perturbations of semigroups and cosine families generators

On multiplicative time-dependent perturbations of semigroups and cosine families generators

Metabolomic Changes in Plasma of Preterminal Stage of Rhesus Nonhuman Primates Exposed to Lethal Dose of Radiation.

Ionizing radiation exposure is known to induce molecular and cellular injury, inflicting a cascade of potentially catastrophic events leading to tissue and organ damage. Metabolomic analysis allows for the identification and quantification of small molecules downstream of genomic changes induced by radiation exposure. We aimed to characterize metabolomic changes that underscore the prefinal stage of lethally irradiated rhesus nonhuman primates (NHPs). Peripheral blood was drawn at baseline, post-exposure, as well as at the preterminal stage in NHPs (immediately prior to death in moribund NHPs) that did not survive exposure with 7.2 Gy total-body radiation (LD70/60). Herein, we analyzed global metabolomic changes using ultra-performance liquid chromatography (UPLC) quadrupole time-of-flight mass spectrometry (QTOF-MS) in plasma samples of NHPs collected at various timepoints in relation to irradiation. The overall goal was to identify metabolic shifts present immediately prior to death. Our findings showed radiation induced significant time-dependent metabolic perturbations when compared to pre-irradiation profiles, particularly in glycerophospholipid metabolism and steroid hormone biosynthesis and metabolism pathways. These findings provide valuable insights for identifying biomarkers for lethality, which may be helpful for triage during a mass casualty scenario.

Exact Response Theory for Time-Dependent and Stochastic Perturbations.

The exact, non perturbative, response theory developed within the field of non-equilibrium molecular dynamics, also known as TTCF (transient time correlation function), applies to quite general dynamical systems. Its key element is called the dissipation function because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time-independent external perturbations, and then it has been extended to time-dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated with, e.g., linear response theory. The present work includes time-dependent stochastic perturbations in the theory using the Karhunen-Loève theorem. This leads to three different investigations of a given process. In the first, a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigation, one averages over both initial conditions and stochastic coefficients. We conclude by illustrating the applicability of the resulting exact response theory with simple examples.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory.

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

A robust finite–time model reference adaptive controller for arbitrary order disturbed LTI systems

This manuscript deals with the trajectory-tracking problem for linear time-invariant systems with parameter uncertainties and time-dependent external perturbations. A robust finite-time model reference adaptive controller is proposed. In the absence of external perturbations, the proposed controller ensures finite-time convergence to zero of the tracking and parameter identification errors. In presence of time-dependent external perturbations, the tracking and parameter identification errors converge to a region around the origin in a finite time. The convergence proofs are developed based on Lyapunov and input-to-state stability theory. Finally, simulation results in an academic example and a flexible-joint robot manipulator show the feasibility of the proposed approach.

Local Smoothing Estimates for Schrödinger Equations on Hyperbolic Space

We establish global-in-time frequency localized local smoothing estimates for Schrödinger equations on hyperbolic space H d \mathbb {H}^d , d ≥ 2 d \geq 2 . In the presence of symmetric first and zeroth order potentials, which are possibly time-dependent, possibly large, and have sufficiently fast polynomial decay, these estimates are proved up to a localized lower order error. Then in the time-independent case, we show that a spectral condition (namely, absence of threshold resonances) implies the full local smoothing estimates (without any error), after projecting to the continuous spectrum. In the process, as a means to localize in frequency, we develop a general Littlewood–Paley machinery on H d \mathbb {H}^d based on the heat flow. Our results and techniques are motivated by applications to the problem of stability of solitary waves to nonlinear Schrödinger-type equations on H d \mathbb {H}^{d} . Specifically, some of the estimates established in this paper play a crucial role in the authors’ proof of the nonlinear asymptotic stability of harmonic maps under the Schrödinger maps evolution on the hyperbolic plane; see Lawrie, Lührmann, Oh, and Shahshahani, 2023. As a testament of the robustness of approach, which is based on the positive commutator method and a heat flow based Littlewood-Paley theory, we also show that the main results are stable under small time-dependent perturbations, including polynomially decaying second order ones, and small lower order nonsymmetric perturbations.

Large time well-posedness for a Dirac–Klein–Gordon system

In this paper, we prove well-posedness for a Dirac equation perturbed with a moving potential W that satisfies a Klein–Gordon equation. This represents a “toy model” for atoms with relativistic corrections, as the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation: these represent a result of independent interest.

Integrated Transcriptomic and Metabolomic Mapping Reveals the Mechanism of Action of Ceftazidime/Avibactam against Pan-Drug-Resistant Klebsiella pneumoniae.

Here, we employed an integrated metabolomics and transcriptomics approach to investigate the molecular mechanism(s) of action of ceftazidime/avibactam against a pan-drug-resistant K. pneumoniae clinical isolate from a patient with urinary tract infection. Ceftazidime/avibactam induced time-dependent perturbations in the metabolome and transcriptome of the bacterium, mainly at 6 h, with minimal effects at 1 and 3 h. Metabolomics analysis revealed a notable reduction in essential lipids involved in outer membrane glycerolipid biogenesis. This disruption effect extended to peptidoglycan and lipopolysaccharide biosynthetic pathways, including lipid A and O-antigen assembly. Importantly, ceftazidime/avibactam not only affected the final steps of peptidoglycan biosynthesis in the periplasm, a common mechanism of ceftazidime action, but also influenced the synthesis of lipid-linked intermediates and early stages of cytoplasmic peptidoglycan synthesis. Furthermore, ceftazidime/avibactam substantially inhibited central carbon metabolism (e.g., the pentose phosphate pathway and tricarboxylic acid cycle). Consistently, the dysregulation of genes governing these metabolic pathways aligned with the metabolomics findings. Certain metabolomics and transcriptomics signatures associated with ceftazidime resistance were also perturbed. Consistent with the primary target of antibiotic activity, biochemical assays also confirmed the direct impact of ceftazidime/avibactam on peptidoglycan production. This study explored the intricate interactions of ceftazidime and avibactam within bacterial cells, including their impact on cell envelope biogenesis and central carbon metabolism. Our findings revealed the complexities of how ceftazidime/avibactam operates, such as hindering peptidoglycan formation in different cellular compartments. In summary, this study confirms the existing hypotheses about the antibacterial and resistance mechanisms of ceftazidime/avibactam while uncovering novel insights, including its impact on lipopolysaccharide formation.

Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation.

We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equationwith a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equationdescribing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.