Perturbative Results Research Articles

Swing-phase pelvis perturbation improves dynamic lateral balance during walking in individuals with spinal cord injury.

The purpose of this study was to determine whether the control of lateral balance can be improved by applying repeated lateral perturbation force to the pelvis during swing versus stance phase walking in individuals with spinal cord injury (SCI). Fourteen individuals with incomplete SCI were recruited in this study. Each participant visited the lab once and was tested in two experimental sessions that consisted of (1) treadmill walking with bilateral perturbation force applied to the pelvis in the lateral direction during either swing or stance phase of each leg and (2) overground walking pre- and post-treadmill walking. Applying the swing-phase perturbation during walking induced a greater increase in the muscle activation of hip abductors and ankle plantar flexors and a greater improvement in lateral balance control after the removal of perturbation force, in comparison to the results of the stance-phase perturbation condition (P ≤ 0.03). Participants also exhibited a greater reduction in overground step width and a greater improvement in overground walking speed after a session of treadmill walking practice with the swing-phase perturbation, compared with the result of the stance-phase perturbation (P = 0.01). These findings suggest that applying perturbation force to the pelvis during the swing phase of gait while walking may enhance muscle activities of hip abductors and improve lateral balance control in individuals with SCI. A walking practice with the swing-phase pelvis perturbation can be used as a rehabilitation approach to improve the control of lateral balance during walking in people with SCI.

Generalization of some commutative perturbation results

Generalization of some commutative perturbation results

Bootstrapping conformal QED3 and deconfined quantum critical point

We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED3) coupled to Nf flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(Nf) adjoint and textrm{SO}left({N}_f^2-1right) vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the textrm{SO}left({N}_f^2-1right) symmetry, the SU(Nf) adjoint bootstrap bounds with large Nf converge to the 1/Nf perturbative results of QED3. Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED3 is slightly above 2: {N}_f^{ast}in left(2,4right) . Bootstrap results near {N}_f^{ast } are well consistent with the merger and annihilation mechanism for the loss of conformality in QED3.

Comparative Analysis of Temperature Distributions in a Convective-Radiative Porous Fin using Homotopy Perturbation and Differential Transformation and Methods

In this work, a comparative study of two approximate analytical methods for the thermal behaviour of convective-radiative porous fin subjected to the magnetic field using homotopy perturbation and differential transform methods is presented. Also, parametric studies of the effects of thermal-geometric and thermo-physical fin parameters are investigated. From the study, it is found that an increase in a magnetic field, porosity, convective, radiative, and parameters increase the rate of heat transfer from the fin and consequently improves the efficiency of the fin. There are good agreements between the results of the homotopy perturbation and differential transform method with the results of the numerical method. Also, the results of the two approximate analytical methods agree very well with each other. It is hoped that the present work will serve as the basis of verifications of the other works on the nonlinear thermal analysis of the extended surface.

Study of the electrothermal and MHD instabilities in exploding cylindrical foil liner

An experimental and numerical study of the plasma instabilities in an electrical exploding cylindrical Al liner is reported. The Al liner 3 mm in diameter and 10 μm in thickness is exploded at the Qin-1 facility (450 ns, 400 kA). Various diagnostics, such as multi-frame laser shadowgraphy, an x-ray framing camera, and an x-ray backlighting system are developed. The different imaging systems are sensitive to plasma of different areal densities based on the comparison between the experiments and simulation, which reveal the dynamics of the exploding liner in more detail. The laser shadow images show the low-density plasma (∼1–2 × 10−4 g cm−2) at the edge of the liner, and both the amplitude and wavelength of the plasma instabilities increase over time, which are considered to be magnetohydrodynamic (MHD) instabilities rather than electrothermal instabilities. During the ablation of the liner, quasi-periodic azimuthally correlated striations are directly observed in extreme ultraviolet (EUV) self-emission images. Meanwhile, the vertical filaments, which are electrothermal instabilities for plasma under the condition of ∂η/∂T < 0, are also observed in EUV self-emission images. The x-ray backlighting images of the exploding liner are obtained by placing an X-pinch load on the current-return path to serve as an x-ray point source (∼1 ns, ∼10 μm). The x-ray backlighting results show the behavior of the high-density plasma (∼1.89 × 10−3 g cm−2), which includes the transition from electrothermal to MHD instabilities. Finally, we realized a 2D MHD simulation of the exploding liner under experimental conditions, which shows good agreement with the results of the experimental perturbation.

Transcriptional deregulation of stress-growth balance in Nicotiana benthamiana biofactories producing insect sex pheromones.

Plant biofactories are a promising platform for sustainable production of high-value compounds, among which are insect sex pheromones, a green alternative to conventional insecticides in agriculture. Recently, we have constructed transgenic Nicotiana benthamiana plants ("Sexy Plants", SxP) that successfully produce a blend of moth (Lepidoptera) sex pheromone compounds (Z)-11-hexadecen-1-ol and (Z)-11-hexadecenyl acetate. However, efficient biosynthesis of sex pheromones resulted in growth and developmental penalty, diminishing the potential for commercial use of SxP in biomanufacturing. To gain insight into the underlying molecular responses, we analysed the whole-genome transcriptome and evaluated it in relation to growth and pheromone production in low- and high-producing transgenic plants of v1.0 and v1.2 SxP lines. In our study, high-producing SxPv1.2 plants accumulated the highest amounts of pheromones but still maintained better growth compared to v1.0 high producers. For an in-depth biological interpretation of the transcriptomic data, we have prepared a comprehensive functional N. benthamiana genome annotation as well as gene translations to Arabidopsis thaliana, enabling functional information transfer by using Arabidopsis knowledge networks. Differential gene expression analysis, contrasting pheromone producers to wild-type plants, revealed that while only a few genes were differentially regulated in low-producing plants, high-producing plants exhibited vast transcriptional reprogramming. They showed signs of stress-like response, manifested as downregulation of photosynthesis-related genes and significant differences in expression of hormonal signalling and secondary metabolism-related genes, the latter presumably leading to previously reported volatilome changes. Further network analyses confirmed stress-like response with activation of jasmonic acid and downregulation of gibberellic acid signalling, illuminating the possibility that the observed growth penalty was not solely a consequence of a higher metabolic burden imposed upon constitutive expression of a heterologous biosynthetic pathway, but rather the result of signalling pathway perturbation. Our work presents an example of comprehensive transcriptomic analyses of disadvantageous stress signalling in N. benthamiana biofactory that could be applied to other bioproduction systems.

Perturbing the spectrum of operator $$T_n^d(A)$$

Let $$T_n^d(A)$$ denote a partial upper triangular operator matrix whose diagonal entries are given and the others unknown. In this article we have aim to find characterizations of (left, right) invertibility of $$T_n^d(A)$$ in terms of diagonal entries solely, and hence we provide statements which generalize and correct results of Zhang and Wu (J. Math. Anal. Appl. 392:103–110, 2012). We pose our results without invoking separability condition, thus improving results of Zhang and Wu (J. Math. Anal. Appl. 392:103–110, 2012), and we give appropriate n-dimensional analogues, without assuming separability as well. We recover many perturbation results of Djordjević (J. Oper. Theory 48:467–486, 2002), and obtain some results of Du and Pan (Proc. Amer. Math. Soc. 121: 761–766, 1994) and Han et al. (Proc. Amer. Math. Soc. 128:119–23, 2000) in the case of the Hilbert space setting.

Scrutinization of coating thickness of Sutterby fluid during isothermal blade coating using lubrication theory: the case of plane coater and exponential coater

In the literature, there is a gap regarding the analysis of coating thickness of Sutterby fluid during isothermal blade coating using lubrication theory, focusing on the case of plane coater and exponential coater. During the blade coating processes, this report presents the outcome of a study on an isothermal and incompressible flow of a Sutterby fluid. Both the planar and exponential coaters were considered in the analysis. Lubrication theory was used to simplify the non-dimensional governing equations, which were then solved using the numerical shooting approach and perturbation technique for small values of the fluid parameter. Furthermore, the perturbation results are compared to the numerical results and are in good agreement. As the fluid parameter increases, the shear-thinning effect is noted, leading to an increased velocity profile and coating thickness while reducing blade load. Sutterby fluid parameter develops to be the controlling parameter for Pressure profile and blade load compared to the Newtonian case, which leads to an effective coating process and improves the substrate life.

Thermal emission of gravitational waves from weak to strong coupling

We study the production of gravitational waves by a thermalized plasma of mathcal{N} =4 Supersymmetric Yang Mills matter. We focus on the large number of colors limit, Nc → ∞, and compute the spectrum of gravitational waves both for infinitely large and infinitesimally small values of the ‘t Hooft coupling constant λ. In the λ → ∞ limit we employ the gauge/gravity duality to compute the emission rate via the analysis of Energy-Momentum tensor thermal correlators. In the λ → 0 limit we employ state-of-the-art perturbative analyses to calculate the complete leading order emission rate. By comparing these extreme limits, we bracket the magnitude of the spectrum induced by this source of gravitational waves. Embedding our results in a cosmological evolution model, we find qualitative and quantitative similarities between the strong coupling spectrum and the extrapolation of the perturbative results up to an intermediate value of the coupling, after an appropriate re-scaling of the effective number of degrees of freedom. We comment on how our results can help better understand the contribution of thermalized matter to the stochastic spectrum of gravitational waves.

Simulation of mixed convection flow for a physiological breakdown of Jeffrey six-constant fluid model with convective boundary condition

This paper deals with a study on flow of fluid which exhibits the characteristics of both ideal fluids and elastic solid and shows partial elastic recovery. For these types of fluids, Jeffrey six-constant model will be used that illustrates the most striking feature connected with the deformation of a viscoelastic substance and simultaneously displays the fluid-like and solid-like characteristics. The flow of the proposed fluid model will be generated in an inclined tube by sinusoidal wave trains propagation with constant speed along the walls of the tube. The governing equations of the fluid along with energy equation are modeled and simplified by using low Reynolds number and long wavelength assumptions. These equations will be solved by utilizing the homotopy perturbation technique and results of flow will be displayed in graphical form under the effects of Jeffrey model’s parameters.

Dual QCD thermodynamics at finite temperature and chemical potential

A Dual QCD formulation for [Formula: see text] color gauge has been developed in terms of dual gauge potentials, building on our previously published study for the [Formula: see text] case with zero bario-chemical potential [H. C. Chandola, G. Punetha and H. Dehnen, Nucl. Phys. A 945, 226 (2016).] and taking into account the local as well as topological structure of the color gauge group into its dynamics. For the purpose of examining the nonperturbative characteristics of QCD, the dynamical configuration of the resulting dual QCD vacuum and its flux tube configuration have been examined. The thermal behavior of the nonperturbative QCD vacuum has been investigated for exploring the dynamics of quark-hadron phase transition at finite chemical potential. Related thermodynamic quantities and equation of state (EoS) to characterize quark matter have also been discussed within the framework of dual QCD-based hadronic bag which guarantees the critical parameters and the associated critical points for quark-hadron phase transition. These thermodynamic quantities are expected to play important roles in understanding the order of quark-hadron phase transition and are likely to predict the features of a first-order quark-hadron phase transition for finite chemical potential. Moreover, we have investigated the bulk properties of quark matter by constructing the free energy change and the associated surface tension for quark-hadron phase transition. For consistency and compatibility check, we have also compared our results with state-of-the-art three-loop Hard Thermal Loop perturbative results and available lattice QCD results and in the process found reasonable agreements.

Method to Estimate Thermal Transients in Reactors and Determine Their Parameter Sensitivities without a Forward Simulation

Thermal response time is an important parameter for the control of fast reactors. Modern thermal hydraulic codes allow for the modeling of transient responses and can also be used to understand the dominant factors that affect them. However, simulations can be computationally expensive, particularly for performing parametric analyses of how thermophysical properties affect transient behavior. Here, we present a method for using linear stability analysis to estimate thermal response time and determine the key parameters that affect transient behavior without performing a forward simulation. The approach can also be used to corroborate simulation results and is tested against simulation results produced with a 2D finite difference model. The results show that this approach produces time-dependent temperature profiles that are within 2 × 10−5–0.1% of the numerical results for a single node perturbation. Changes in temperature have the greatest effect on thermal response time, followed by changes to thermal conductivity.

High order quark number susceptibilities in hot QCD from lattice electrostatic QCD

Building on the experience of [1], we develop a formalism to construct operators for higher derivatives of the pressure in hot QCD with respect to the quark chemical potential $\mu$. We provide formulae for the operators up to the sixth derivative, and obtain continuum-extrapolated results from lattice EQCD at zero and finite $\mu$ and at six different pairs of temperature T and number of massless quark flavors $n_f$. Our data is benchmarked against full-QCD lattice and perturbative results, allowing to judge the quality of the perturbative series expansion in EQCD and the dimensional reduction procedure as a whole.

Positive observers for semilinear positive systems

Abstract The problem of designing a positive Luenberger observer for a class of infinite-dimensional semilinear positive systems is addressed. The proposed observer is positive. That is, it ensures that the state estimates are non-negative at any time. The positive observer is designed based on positive bounded perturbation results. In particular it is shown that, under suitable conditions the state estimation error converges exponentially to zero. The results are illustrated by numerical simulations based on an exothermic Plug-Flow Tubular reactor model and show the effectiveness of the proposed positive observer.

Composition of dissolved organic matter (DOM) in lakes responds to the trophic state and phytoplankton community succession

Dissolved organic matter (DOM), a heterogeneous mixture of diverse compounds with different molecular weights, is crucial for the lake carbon cycle. The properties and concentration of DOM in lakes are closely related to anthropogenic activities, terrigenous input, and phytoplankton growth. Thus, the lake's trophic state, along with the above factors, has an important effect on DOM. We determined the DOM sources and molecular composition in six lakes along a trophic gradient during and after phytoplankton bloom by combining optical techniques and the Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS). CDOM pools in eutrophic lakes may be more biologically refractory than in oligotrophic and mesotrophic lakes. Molecular formulas of DOM were positively correlated with the TSI (trophic state index) value (R2 = 0.73), with the nitrogen-containing compounds (CHON) being the most abundant formulas in all studied lakes. Eutrophication modified the molecular formulas of DOM to have less CHO% and more heteroatom S-containing compounds (CHOS% and CHNOS%), and this was the synactic result of the anthropogenic perturbation and phytoplankton proliferation. In eutrophic lakes, summer DOM showed higher molecular lability than in autumn, which was related to the seasonal phytoplankton community succession. Although the phytoplankton-derived DOM is highly bioavailable, we detected a simpler and more fragile phytoplankton community ecosystem in autumn, which may be accompanied by a lower phytoplankton production and metabolic activity. Therefore, we concluded that the lake eutrophication increased the allochthonous DOM accumulation along with sewage and nutrient input, and subsequently increased its release with phytoplankton bloom. Eutrophication and phytoplankton growth are accompanied by more highly unsaturated compounds, O3S+O5S compounds, and carboxylic-rich alicyclic compounds (CRAMs), which are the biotransformation product of phytoplankton-derived DOM. Eutrophication may be a potential source of refractory DOM compounds for biodegradation and photodegradation. Our results can clarify the potential role of water organic matter in the future global carbon cycle processes, considering the increasing worldwide eutrophication of inland waters.

Relative oscillation theory and essential spectra of Sturm–Liouville operators

We develop relative oscillation theory for general Sturm–Liouville differential expressions of the form1r(−ddxpddx+q) and prove perturbation results and invariance of essential spectra in terms of the real coefficients p, q, r. The novelty here is that we also allow perturbations of the weight function r in which case the unperturbed and the perturbed operator act in different Hilbert spaces.

Two-loop power spectrum with full time- and scale-dependence and EFT corrections: impact of massive neutrinos and going beyond EdS

We compute the density and velocity power spectra at next-to-next-to-leading order taking into account the effect of time- and scale-dependent growth of massive neutrino perturbations as well as the departure from Einstein-de-Sitter (EdS) dynamics at late times non-linearly. We determine the impact of these effects by comparing to the commonly adopted approximate treatment where they are not included. For the bare cold dark matter (CDM)+baryon spectrum, we find percent deviations for k ≳ 0.17h Mpc-1, mainly due to the departure from EdS. For the velocity and cross power spectrum the main difference arises due to time- and scale-dependence in presence of massive neutrinos yielding percent deviation above k ≃ 0.08, 0.13, 0.16h Mpc-1 for ∑mν = 0.4, 0.2, 0.1 eV, respectively. We use an effective field theory (EFT) framework at two-loop valid for wavenumbers k ≫ k FS, where k FS is the neutrino free-streaming scale. Comparing to Quijote N-body simulations, we find that for the CDM+baryon density power spectrum the effect of neutrino perturbations and exact time-dependent dynamics at late times can be accounted for by a shift in the one-loop EFT counterterm, Δγ̅1 ≃ - 0.2 Mpc2/h 2. We find percent agreement between the perturbative and N-body results up to k ≲ 0.12h Mpc-1 and k ≲ 0.16h Mpc-1 at one- and two-loop order, respectively, for all considered neutrino masses ∑mν ≤ 0.4 eV.

Field-controlled flow and shape of a magnetorheological fluid annulus.

We investigate the behavior of a magnetorheological (MR) fluid annulus, bounded by a nonmagnetic fluid and confined in a Hele-Shaw cell, under the simultaneous effect of in-plane, external radial and azimuthal magnetic fields. A second-order mode-coupling theory is used to study the early nonlinear stage of the pattern-forming dynamics. We examine changes in the morphology of the MR fluid annular structure as a function of its magnetic-field-tunable rheological properties, as well as the combined magnetic field's intensities, and thickness of the ring. Our weakly nonlinear perturbative results show that, depending on the system control parameters, the MR fluid annulus adopts various stationary shapes. These equilibrium annular structures present slightly bent, asymmetric fingered protrusions which may emerge on the inner, outer, or even on both boundaries of the magnetic fluid ring. On top of these morphological changes, we find that the resulting permanent shape patterns rotate with a well defined angular velocity. We focus on analyzing how the overall shape of the fingered patterns, in particular their sharpness and asymmetric form, as well as the number of resulting fingers are impacted by the magnetic-field-dependent yield stress of the MR fluid annulus. The influence of the magnetically controlled rheological properties of the MR fluid on the angular velocity of the rotating annulus is also scrutinized.

A large-N tensor model with four supercharges

We study a supersymmetric tensor model with four supercharges and O(N)3 global symmetry. The model is based on a chiral scalar superfield with three indices and quartic tetrahedral interaction in the superpotential, which is relevant below three dimensions. In the large-N limit the model is dominated by melonic diagrams. We solve the Dyson-Schwinger equations in superspace for generic d and extract the dimension of the chiral field and the dimensions of bilinear operators transforming in various representations of O(N)3. We find that all operator dimensions are real and above the unitarity bound for 1 < d < 3. Our results also agree with perturbative results in 3 − ε expansion. Finally, we extract the large spin behaviour of bilinear operators and discuss the connection with lightcone bootstrap.

Two loop ghost free quantisation of Wilson loops in [formula omitted] supersymmetric Yang-Mills

We report a perturbative calculation of the expectation value of the infinite straight line Maldacena-Wilson loop in N=4 supersymmetric Yang-Mills theory to order g6. Thus, we extend the previous perturbative result by one order. The vacuum expectation value is reformulated in terms of a non-linear and non-local transformation, the Nicolai map, mapping the full functional measure of the interacting theory to that of a free bosonic theory. The results are twofold. The perturbative cancellations of the different contributions to the Maldacena-Wilson loop are by no means trivial and seem to resemble those of the circular Maldacena-Wilson loop at order g4. Furthermore, we argue that our approach to computing quantum correlation functions is competitive with more standard diagrammatic techniques.