Order Perturbation Analysis Research Articles

Instabilities and self–organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Estimation of the diffusion coefficient of heavy quarks in light of Gribov-Zwanziger action

The heavy quark momentum diffusion coefficient (κ) is one of the most essential ingredients for the Langevin description of heavy quark dynamics. In the temperature regime relevant to the heavy ion collision phenomenology, a substantial difference exists between the lattice estimations of κ and the corresponding leading order (LO) result from the hard thermal loop (HTL) perturbation theory. Moreover, the indication of poor convergence in the next-to-leading order (NLO) perturbative analysis has motivated the development of several approaches to incorporate the non-perturbative effects in the heavy quark phenomenology. In this work, we estimate the heavy quark diffusion coefficient based on the Gribov-Zwanziger prescription. In this framework, the gluon propagator depends on the temperature-dependent Gribov mass parameter, which has been obtained self-consistently from the one-loop gap equation. Incorporating this modified gluon propagator in the analysis, we find a reasonable agreement with the existing lattice estimations of κ within the model uncertainties.

How do cell crowding and starvation affect avascular tumor growth of the EMT6/Ro tumor?

Here we re-examine experimental in vitro data for the EMT6/Ro tumor volume and viable rim thickness. This shows that the growth speed is constant in time, and independent of nutrient concentration at large concentrations, but that the viable rim thickness increases in this high concentration regime. We then present a simple mechanistic reaction-diffusion equation that includes crowding and starvation effects, and show that the model qualitatively captures the experimental observations. Moreover, the model predicts that the cancer cell concentration is characterised by a wave pulse (soliton), and the pulse shape is explored through zero’th order perturbation analysis corresponding to large wave speeds. It is shown that this zero’th order term is dominant for the experimental condition, further indicating that the non-linear reaction governs the pulse characteristic shape. Finally, at low nutrient concentrations we find that the front is a pulled-front, that is, the growth speed is determined by the cell multiplication at the wave front edge in accordance with earlier modelling approaches.

Output based resilient model predictive control of Cyber–Physical Systems under cover attacks

In this article, a state estimate based robust model predictive control strategy is developed for networked cyberphysical systems under false data injections. The core of the proposed approach consists in elaborating an observed based general framework whose main feature relies on its adaptability to different classes of attacks. The main feature of the proposed scheme relies on the capability to mitigate undesired system behaviors due to external malicious actions. This is achieved by showing that an augmented state-estimate/estimation error set-membership conditions allow us to quickly detect data integrity anomalies and, as a consequence, to implement adequate counter-measures. In particular, set-theoretic model predictive arguments are combined with the perturbation analysis and sequential quadratic programming in order to reduce as much as possible the occurrence of refresh procedures on the communication network when resilient command actions are no longer available. As one of its main merits, these arguments allow to remove the constructive assumptions present in very recent competitors. In this respect, the framework is customized for covert attacks by specifying actuation and detection phases and proving feasibility and closed-loop stability properties. The core of the resulting solution exploits output feedback receding horizon and set-theoretic control ideas so that the resilient nature of the virtual control moves is formally put in light.

THERMODYNAMIC AND REACTIVITY ASPECT OF β-CYCLODEXTRINE INCLUSION COMPLEXES WITH COUMARIN DERIVATIVES

In this study, the thermodynamic and reactivity characteristics of coumarin-derived ligand inclusion complexes with βCD were described, in addition to the in situ reactivity of these ligands and their changes in the complex cavity. For this purpose, computational tools such as molecular docking, second order perturbative analysis (E2PERT), ONIOM2 (DFT/PM6) methods were employed to obtain the global and local reactivity indices, and thermodynamic parameters, in addition to non-covalent interaction (NCI) analysis. As a result, it can be observed that the inclusion complexes are stable and viable given the ability to form non-covalent interactions, but their formation is not spontaneous under the modeling conditions. The global and local reactivity indices show that the ligands change their chemical reactivity inside the inclusion complex, demonstrating that the studied ligands present AOX SET activity outside the cavity, and HAT activity inside the cavity, mainly the C1 and C3 ligands.

Gravitational wave induced baryon acoustic oscillations

We study the impact of gravitational waves originating from a first order phase transition on structure formation. To do so, we perform a second order perturbation analysis in the 1+31+3 covariant framework and derive a wave equation in which second order, adiabatic density perturbations of the photon-baryon fluid are sourced by the gravitational wave energy density during radiation domination and on sub-horizon scales. The scale on which such waves affect the energy density perturbation spectrum is found to be proportional to the horizon size at the time of the phase transition times its inverse duration. Consequently, structure of the size of galaxies and bigger can only be affected in this way by relatively late phase transitions at \ge 10^{6}\,\text{s}≥106s. Using cosmic variance as a bound we derive limits on the strength \alphaα and the relative duration (\beta/H_*)^{-1}(β/H*)−1 of phase transitions as functions of the time of their occurrence which results in a new exclusion region for the energy density in gravitational waves today. We find that the cosmic variance bound forbids only relative long lasting phase transitions, e.g. \beta/H_*\lesssim 6.8β/H*≲6.8 for t_*\approx 5\times10^{11}\,\text{s}t*≈5×1011s, which exhibit a substantial amount of supercooling \alpha>20α>20 to affect the matter power spectrum.

A contribution to the conditioning theory of the indefinite least squares problems

The conditioning theory of the indefinite least squares (ILS) problems is considered in the paper. Based on the well acknowledged fact that utilizing the intermediate results produced in the process of solving the problem can largely reduce the computational burden of computing the condition numbers, we employ two hyperbolic matrix decomposition based numerical algorithms to solve the ILS problems, and with its intermediate results the first order perturbation analysis and condition number theory of the ILS problems are fully investigated. The first order perturbation analysis gives a precise characterization of the matrix factors in influencing the forward errors. For the new explicit expressions of the condition numbers consisting of intermediate results, some compact forms or upper bounds are proposed to reduce its computational burden and storage requirement. Moreover, we also devise some efficient numerical algorithms to estimate the condition numbers by exploiting its special structures. Numerical experiments are given to illustrate the efficiency of our results.

Ultracompact rotating gravastars and the problem of matching with Kerr spacetime

A number of authors provided arguments that a rotating gravastar is a good candidate for a source of the Kerr metric. These arguments were based on the second order perturbation analysis. In the following paper, we construct a perturbative solution of the rotating gravastar up to the third perturbation order and show that it cannot be continuously matched with the Kerr spacetime.

Analytical Deflection Profiles and Pull-In Voltage Calculations of Prestressed Electrostatic Actuated MEMS Structures

This paper presents a zeroth and first order perturbative analysis of prestressed electrostatic actuated Microelectromechanical systems (MEMS). Perturbation theory is used to calculate the deflection profile of various MEMS structures, from which the pull-in voltage is estimated using the weighed residual method, where both a Galerkin expression and a Dirac delta function have been used as weight functions. A prestressed circular Capacitative Micromachined Ultrasonic Transducer (CMUT) is used as the main example in this paper. This device is modeled as a circular clamped plate subjected to an electrostatic pressure. The calculated pull-in voltage has been compared with experimental data of highly prestressed CMUTs, where a relative error between -36% and -8% is observed for a model that does not include stress. The model that includes the residual stress lowers the range of the relative error to values between -5% and 21%. To improve the accuracy of the pull-in voltage estimate Richardson extrapolation has been calculated from the zeroth and first order estimates. The pull-in voltage models are compared with a Finite Element Model (FEM), where an overestimation, in the high stress regime, of 10% is observed for the zeroth order model, less than 5% for the Galerkin method and 3% for the Richardson extrapolation. [2020-0358]

Boson stars and solitons confined in a Minkowski box

We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen U(1) gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the box surface layer determine the stress tensor that the box must have to confine the scalar hair. Some of these horizonless hairy solutions exist for any value of the scalar field charge and not only above the natural critical charges of the theory (namely, the critical charges for the onset of the near-horizon and superradiant instabilities of the Reissner-Nordström black hole). However, the ground state solutions have a non-trivial intricate phase diagram with a main and a secondary family of solitons (some with a Chandrasekhar mass limit but others without) and there are a third and a fourth critical scalar field charges where the soliton spectra changes radically. Most of these intricate properties are not captured by a higher order perturbative analysis of the problem where we simply back-react a normal mode of the system.

A second order analysis of McKean–Vlasov semigroups

We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean–Vlasov diffusions. This methodology provides second order Taylor type expansions with remainder for both the evolution semigroup as well as the stochastic flow associated with this class of nonlinear diffusions. Bismut–Elworthy–Li formulae for the gradient and the Hessian of the integro-differential operators associated with these expansions are also presented. The article also provides explicit Dyson–Phillips expansions and a refined analysis of the norm of these integro-differential operators. Under some natural and easily verifiable regularity conditions we derive a series of exponential decays inequalities with respect to the time horizon. We illustrate the impact of these results with a second order extension of the Alekseev–Gröbner lemma to nonlinear measure valued semigroups and interacting diffusion flows. This second order perturbation analysis provides direct proofs of several uniform propagation of chaos properties w.r.t. the time parameter, including bias, fluctuation error estimate as well as exponential concentration inequalities.

Quantum phases of canted dipolar bosons in a two-dimensional square optical lattice

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\theta$ of the dipolar bosons. At low tilt angles $0^{\circ}\leqslant\theta\apprle25^{\circ}$, the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles $55^{\circ}\apprge\theta\apprge35^{\circ}$, phases with striped order of supersolid or density wave are preferred. In the intermediate domain $25^{\circ}\apprle\theta\apprle35^{\circ}$ an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for $\theta\apprge55^{\circ}$, which renders the system unstable and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results.

The shape dependence of Vainshtein screening in the cosmic matter bispectrum

One of the most pressing questions in modified gravity is how deviations from general relativity can manifest in upcoming galaxy surveys. This is especially relevant for theories exhibiting Vainshtein screening, where such deviations are efficiently suppressed within a (typically large) Vainshtein radius. However, Vainshtein screening is known to be shape dependent: it is most effective around spherical sources, weaker around cylindrical objects and completely absent for planar sources. The Cosmic Web therefore offers a testing ground, as it displays many shapes in the form of clusters, filaments and walls. In this work, we explicitly derive the signature of the shape dependence of Vainshtein screening on the matter bispectrum, by considering a cubic Galileon model with a conformal coupling to matter and a cosmological constant. We perform a second order perturbative analysis, deriving analytic, integral expressions for the bispectrum, which we integrate using hi_class. We find that the shape dependence of Vainshtein screening enters the bispectrum with a unique scale-factor dependence of ∝ a3/2. The magnitude of the effect today is up to 2% for a model whose linear growth rate deviates up to 5% from ΛCDM.

DYNAMICS OF CLUSTERS OF GALAXIES WITH EXTENDED F(chi) GRAVITY

In this article, we present the results of a fourth order perturbation analysis of the metric theory of gravity f(chi) = chi^(3/2) , with chi a suitable dimensionless Ricci scalar. Such a model corresponds to a specific f(R) metric theory of gravity, where the mass of the system is included in the gravitational field's action. In previous works we have shown that, up to the second order in perturbations, this theory reproduces the flat rotation curves of galaxies and the details of the gravitational lensing in individual, groups, and clusters of galaxies. Here, leaving fixed the results from our previous works, we show that the theory reproduces the dynamical masses of 12 Chandra X-ray galaxy clusters, without the need of dark matter, through the metric coefficients up to the fourth order of approximation. In this sense, we calculate the first relativistic correction of the f(chi) metric theory and apply it to fit the dynamical masses of clusters of galaxies.

Modal analysis of historical masonry structures: Linear perturbation and software benchmarking

The mechanical behavior of masonry materials has a common feature: a nonlinear behavior with high compressive strength and very low tensile strength. As a consequence, old masonry buildings generally present cracks due to permanent loads and/or accidental events. Therefore, the characterization of the global dynamic behavior of masonry structures should take into account the presence of existing cracks. This paper presents a numerical approach coupling linear perturbation and modal analysis in order to estimate the dynamic properties of masonry constructions, taking into account the existence of structural damage. First, the approach is validated on a masonry arch subjected to increasing loads, via three FE codes. Then, the same procedure is applied to a real masonry structure affected by a severe crack distribution.

High-Order Analysis of the Efficiency Gap for Maximum Likelihood Estimation in Nonlinear Gaussian Models

In Gaussian measurement models, the measurements are given by a known function of the unknown parameter vector, contaminated by additive zero-mean Gaussian noise. When the function is linear, the resulting maximum likelihood estimate (MLE) is well-known to be efficient [unbiased, with a mean square estimation error (MSE) matrix attaining the Cramer–Rao lower bound (CRLB)]. However, when the function is nonlinear, the MLE is only asymptotically efficient. The classical derivation of its asymptotic efficiency uses a first-order perturbation analysis, relying on a “small-errors” assumption, which under subasymptotic conditions turns inaccurate, rendering the MLE generally biased and inefficient. Although a more accurate (higher-order) performance analysis for such cases is of considerable interest, the associated derivations are rather involved, requiring cumbersome notations and indexing. Building on the recent assimilation of tensor computations into signal processing literature, we exploit the tensor formulation of higher-order derivatives to derive a tractable formulation of a higher (up to third-) order perturbation analysis, predicting the bias and MSE matrix of the MLE of parameter vectors in general nonlinear models under subasymptotic conditions. We provide explicit expressions depending on the first three derivatives of the nonlinear measurement function, and demonstrate the resulting ability to predict the “efficiency gap” (relative excess MSE beyond the CRLB) in simulation experiments. We also provide MATLAB code for easy computation of our resulting expressions.

Relay synchronization in multiplex networks

Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.

Numerical analysis of <i>H</i><SUB align="right">∞ filter for system parameter identification

The numerical analysis of the H∞ filter algorithm for system parameter identification is addressed in this paper. After presenting the filter under study and the convergence characteristics of the algorithm, a first order perturbation analysis is conducted. More specifically, norm-wise bounds are derived for the sensitivities, condition numbers, forward errors, backward errors and rounding errors of the iterative computational operations of the algorithm. Consequently, numerical stability and accuracy rules can be potentially composed as measures of algorithmic reliability and dynamical numerical performance. For exploring the impact of incorporating the specific algorithm dynamics in the numerical analysis, a similar framework is presented for the computed solutions irrespective of the used algorithm. The paper further exploits the application of the synthesised numerical analysis framework to parameter identification of linear state space systems. Finally some numerical examples are given for demonstration purposes.

Density Functional Theory Study on the Complexation of NOTA as a Bifunctional Chelator with Radiometal Ions.

1,4,7-Triazacyclononane-1,4,7-triacetic acid (NOTA) is a key bifunctional chelator utilized for the complexation of metal ions in radiopharmaceutical applications; the ability of these chelators depends on the strength of their binding with ions. The focus of the present work is to evaluate the complexation of Cu2+, Ga3+, Sc3+, and In3+ radiometal ions with NOTA using density functional theory (B3LYP functional) and 6-311+G(2d,2p)/DGDZVP basis sets. The significant role of ion-water interactions in the chelation interaction energies in solution reflects the competition between ion-water and NOTA-ion interaction in the chelation process. There is reasonable agreement between experimental and theoretical binding constants, geometries, and 1H NMR chemical shifts. Chelation interaction energies, Gibbs free energies, and entropies in solution show that the NOTA-Ga3+ and NOTA-Cu2+ are the most and least stable complexes, respectively. The natural atomic charges and second order perturbation analysis reveal charge transfer between NOTA and radiometal ions. The theoretical 1H NMR chemical shifts of NOTA are in good agreement with experiment; these values are influenced by the presence of the ions, which have a deshielding effect on the protons of NOTA. Global scalar properties such as EHOMO/ELUMO, ΔELUMO-HOMO, and chemical hardness/softness confirm that the NOTA-Cu2+ complex, which has a singly occupied molecular orbital, has the lowest ΔELUMO-HOMO value, the least chemical hardness, and the highest chemical softness. The significant variation of the hardness and ΔELUMO-HOMO values of the complexes can be attributed to the different positions of the metal ions on the periodic table. This study affirms that, among the radiometal ions, Ga3+ can be used to effectively radiolabel NOTA chelator for radiopharmaceutical usage as it binds most stably with NOTA.

On Time-Fractional Cylindrical Nonlinear Equation**Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under Grant No 2016/01/6239.

Properties of cylindrical electron acoustic solitons are studied in vortex plasmas. The modified cylindrical Korteweg-de Vries (KdV) equation is acquired and converted into the time fractional cylindrical modified KdV equation by Agrawal's analysis. Via the Adomian decomposition method, a cylindrical soliton solution to the equation is obtained. The cylindrical time fractional effect on the wave properties is investigated. Further, the increase of the fractional order of time a and hot to trapped electrons temperature β are minimized in both solitary width and amplitude. These influences on the structures of the soliton may be an alternative to the use of higher order perturbation analysis.