Perturbation Estimation Research Articles

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Abstract In this paper we investigate the nonlinear matrix equation X + A T X − 1 A = P , for the existence of positive definite solutions. Bounds for ∥ X L − 1 ∥ and ∥ X − 1 ∥ are derived where X L is the maximal solution and X is any other positive definite solution of this matrix equation. A perturbation estimate for the maximal solution and an error bound for approximate solutions are derived. A numerical example is given to illustrate the reliability of the obtained results.

Development of perturbation Monte Carlo methods for polarized light transport in a discrete particle scattering model

We present a polarization-sensitive, transport-rigorous perturbation Monte Carlo (pMC) method to model the impact of optical property changes on reflectance measurements within a discrete particle scattering model. The model consists of three log-normally distributed populations of Mie scatterers that approximate biologically relevant cervical tissue properties. Our method provides reflectance estimates for perturbations across wavelength and/or scattering model parameters. We test our pMC model performance by perturbing across number densities and mean particle radii, and compare pMC reflectance estimates with those obtained from conventional Monte Carlo simulations. These tests allow us to explore different factors that control pMC performance and to evaluate the gains in computational efficiency that our pMC method provides.

Sliding Mode Control with Perturbation Estimation and Hysteresis Compensator Based on Bouc-Wen Model in Tackling Fast-Varying Sinusoidal Position Control of a Piezoelectric Actuator

In this paper, a sliding mode control with perturbation estimation (SMCPE) coupled with an inverse hysteresis compensator is proposed for the motion tracking control of a microposition system with piezoelectric actuation. The inverse hysteresis compensator is employed to cancel the hysteresis nonlinearity, thus reducing the nonlinear system to a linear system with an inversion error. Then, a SMCPE controller is adopted to deal with all the unmodeled dynamics and disturbances, aiming at improving the dynamic performance and the robustness of system. An experiment of a piezoelectric actuator is presented to demonstrate the feasibility and effectiveness of the proposed control scheme. The result shows that for a fast-rate control input, the proposed method is capable of leading to a good performance of system behavior.

A Density Functional Theory and ab Initio Investigation of the Oxidation Reaction of CO by IO Radicals.

To get an insight into the possible reactivity between iodine oxides and CO, a first step was to study the thermochemical properties and kinetic parameters of the reaction between IO and CO using theoretical chemistry tools. All stationary points involved were optimized using the Becke's three-parameter hybrid exchange functional coupled with the Lee-Yang-Parr nonlocal correlation functional (B3LYP) and the Møller-Plesset second-order perturbation theory (MP2). Single-point energy calculations were performed using the coupled cluster theory with the iterative inclusion of singles and doubles and the perturbative estimation for triple excitations (CCSD(T)) and the aug-cc-pVnZ (n = T, Q, and 5) basis sets on geometries previously optimized at the aug-cc-pVTZ level. The energetics was then recalculated using the one-component DK-CCSD(T) approach with the relativistic ANO basis sets. The spin-orbit coupling for the iodine containing species was calculated a posteriori using the restricted active space state interaction method in conjunction with the multiconfigurational perturbation theory (CASPT2/RASSI) employing the complete active space (CASSCF) wave function as the reference. The CCSD(T) energies were also corrected for BSSE for molecular complexes and refined with the extrapolation to CBS limit while the DK-CCSD(T) values were refined with the extrapolation to FCI. The exploration of the potential energy surface revealed a two-steps mechanism with a trans and a cis pathway. The rate constants for the direct and complex mechanism were computed as a function of temperature (250-2500 K) using the canonical transition state theory. The three-parameter Arrhenius expressions obtained for the direct and indirect mechanism at the DK-CCSD(T)-cf level of theory is 1.49 × 10(-17) × T(1.77) exp(-47.4 (kJ mol(-1))/RT).

Output-Only Identification of Vibratory Machine Suspension Parameters under Exploitational Conditions

The paper concerns model based identification of vibratory machine body suspension system on the basis of dynamic responses measured under exploitational conditions. The research was carried out by means of the restoring force, boundary perturbation and direct parameter estimation techniques which, on the contrary to classical nonlinear system identification methods, requires neither excitation measurements nor linear behaviour of the considered system around an operating point. At the first stage of the research, parameters of the machine body suspension system were identified. Results accuracy was verified by determining percentage relative error of mass estimation with respect to the value calculated based on the machine geometrical and material properties. In the next step, the suspension system was modified by introduction of a nonlinear damping system. Obtained results proved that the assumed identification method is convenient for vibratory machine suspension condition monitoring and determining forces transferred on machine foundations.

Thermal photon, dilepton production, and electric charge transport in a baryon rich strongly coupled QGP from holography

We obtain the thermal photon and dilepton production rates in a strongly coupled quark-gluon plasma (QGP) at both zero and nonzero baryon chemical potential using a bottom-up Einstein-Maxwell-Dilaton (EMD) holographic model that is in good quantitative agreement with the thermodynamics of $(2+1)$-flavor lattice QCD around the crossover transition for baryon chemical potentials up to 400 MeV, which may be reached in the beam energy scan (BES) at RHIC. We find that increasing the temperature $T$ and the baryon chemical potential $\mu_B$ enhances the peak present in both spectra. We also obtain the electric charge susceptibility, the DC and AC electric conductivities and the electric charge diffusion as functions of $T$ and $\mu_B$. We find that electric diffusive transport is suppressed as one increases $\mu_B$. At zero baryon density, we compare our results for the DC electric conductivity and the electric charge diffusion with the latest lattice data available for these observables and find reasonable agreement around the crossover transition. Therefore, our holographic results may be used to constraint the magnitude of the thermal photon and dilepton production rates in a strongly coupled QGP, which we found to be at least one order of magnitude below perturbative estimates.

Pitch control for wind turbine systems using optimization, estimation and compensation

Delays caused by hydraulic pressure driven units in wind turbines may degrade and even destabilize pitch control system, leading to the performance degradation or collapse of the whole wind turbine energy conversion system. As a result, there is a strong motivation to improve pitch control technique to overcome the adverse effects from the unknown delays caused by the hydraulic driven units. In this study, a novel pitch control approach is developed by integrating optimization, delay-perturbation estimation, and signal compensation techniques. Specifically, an optimal PI controller is designed by applying direct search optimization to ideal delay-free pitch model. A delay estimator is next designed to estimate the perturbation caused by the delay. The signal compensation technique is then implemented to remove the effect from the delay-perturbation to the turbine output so that the actual output is consistent with the optimal output of the ideal delay-free model. Furthermore, the technique is extended to PID-based pitch control systems. The blade-tower dynamics models of three wind turbines, respectively with rated powers 1.5 MW, 275 kW and 50 kW, are investigated and the effectiveness of the proposed techniques are demonstrated by detailed simulation studies. It is worthy to point out a priori on the delay is not necessary in this design, which much meets the situations in practical wind turbine systems. Finally, a 4.8 MW benchmark wind turbine energy conversion system is investigated via the proposed pitch control technique, which has shown that delay perturbation estimate based compensation can effectively improve the pitch control performance in the real-time wind turbine energy conversion system.

Contribution of bacteriochlorophyll conformation to the distribution of site-energies in the FMO protein

The structural data for the Fenna–Matthews–Olson (FMO) protein indicate that the bacteriochlorophylls (BChls) display a significant degree of conformational heterogeneity of their peripheral substituents and the protein-induced nonplanar skeletal deformations of the tetrapyrrole macrocycle. As electronic properties of chromophores are altered by such differences, a conformational effect may influence the site-energies of specific pigments and thus play a role in mediating the excitation energy transfer dynamics, but this has not yet been established. The difficulty of assessing this question is shown to be partly the result of the inability of the sequential truncation approach usually employed to account for interactions between the conformations of the macrocycle and its substituents and an alternative approach is suggested. By assigning the BChl atoms to meaningful atom groups and performing all possible permutations of partial optimizations in a full-factorial design, where each group is either frozen in the crystal geometry or optimized in vacuo, followed by excited state calculations on each resulting structure (PM6//ZIndo/S), the specific effects of the conformations of each BChl component as well as mutual interactions between the molecular fragments on the site-energy can be delineated. This factorial relaxation procedure gives different estimates of the macrocycle conformational perturbation than the approach of sequentially truncating the BChl periphery. The results were evaluated in the context of published site-energies for the FMO pigments from three species to identify how conformational effects contribute to their distribution and instances of cross-species conservation and functional divergence of the BChl nonplanarity conformational contribution are described.

Estimate of ULF electromagnetic noise caused by a fluid flow during seismic or volcano activity

<p>The elaboration of theoretical models, even oversimplified, capable to estimate an expected electromagnetic effect during earthquake preparation process is not less important than the advancement of observational technique to detect seismic-related electromagnetic perturbations. Here possible mechanisms of ULF electromagnetic noise associated with seismic or volcanic activity are discussed. The electrokinetic (EK) and magnetohydrodynamic (MHD) effects due to an irregular flow of conducting rock fluid or magma flow are being revised. The conventional theory of EK effect in a water-saturated rock has been advanced by consideration of elliptic-shaped channels. A contribution of both mechanisms to observed ULF signal on the ground is shown to be dependent on the pore channel size/rock permeability. Estimates of magnetic and electrotelluric perturbations caused by magma motion along a volcano throat indicate on the important role of the surrounding rock conductivity. These estimates have proven that the mechanisms under consideration are able to generate ULF electromagnetic perturbations which could be detected by modern magnetometers under favorable conditions.</p>

Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations

In this paper, we consider a class of nonlinear matrix equation of the type \(X+\sum _{i=1}^mA_i^{*}X^{-q}A_i-\sum _{j=1}^nB_{j}^{*}X^{-r}B_j=Q\), where \(0<q,\,r\le 1\) and Q is positive definite. Based on the Schauder fixed point theorem and Bhaskar–Lakshmikantham coupled fixed point theorem, we derive some sufficient conditions for the existence and uniqueness of the positive definite solution to such equations. An iterative method is provided to compute the unique positive definite solution. A perturbation estimation and the explicit expression of Rice condition number of the unique positive definite solution are also established. The theoretical results are illustrated by numerical examples.

Perturbation estimation based coordinated adaptive passive control for multimachine power systems

This paper proposes a perturbation estimation based coordinated adaptive passive control (PECAPC) of generators excitation system and thyristor-controlled series capacitor (TCSC) devices for complex, uncertain and interconnected multimachine power systems. Discussion begins with the PECAPC design, in which the combinatorial effect of system uncertainties, unmodelled dynamics and external disturbances is aggregated into a perturbation term, and estimated online by a perturbation observer (PO). PECAPC aims to achieve a coordinated adaptive control between the excitation controller (EC) and TCSC controller based on the nonlinearly functional estimate of the perturbation. In this control scheme an explicit control Lyapunov function (CLF) and the strict assumption of linearly parametric uncertainties made on system structures can be avoided. A decentralized stabilizing EC for each generator is firstly designed. Then a coordinated TCSC controller is developed to passivize the whole system, which improves system damping through reshaping the distributed energies in power systems. Case studies are carried out on a single machine infinite bus (SMIB) and a three-machine system, respectively. Simulation results show that the PECAPC-based EC and TCSC controller can coordinate each other to improve the power system stability, finally a hardware-in-the-loop (HIL) test is carried out to verify its implementation feasibility.

Eigenvalue Statistics for Random Schrödinger Operators with Non Rank One Perturbations

We prove that certain natural random variables associated with the local eigenvalue statistics for generalized lattice Anderson models constructed with finite-rank perturbations are compound Poisson distributed. This distribution is characterized by the fact that the Levy measure is supported on at most a finite set determined by the rank. The proof relies on a Minami-type estimate for finite-rank perturbations. For Anderson-type continuum models on $\R^d$, we prove a similar result for certain natural random variables associated with the local eigenvalue statistics. We prove that the compound Poisson distribution associated with these random variables has a Levy measure whose support is at most the set of positive integers.

The fully non-linear post-Friedmann frame-dragging vector potential: magnitude and time evolution fromN-body simulations

Newtonian simulations are routinely used to examine the matter dynamics on non-linear scales. However, even on these scales, Newtonian gravity is not a complete description of gravitational effects. A post-Friedmann approach shows that the leading order correction to Newtonian theory is a vector potential in the metric. This vector potential can be calculated from N-body simulations, requiring a method for extracting the velocity field. Here, we present the full details of our calculation of the post-Friedmann vector potential, using the Delauney Tesselation Field Estimator (DTFE) code. We include a detailed examination of the robustness of our numerical result, including the effects of box size and mass resolution on the extracted fields. We present the power spectrum of the vector potential and find that the power spectrum of the vector potential is $\sim 10^5$ times smaller than the power spectrum of the fully non-linear scalar gravitational potential at redshift zero. Comparing our numerical results to perturbative estimates, we find that the fully non-linear result can be more than an order of magnitude larger than the perturbative estimate on small scales. We extend the analysis of the vector potential to multiple redshifts, showing that this ratio persists over a range of scales and redshifts. We also comment on the implications of our results for the validity and interpretation of Newtonian simulations.

The force model for asteroid (3200) Phaethon

Asteroid (3200) Phaethon is an Apollo asteroid having very small (0.14au) perihelion distance. We analyze the influence of various perturbing factors on the asteroid motion. Most of them were studied on the base of (O–C) residuals and/or the orbital evolution. This set of estimated perturbing accelerations contains: gravitational perturbations from all major planets, Pluto, the Moon, Ceres, Pallas, Vesta; the Earth, the Sun and Jupiter oblateness, the relativistic effects of the Sun and the solar radiation pressure. The perturbation estimation was done by five various methods. The purpose was to classify the perturbing accelerations as powerful, medium or weak ones, and the criteria for classification were built on the value of the mean accuracy of positional observations from the Earth. All five methods showed a good consistency. We found that the solar radiation pressure exerts a weak influence on the Phaethon motion, while the relativistic effects of the Sun and the Sun oblateness could be classified as medium perturbations. For the most complete and correct description of (3200) Phaethon motion we recommend to include gravitational influence from the planets and the Moon, the relativistic effects of the Sun and the Sun oblateness in the force model.Some other factors we considered separately. They are the recoil acceleration from the recurrent mass loss at perihelia, the Yarkovsky acceleration and relativistic effects of planets, Pluto and the Moon. It was obtained that their contributions to the total acceleration are negligible.We analyzed the next close encounter of Phaethon with the Earth in 2017 and found that neglecting gravitational perturbations from Neptune and Pluto, the Earth and Jupiter oblateness give an error less than 100km in the asteroid position. Gravitational perturbations from the inner planets (including the Moon) and Jupiter are the strongest and neglecting one of them results in the asteroid position error 104–106km.

Perturbative charm production and the prompt atmospheric neutrino flux in light of RHIC and LHC

We re-evaluate the prompt atmospheric neutrino flux, using the measured charm cross sections at RHIC and the Large Hadron Collider to constrain perturbative QCD parameters such as the factorization and renormalization scales, as well as modern parton distribution functions and recent estimates of the cosmic-ray spectra. We find that our result for the prompt neutrino flux is lower than previous perturbative QCD estimates and, consequently, alters the signal-to-background statistics of the recent IceCube measurements at high energies.

Design of terminal block backstepping controllers for perturbed systems in semi-strict feedback form

Based on finite-time stability approach, a terminal block backstepping control with perturbation estimation scheme is proposed in this paper for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The design procedure of the proposed control scheme mainly contains two parts. The first part is the design of pseudo-control inputs, the second part is the design of control input functions. In order to eliminate the problem of ‘explosion of complexity’ and overcome the problem of singularity, a derivative estimation algorithm embedded in the controller is utilised to estimate the perturbations. The control efforts are capable of suppressing the mismatched perturbations in most cases effectively so that the controlled states are able to reach zero within finite time. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.

Global change in action due to trapping: How to derive it whatever the rate of variation of the dynamics.

In this paper, we investigate the motion of a set of charged particles acted upon by a growing electrostatic wave in the limit when the initial wave amplitude is vanishingly small and when all the particles have the same initial action, I(0). We show, both theoretically and numerically, that when all the particles have been trapped in the wave potential, the distribution in action exhibits a very sharp peak about the smallest action. Moreover, as the wave keeps growing, the most probable action tends toward a constant, I(f), which we estimate theoretically. In particular, we show that I(f) may be calculated very accurately when the particles' motion before trapping is far from adiabatic by making use of a perturbation analysis in the wave amplitude. This fills a gap regarding the computation of the action change, which, in the past, has only been addressed for slowly varying dynamics. Moreover, when the variations of the dynamics are fast enough, we show that the Fourier components of the particles' distribution function can be calculated by connecting estimates from our perturbation analysis with those obtained by assuming that all the particles have the same constant action, I=I(f). This result is used to compute theoretically the imaginary part of the electron susceptibility of an electrostatic wave in a plasma. Moreover, using our formula for the electron susceptibility, we can extend the range in ε(a) (the parameter that quantifies the slowness of the dynamics) for our perturbative estimate of I(f)-I(0). This range can actually be pushed down to values of ε(a) allowing the use of neoadiabatic techniques to compute the jump in action. Hence, this paper shows that the action change due to trapping can be calculated theoretically, regardless of the rate of variation of the dynamics, by connecting perturbative results with neoadiabatic ones.

A Revisiting of the $$L^2$$ L 2 -Stability Theory of the Boltzmann Equation Near Global Maxwellians

We study the \(L^2\)-stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the \(L^2\)-distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in \(L^2\)-topology. Our local-in-time \(L^2\)-stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657–688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the \(L^2\)-stability theory for the Boltzmann equation near a global Maxwellian. For this \(L^2\)-stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform \(L^2\)-stability of the Boltzmann equation.

The energetic of (CH2F2)2 investigated by TDL IR spectroscopy and DFT computations: From collision induced relaxation of ro-vibrational transitions to non-covalent interactions.

Difluoromethane (CH2F2) is an atmospheric pollutant presenting strong absorptions within the 8-12 μm atmospheric window, hence it can contribute to global warming. Its dimer, (CH2F2)2, is bound through weak hydrogen bonds (wHBs). Theoretically, wHBs are of paramount importance in biological systems, though their modeling at density functional theory (DFT) level requires dispersion correlations to be accounted for. In this work, the binding energy (3.1 ± 0.5 kcal mol(-1)) of (CH2F2)2 is experimentally derived from the foreign broadening coefficients of the monomer compound, collisionally perturbed by a range of damping gases. Measurements are carried out on CH2F2 ro-vibrational transitions by means of tunable diode laser spectroscopy. Six stationary points on the potential energy surface (PES) of the dimer are investigated at DFT level by using some of the last generation density functionals (DFs). The Minnesota M06 suite of functionals as well as range separated DFs and DFs augmented by the non-local (NL) van der Waals (vdW) dispersion corrections are considered. DFT results are compared to reference values at the estimated complete basis set (CBS) limit of CCSD(T) theory (coupled cluster with singles and doubles augmented by a perturbational estimate of connected triples) and to the experimental binding energy. The M06-2X, M06-HF, VV10, BLYP-NL, and B3LYP-NL DFs reproduce CCSD(T)/CBS binding energies with a mean absolute deviation <0.4 kcal mol(-1) and about the same deviation from the experimental value. The present results are of twofold relevance: (i) they show that binding energy of homodimers can be conveniently obtained from the monomer's foreign broadening coefficients and that the correct simulation of hydrogen bonds involved in (CH2F2)2 needs non-covalent interactions to be included into DFT; (ii) O2- and N2-pressure broadening parameters represent fundamental data for exploiting the efficacy of remote sensing measurements employed to retrieve temperature and concentration profiles of our atmosphere.

Renormalization of the jet-quenching parameter

In the context of the recently derived probabilistic picture of in-medium jet evolution, we study radiative corrections which yield potentially large double logarithms, αs ln2 L, for large enough medium length L. We show that these large corrections are universal and can be reabsorbed in a renormalization of the jet quenching parameter controlling both momentum broadening and energy loss. The renormalized jet-quenching parameter is enhanced compared to its standard perturbative estimate. As a particular consequence, the radiative energy loss scales with medium size L as L2+γ, with γ = , as compared to the standard scaling in L2.