Concept Of Response Function Research Articles

The global temperature anomalies related to the slowdown of atmospheric CO2 concentration observed from 1939 up to 1950

It is very well known that carbon dioxide (CO2) accumulated in the atmosphere is the main climate driver. The first precise direct continuous measurements of the atmospheric CO2concentration were provided from Keeling since 1958 at Mauna Loa Observatory. The measurements are going on up to day. Law Dom ice core drilling was started in 1969 by the Australian ANARE program. The slowdown of the World economic development during the World War I, the Great Depression and the World War II, lead to deaccelerating the CO2 emissions. The integration of the total CO2emissions using the impulse response function concept shows that the observed slowdown of the CO2 emission is not sufficient to explain the CO2 plateau and additional CO2 sinks are necessary. Based on multiple regression models adjusted global temperatures were determined by removal of temperature influences other than related to CO2. The adjusted temperatures follow close the CO2 radiation term. The difference between the estimated adjusted temperature time evolution with and without the CO2 slowdown and also the short time trends demonstrate very clear the close relation between the temperature change and the CO2 radiative forcing. It is shown that the slowdown of the CO2 emission in the period from 1939 up to 1950 and the related CO2 concentration in the atmosphere, caused at least partially by human activities, generate a more slow increase of the temperature anomalies. Consequently CO2 is the leading variable of the relation surface temperature - CO2.

Prediction of parametric rolling of ships in single frequency regular and triple frequency group waves

A 3D nonlinear time domain simulation method based on the impulse response function concept is applied to the investigation of parametric rolling of the ITTC-A1 containership. In the numerical simulation, the hydrodynamic coefficients are determined beforehand by a 3D frequency domain panel code on the basis of linear potential theory, whereas the most nonlinear terms in the equations of motion are taken into account, such as the excitation by large amplitude waves (exact Froude–Krylov forces/moments), exact restoring forces/moments resulting from integration of the hydrostatic pressures over the actually wetted surface of the ship and the semi-empirical nonlinear viscous damping correction. In addition, all nonlinear inertia terms are retained when considering solution of large amplitude motions. The parametric rolling is predicted by solving the 6 degrees of freedom (DoF) nonlinear equations of ship motion in the time domain in response to single frequency regular waves and triple frequency group waves. The obtained numerical results are compared with corresponding experimental measurements and numerical predictions of an earlier conducted international benchmark study proving the good performance of the developed method in terms of the predictability of parametric roll phenomena and to a lesser degree to the accuracy of predicted roll amplitude values.

A nonlinear causality measure in the frequency domain: Nonlinear partial directed coherence with applications to EEG

Frequency domain Granger causality measures have been proposed and widely applied in analyzing rhythmic neurophysiological and biomedical signals. Almost all these measures are based on linear time domain regression models, and therefore can only detect linear causal effects in the frequency domain. A frequency domain causality measure, the partial directed coherence, is explicitly linked with the frequency response function concept of linear systems. By modeling the nonlinear relationships between time series using nonlinear models and employing corresponding frequency-domain analysis techniques (i.e., generalized frequency response functions), a new nonlinear partial directed coherence method is derived. The advantages of the new method are illustrated via a numerical example of a nonlinear physical system and an application to electroencephalogram signals from a patient with childhood absence epilepsy. The new method detects both linear and nonlinear casual effects between bivariate signals in the frequency domain, while the existing measures can only detect linear effects. The proposed new method has important advantages over the classical linear measures, because detecting nonlinear dependencies has become more and more important in characterizing functional couplings in neuronal and biological systems.

No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth

The recent macro-finance literature does not agree either about the empirical properties of the expectation part and of the term premium on long-term bonds or about the importance or even the direction of the relationship between the term premium and future economic activity. This paper proposes a two-step approach to handle both problems. First, in a VAR setting, we extract a reliable measure of the term premium by means of averaging estimator techniques aiming at optimally solving prediction problems when highly persistent processes are present and, thus, providing a so called Near-Cointegrated VAR(p) approach. Second, we analyze the dynamic response of GDP to shocks to the term premium by using the New Information Response Function concept. As far as the first problem is concerned, we find that the NCVAR-based term premium measure is rather stable and counter-cyclical, as suggested by interest rates survey-based estimation of yield curve models and by its risk compensation role. Regarding the second problem, we find that an increase in the long-term spread caused by the term premium induces two effects on future economic activity: the impact is negative for short horizons (less than 1year), whereas it is positive for longer ones.

No-Arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth

The recent macro-finance yield curve literature does not agree neither about term premia empirical properties nor about the importance or even the direction of its relationship with future economic activity. This paper proposes a two-step approach to handle both problems. First, in a VAR setting, we extract a reliable measure of the term premia by means of averaging estimators techniques aiming at optimally solving prediction problems when highly persistence processes are present and, thus, providing a so called Near-Cointegrated VAR(p) approach. Second, we analyze the dynamic response of the GDP to shocks on the term premia by using the New Information Response Function concept. First,we find that the NCVAR-based term premium measure is rather stable and contra-cyclical, with the expectation part accounting for most of the yield variability, which is consistent with the typical macroeconomic view. Second, we find that an increase of the long-term spread caused by a rise of a term premium induces two effects on future economic activity: the impact is negative for short horizons (less than one year), whereas it is positive for longer ones. Therefore, this result suggests that the above mentioned ambiguity could come from the fact that the sign of this relationship is changing over the period that follows the shock.

Approximate solution to the diffusion equation and its application to seepage-related problems

Effective dam safety procedures require pore pressure measurements to be interpreted as soon as possible after readings have been taken. Direct interpretations based on partial differential equations are not appropriate. Here, we took a different approach which consisted in applying the impulse response function concept to a dam site. Consequently, two models were designed so that their parameters matched the temporal moments of Green’s function of the associated parabolic problem. These models were compared with closed-form solutions. The first model was the exponential decay model, which gave good results, but did not account for high loading harmonics. The second model, based on the fundamental solution of a parabolic problem, was surprisingly accurate. As an example problem we considered monitoring data obtained from a zoned earth dam. The results show that the main aspects of the processes reflected in most cell recordings can be described in a linear framework, and that they are accounted for by both models.

Theory of weak switching of arbitrary collector voltages in non-neutral plasma diodes

The response function concept is used to describe analytically the dynamics of electrons in a non-neutral diode in which the collector voltage is switched on at t = 0 from zero to a weak but otherwise arbitrary time-dependent voltage. It generalizes previous investigations of simple switching (Akimov et al 2003 J. Appl. Phys. 93 1246; Ender et al 2004 Phys. Plasmas 11 3212), where the final voltage is assumed to be constant. Use is made of the Laplace transformation technique and a remarkably simple expression is found for the Laplace-transformed emitter electric field from which analytic solutions for the time-dependent, highly transient response of the diode can be obtained. As an application, the switching to a final harmonic collector potential called cos-switching is investigated and the usefulness of an approximative response function approach is demonstrated by a comparison of the approximative with the exact results. For diodes with different charge non-neutrality parameter and branches with no electron reflection various scenarios for cos-switching are explored, revealing the exact time behaviour of the emitter electric field and of the net current density. The amplitude A∞(ω) of the asymptotically driven oscillation as a function of the driven frequency ω is also presented. Of upmost importance is a novel resonance phenomenon we found in that part of the second zone of generalized Pierce diodes for which the non-reflecting equilibria are linearly stable against aperiodic and oscillatory eigenmodes. In a narrow band region A∞(ω) amplifies by a factor 50. This driven internal oscillation takes place on a high current level raising high promises e.g. for microwave generators and/or circuit current amplifiers as well as for diagnostic purposes.

Sensitivity of spectral lines to temperature, velocity, and magnetic field

We present an analytical and numerical study of the sensitivity of weak solar photospheric lines to tempera- ture, velocity, and magnetic fields. Our investigation is based on the concept of response functions (Landi degl'Innocenti & Landi degl'Innocenti 1977; Ruiz Cobo & del Toro Iniesta 1994). Lines commonly used in solar spectropolarimetry, like Fe  630.25 nm in the visible and Fe  1564.85 nm in the infrared, are examined in detail as emerging from reference quiet Sun and sunspot models. We develop a simple phenomenological model capable of describing the response of any given line to these atmospheric parameters. We find that: (a) the sensitivity of the lines to velocity and magnetic fields increases with the sharpness of the intensity and circular polarization profiles; (b) the sensitivity to temperature is determined mainly by the variation of the source function with temperature, which is smaller at longer wavelengths; and (c) lines quoted to be insensitive to temperature, like Fe  1564.85 nm and Fe  557.61 nm, exhibit larger changes in equivalent width than lines presumed to have higher sensitivities to T ,s uch as Fe 630.25 nm. The relations provided by our model are universal and can be used to decide which line is better suited to measuring a given atmospheric parameter. The results of this study are of practical interest for the design of new instruments and for better exploitation of existing ones.

Non‐LTE Inversion of Stokes Profiles Induced by the Zeeman Effect

This paper presents a new diagnostic tool for the inference of the thermal, dynamic, and magnetic properties of the solar chromosphere. It consists of a non-LTE inversion code of Stokes profiles induced by the Zeeman effect in magnetized stellar atmospheres. This code is the generalization, to the non-LTE Stokes transfer case, of the inversion code for unpolarized line profiles of Socas-Navarro, Ruiz Cobo, & Trujillo Bueno. It is based upon a full non-LTE multilevel treatment of Zeeman line transfer in which the thermal, magnetic, and dynamic properties of the atmospheric model are adjusted automatically by means of nonlinear least-squares-fitting techniques until a best fit to the observed Stokes profiles is obtained. Our non-LTE inversion approach is based on the concept of response functions, which measure the emergent Stokes profiles' first-order reaction to changes in the atmospheric parameters. We generalize our fixed departure coefficients (FDC) approximation in order to allow fast computation of such response functions in the present non-LTE Zeeman line transfer context. We present several numerical tests showing the reliability of our inversion method for retrieving the information about the thermodynamics and the magnetic field vector that is contained in the polarization state of the chosen spectral lines. We also explore the limitations of the inversion code by applying it to simulated observations where the physical hypotheses on which it is based on are not met. Finally, we apply our non-LTE Stokes inversion code to real spectropolarimetric observations of a sunspot observed in the IR triplet lines of Ca II. As a result, a new mean model of the sunspot chromosphere is provided.

Non‐LTE Inversion of Line Profiles

In this paper we address the problem of the non-LTE (NLTE) inversion of line profiles by means of a nonlinear least-squares minimization procedure combined with very efficient multilevel transfer methods. Our approach is based on the concept of response functions, which measure the first-order response of the emergent profiles to changes in the atmospheric conditions. We introduce the fixed departure coefficients (FDC) approximation in order to compute these response functions in a fast and straightforward manner. The accuracy of this approximation is checked comparing FDC response functions with those obtained from full NLTE computations. An NLTE inversion code based on these response functions has been developed and extensively tested. Reference synthetic profiles, similar to those expected from real observations, are given as input to the inversion algorithm and the recovered models are shown to be compatible with the reference models within the error bars. Our NLTE inversion code thus provides a new tool for the investigation of the chromospheres of the Sun and other stars.

Electromagnetic induction in thin sheets: integral equations and model studies in two dimensions

The model consists of a thin sheet of variable conductance in one horizontal direction above a conducting substructure of lateral uniformity. Transition anomalies are permitted, i.e. The anomalous range of varying conductance may be bounded by uniform half sheets of different conductances. For E-polarization the inducing external source field may be non-uniform. Two complementary integral equations are derived in the frequency-distance domain, to find the anomalous electric field or alternatively to find the anomalous sheet current density for each polarization. The equations involve two sets of response functions for the normal structure outside the anomalous range. A first set generates for a given source field at ground level the internal magnetic field by induction and the normal electric field which serves as an input function for the derivation of the anomalous field. A second set accounts for the inductive coupling of the anomalous fields in sheet and substrucutre. Various tests are performed: for the compatibility of complementary solutions, for the correct asymptotic behaviour at infinity in the horizontal direction, and for the accuracy of numerical integrations as controlled by the grid-point spacing. The numerical solutions are also tested against analytical solutions and against numerical solutions by other methods, in particular with regard to the validity of the thin-sheet approximation. A comparison with results from integral equations, which involve conventional Green's functions, reveals in the case of B-polarization complications where a strong influx of currents exists from the substructure into the thin sheet. A source transfer function is introduced which allows the extension of the response function concept to induction by non-uniform sources. Two types are studied: a stationary jet field source and a travelling Sq source above a sedimentary basin and a coastline. Resulting magnetotelluric and geomagnetic deep sounding responses are compared with the respective responses, when the inducing field is quasi-uniform.

Numerical test of a newV-profile inversion technique

The diagnostic method proposed by Landi Degl'Innocenti and Landolfi (1982), based on the observation of circular polarization, has been generalized to derive the thermodynamic properties of unresolved magnetic elements in the solar atmosphere. The final aim is to derive the height dependence of several parameters of the flux tube atmosphere (such as temperature, magnetic field and velocity distributions, macroturbulence and filling factor). We have used a perturbation method based on the concept of response functions for the Stokes profiles introduced by Landi Degl'Innocenti and Landi Degl'Innocenti (1977). We present here the preliminary results of invertingV-profiles by an iterative standard least-squares technique, which allows to find the magnetic 1-D atmosphere consistent with simulated data.

A possible diagnostic method for magnetic field and velocity gradients in sunspots

We present a diagnostic method for detecting magnetic field gradients and velocity gradients in sunspots through the analysis of Stokes parameters profiles in magnetoactive lines. On one hand, the method is based on the concept of response functions for the Stokes profiles introduced by Landi Degl'Innocenti and Landi Degl'Innocenti (1977); on the other hand, it takes advantage of the diagnostic content of the residuals between observed Stokes profiles and best-fit ‘Unno’-profiles. The analysis of synthesis profiles obtained for the line λ6302.502 FeI forming in the Sunspot Sunspot Model (Avrett, 1981) suggests that the method could actually be promising, at least if the dependence of the magnetic field vector on optical depth is sufficiently simple.

Thermodynamical properties of unresolved magnetic flux tubes

We propose a diagnostic method, based on the observation of circular polarization signals in line pairs, to derive the thermodynamical properties of unresolved magnetic elements in the solar atmosphere. The concept of response function for the ratio of circular polarization signals in two lines is introduced and its main properties are analyzed. Some detailed calculations for suitably selected line pairs are presented.

Response function for transient heat conduction in semi-infinite media

The concept of response function is used to investigate the transient heat conduction in a semi-infinite medium, when the temperature of the surface is an arbitrary function of time. First, the response of the system to a unit step function of surface temperature T s ( t) is obtained. The temperature distribution in the medium corresponding to arbitrary surface temperature T s ( t) is then expressed in terms of the response function and convolution integral. The analytical solution of the convolution integral is obtained for a periodic variation of T s ( t). The resulting expression for T( x, t) is identical with that obtained by the usual periodic analysis. Numerical computations are carried out to investigate the dependence of the accuracy of numerical results on the upper limit of time ( t o ) in the convolution integral.