Multivector Fields and Connections. Setting Lagrangian Equations in Field Theories

The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle $J^1E\to E\to M$, it is shown that integrable multivector fields in $E$ are equivalent to integrable connections in the bundle $E\to M$ (that is, integrable jet fields in $J^1E$). This result is applied to the particular case of multivector fields in the manifold $J^1E$ and connections in the bundle $J^1E\to M$ (that is, jet fields in the repeated jet bundle $J^1J^1E$), in order to characterize integrable multivector fields and connections whose integral manifolds are canonical lifting of sections. These results allow us to set the Lagrangian evolution equations for first-order classical field theories in three equivalent geometrical ways (in a form similar to that in which the Lagrangian dynamical equations of non-autonomous mechanical systems are usually given). Then, using multivector fields; we discuss several aspects of these evolution equations (both for the regular and singular cases); namely: the existence and non-uniqueness of solutions, the integrability problem and Noether's theorem; giving insights into the differences between mechanics and field theories.Comment: New sections on integrability of Multivector Fields and applications to Field Theory (including some examples) are added. The title has been slightly modified. To be published in J. Math. Phy

Lagrangian-Hamiltonian unified formalism for field theory

The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.Comment: LaTeX file, 23 pages. Minor changes have been made. References are update

Geometric quantization of mechanical systems with time-dependent parameters

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the adiabatic assumption. A Hamiltonian of such a system is affine in the temporal derivative of parameter functions. This leads to the geometric Berry factor phenomena.Comment: 20 page

Geometric quantization of completely integrable Hamiltonian systems in the action-angle variables

We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The associated quantum algebra consists of functions affine in action coordinates. We obtain a set of its nonequivalent representations in the separable pre-Hilbert space of smooth complex functions on the torus where action operators and a Hamiltonian are diagonal and have countable spectra.Comment: 8 page

Interpretation of heart rate variability via detrended fluctuation analysis and alpha-beta filter

Detrended fluctuation analysis (DFA), suitable for the analysis of nonstationary time series, has confirmed the existence of persistent long-range correlations in healthy heart rate variability data. In this paper, we present the incorporation of the alpha-beta filter to DFA to determine patterns in the power-law behaviour that can be found in these correlations. Well-known simulated scenarios and real data involving normal and pathological circumstances were used to evaluate this process. The results presented here suggest the existence of evolving patterns, not always following a uniform power-law behaviour, that cannot be described by scaling exponents estimated using a linear procedure over two predefined ranges. Instead, the power law is observed to have a continuous variation with segment length. We also show that the study of these patterns, avoiding initial assumptions about the nature of the data, may confer advantages to DFA by revealing more clearly abnormal physiological conditions detected in congestive heart failure patients related to the existence of dominant characteristic scales.Comment: 18 pages, 14 figure

Prediction of crop coefficients from fraction of ground cover and height: Practical application to vegetable, field and fruit crops with focus on parameterization

Research PaperThe A&P approach, developed by Allen and Pereira (2009), estimates single and basal crop coefficients (Kc and Kcb) from the observed fraction of ground cover (fc) and crop height (h). The practical application of the A&P for several crops was reviewed and tested in a companion paper (Pereira et al., 2020). The current study further addresses the derivation of optimal values for A&P parameter values representing canopy transparency (ML) and stomatal adjustment (Fr), and tests the resulting model performance. Values reported in literature of ML and Fr were analysed. Optimal ML and Fr values were derived by a numerical search that minimized the differences between Kcb A&P with standard Kcb for vegetable, field, and fruit crops as tabulated by Pereira et al. (2021a, 2021b) and Rallo et al. (2021). Sources for fc were literature reviews supplemented by a remote sensing survey. Computed Kcb and Kc for mid- and end-season together with associated parameters values were tabulated. To improve the usability of the ML and Fr parameters a cross validation was performed, which consisted of the linear regression between Kcb computed by A&P and observed Kcb relative to independent data sets obtained from field observations. Results show that both series of Kcb match well, with regression coefficients very close to 1.0, coefficients of determination near 1.0, and root mean square errors (RMSE) of 0.06 for the annual crops and RMSE = 0.07 for the trees and vines. These errors represent less than 10% of most of the computed tabulated Kcb. The tabulated Fr and ML of this paper can be regarded as defaults to support A&P field practice when observations of fc and h are performed. Therefore, the A&P approach shows to be appropriate for use in irrigation scheduling and planning when fc and h are observed using ground and/or remote sensing, hence supporting irrigation water savingsinfo:eu-repo/semantics/publishedVersio