Equivalent Formalism Research Articles

Impedance spectroscopy applied to lithium battery materials: Good practices in measurements and analyses

This paper outlines a critical analysis of the currently available methodological framework for a comprehensive and reliable interpretation of impedance spectroscopy data of aprotic lithium-based secondary batteries. Impedance spectroscopy is a powerful experimental technique that can be used to assess the impedance of batteries over a range of frequencies. However, in typical battery configurations, all components contribute to the impedance response of the whole cell and the overlap of many of the different impedance responses often results in a complex experimental curve that is not easily easy to interpret. Various analytical approaches can be used to evaluate complex impedance data sets of batteries: (a) matching the impedance response of the cells in question with a previously published impedance model; (b) performing additional electrochemical measurements with different settings and/or on different cell designs to support the assignation of impedance contributions to specific physicochemical processes; (c) acquiring external physicochemical determinations, morphological and chemical data that can support or refute the results of impedance analysis; (d) developing theoretical models that reconcile physical insights at different length scales of the battery components with the equivalent circuit formalism.

An Efficient Multiple Scattering Solution to Radiative Transfer Equations in Strong Forward Scattering Environments for Vegetated Land Emission and its Representation Through an Equivalent Albedo-Tau Formalism

An Efficient Multiple Scattering Solution to Radiative Transfer Equations in Strong Forward Scattering Environments for Vegetated Land Emission and its Representation Through an Equivalent Albedo-Tau Formalism

Exploring the self-tuning of the cosmological constant from Planck mass variation

Recently, the variation of the Planck mass in the general relativistic Einstein–Hilbert action was proposed as a self-tuning mechanism of the cosmological constant, preventing standard model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the local self-tuning action by a coupled Gauss–Bonnet term and a companion four-form field strength, graviton loops can be prevented from incapacitating the degravitation of the standard model vacuum energy. For certain cases, we furthermore find that this extension can be recast as a Horndeski scalar–tensor theory and be embedded in the conventional local self-tuning formalism. We then explore the possibility of a unification of inflation with self-tuning. The resulting equations can alternatively be used to motivate a multiverse interpretation. In this context, we revisit the coincidence problem and provide an estimation for the probability of the emergence of intelligent life in our Universe as a function of cosmic age, inferred from star and terrestrial planet formation processes. We conclude that we live at a very typical epoch, where we should expect the energy densities of the cosmological constant and matter to be of comparable size. For a dimensionless quantity to compare the emergence of life throughout the cosmic history of different universes in an anthropic analysis of the multiverse, we choose the order of magnitude difference of the evolving horizon size of a Universe to the size of its proton as the basic building block of atoms, molecules, and eventually life. For our Universe we find this number to form peak at approximately 42. We leave the question of whether the same number is frequently assumed for the emergence of life across other universes or singles out a special case to future exploration.

A canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics in first-order formalism

We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

Mapping barrier island soil moisture using a radiative transfer model of hyperspectral imagery from an unmanned aerial system

The advent of remote sensing from unmanned aerial systems (UAS) has opened the door to more affordable and effective methods of imaging and mapping of surface geophysical properties with many important applications in areas such as coastal zone management, ecology, agriculture, and defense. We describe a study to validate and improve soil moisture content retrieval and mapping from hyperspectral imagery collected by a UAS system. Our approach uses a recently developed model known as the multilayer radiative transfer model of soil reflectance (MARMIT). MARMIT partitions contributions due to water and the sediment surface into equivalent but separate layers and describes these layers using an equivalent slab model formalism. The model water layer thickness along with the fraction of wet surface become parameters that must be optimized in a calibration step, with extinction due to water absorption being applied in the model based on equivalent water layer thickness, while transmission and reflection coefficients follow the Fresnel formalism. In this work, we evaluate the model in both field settings, using UAS hyperspectral imagery, and laboratory settings, using hyperspectral spectra obtained with a goniometer. Sediment samples obtained from four different field sites representing disparate environmental settings comprised the laboratory analysis while field validation used hyperspectral UAS imagery and coordinated ground truth obtained on a barrier island shore during field campaigns in 2018 and 2019. Analysis of the most significant wavelengths for retrieval indicate a number of different wavelengths in the short-wave infra-red (SWIR) that provide accurate fits to measured soil moisture content in the laboratory with normalized root mean square error (NRMSE)< 0.145, while independent evaluation from sequestered test data from the hyperspectral UAS imagery obtained during the field campaign obtained an average NRMSE = 0.169 and median NRMSE = 0.152 in a bootstrap analysis.

The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

Kinetic model for a sol-gel transition: application of the modified Bailey criterion

Precise a priori prediction of time required to achieve colloidal sol-gel transition is a challenging task. This is because not much system-specific theoretical work has been carried out on kinetics of colloidal gelation, where the physical bond formation is strongly affected by the surface characteristics of the colloidal particles. Under such situation, drawing analogies from apparently dissimilar phenomena that share the same physical foundation can prove helpful. Interestingly the physical processes such as the fracture dynamics in a material leading to failure, as represented by the Bailey criterion of durability, and sol-gel transition are known to satisfy the Markovian criterion, suggesting equivalent mathematical formalism. Such equivalence leads to a simple mathematical formalism given by the modified Bailey criterion which is identical in construction to the criterion in fracture dynamics. In this work, we assess the modified Bailey criterion of durability to predict the time required to attain the sol-gel transition in a colloidal dispersion under non-isothermal conditions. The model parameters are derived from the gelation experiments on colloidal clay dispersion conducted under the isothermal conditions. Interestingly, the prediction of the time to attain the sol-gel transition under non-isothermal condition from the modified Bailey criterion matches the experimental observation with remarkable accuracy, thereby validating an independent methodology to obtain vital knowledge on colloidal sol-gel transition. This work, therefore, validates the mathematical formalism of one Markovian process (fracture dynamics) by carrying out experiments on another Markovian process (sol-gel transition), which are otherwise distinctly different from each other. Such correspondence highlights the profound similarity in the microstructural changes occurring in the two distinct systems.

An Equivalent ABCD-Matrix Formalism for Non-Local Wire Media With Arbitrary Terminations

A simple analytical model based on the transmission-matrix approach is proposed for equivalent wire-medium (WM) interfaces. The obtained ABCD matrices for equivalent interfaces capture the non-local effects due to the evanescent transverse magnetic (TM) WM mode and in part due to the propagating transverse electromagnetic (TEM) WM mode. This enables one to characterize the overall response of bounded WM structures by cascading the ABCD matrices of equivalent WM interfaces and WM slabs as transmission lines supporting only the propagating TEM WM mode, resulting in a simple circuit-model formalism for bounded WM structures with arbitrary terminations, including the open-end, patch/slot arrays, and thin metal/2D material, among others. The individual ABCD matrices for equivalent WM interfaces apparently violate the conservation of energy and reciprocity, and therefore, the equivalent interfaces apparently behave as non-reciprocal lossy or active systems. However, the overall response of a bounded WM structure is consistent with the lossless property maintaining the conservation of energy and reciprocity. These unusual features are explained by the fact that in the non-local WM the Poynting vector has an additional correction term which takes into account a "hidden power" due to non-local effects. Results are obtained for various numerical examples demonstrating a rapid and efficient solution for bounded WM structures, including the case of geometrically complex multilayer configurations with arbitrary terminations, subject to the condition that WM interfaces are decoupled by the evanescent TM WM mode below the plasma frequency.

Open-Stopband Suppression via Double Asymmetric Discontinuities in 1-D Periodic 2-D Leaky-Wave Structures

A technique for the open-stopband (OSB) suppression in one-dimensional (1-D) periodic leaky-wave antennas based on a double asymmetric series/shunt discontinuity inside the unit cell is discussed and applied to a canonical 2-D structure. A longitudinal equivalent network formalism is developed here to analyze the unit-cell matching, which confirms that the OSB suppression cannot be achieved using a double symmetric discontinuity. Conversely, an infinite number of matched configurations can be obtained using two unequal passive discontinuities, whose reciprocal distance can be chosen freely inside a continuous range always including a quarter wavelength. The possibility of suppressing the OSB is then shown for both TM and TE leaky modes supported by a metal strip grating on a grounded slab by using independent full-wave modal solvers and considering typical geometries with either narrow metallic strips or narrow slots inside the unit cell.

The Design of Optical Circuit-Analog Absorbers through Electrically Small Nanoparticles

In the last few years, the perfect absorption of light has become an important research topic due to its dramatic impact in photovoltaics, photodetectors, color filters and thermal emitters. While broadband optical absorption is relatively easy to achieve using bulky devices, today there is a strong need and interest in achieving the same effects by employing nanometric structures that are compatible with modern nanophotonic components. In this paper, we propose a general procedure to design broadband nanometer-scale absorbers working in the optical spectrum. The proposed devices, which can be considered an extension to optics of microwave circuit-analog absorbers, consist of several layers containing arrays of elongated nanoparticles, whose dimensions are engineered to control both the absorption level and the operational bandwidth. By combining a surface-impedance homogenization and an equivalent transmission-line formalism, we define a general analytical procedure that can be employed to achieve a final working design. As a relevant example, we show that the proposed approach allows designing an optical absorber exhibiting a 20% fractional bandwidth on a thickness of λ/4 at the central frequency of operation. Full-wave results confirming the effectiveness of the analytical findings, as well as some considerations about the experimental realization of the proposed devices are provided.

Electrooptomechanical Equivalent Circuits for Quantum Transduction

Using the techniques of optomechanics, a high-$Q$ mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input-output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.

Nambu–Goldstone modes in the random phase approximation

I show that the kernel of the random phase approximation (RPA) matrix based on a stable Hartree, Hartree-Fock, Hartree-Bogolyubov or Hartree-Fock-Bogolyubov mean field solution is decomposed into a subspace with a basis whose vectors are associated, in the equivalent formalism of a classical Hamiltonian homogeneous of second degree in canonical coordinates, with conjugate momenta of cyclic coordinates (Nambu-Goldstone modes) and a subspace with a basis whose vectors are associated with pairs of a coordinate and its conjugate momentum neither of which enters the Hamiltonian at all. In a subspace complementary to the one spanned by all these coordinates including the conjugate coordinates of the Nambu-Goldstone momenta, the RPA matrix behaves as in the case of a zerodimensional kernel. This result was derived very recently by Nakada as a corollary to a general analysis of RPA matrices based on both stable and unstable mean field solutions. The present proof does not rest on Nakada's general results.

Generating Functions of Bipartite Maps on Orientable Surfaces

We compute, for each genus $g\geq 0$, the generating function $L_g\equiv L_g(t;p_1,p_2,\dots)$ of (labelled) bipartite maps on the orientable surface of genus $g$, with control on all face degrees. We exhibit an explicit change of variables such that for each $g$, $L_g$ is a rational function in the new variables, computable by an explicit recursion on the genus. The same holds for the generating function $F_g$ of rooted bipartite maps. The form of the result is strikingly similar to the Goulden/Jackson/Vakil and Goulden/Guay-Paquet /Novak formulas for the generating functions of classical and monotone Hurwitz numbers respectively, which suggests stronger links between these models. Our result complements recent results of Kazarian and Zograf, who studied the case where the number of faces is bounded, in the equivalent formalism of dessins d'enfants. Our proofs borrow some ideas from Eynard's "topological recursion" that he applied in particular to even-faced maps (unconventionally called "bipartite maps" in his work). However, the present paper requires no previous knowledge of this topic and comes with elementary (complex-analysis-free) proofs written in the perspective of formal power series.

Intrinsic transfer matrix method and split quaternion formalism for multilayer media

The intrinsic transfer matrix method for 1D longitudinal elastic wave propagation through multilayer media is used to obtain an equivalent split quaternion formalism. Periodic media are analysed in this framework and the presence of a defect is considered. A simple one layer defect and an inversion defect are analysed. A commutative type of split quaternion is identified, which corresponds to defects of the periodic structure that can be placed in any position, the overall acoustic properties of the medium being conserved. Also, a nonperiodic medium composed of such commutative elements has a behaviour independent of the order of elements. Several possible applications in sound wave measurement and processing are outlined. The proposed split quaternion formalism is compact and can make analytical and numerical computations easier.

Generating functions of bipartite maps on orientable surfaces (extended abstract)

We compute, for each genus $g$ &amp;ge; 0, the generating function $L$&lt;sub&gt;$g$&lt;/sub&gt; &amp;equiv; $L$&lt;sub&gt;$g$&lt;/sub&gt;($t$;$p$&lt;sub&gt;1&lt;/sub&gt;,$p$&lt;sub&gt;2&lt;/sub&gt;,...) of (labelled) bipartite maps on the orientable surface of genus $g$, with control on all face degrees. We exhibit an explicit change of variables such that for each $g$, $L$&lt;sub&gt;$g$&lt;/sub&gt; is a rational function in the new variables, computable by an explicit recursion on the genus. The same holds for the generating function $L$&lt;sub&gt;$g$&lt;/sub&gt; of &lt;i&gt;rooted&lt;/i&gt; bipartite maps. The form of the result is strikingly similar to the Goulden/Jackson/Vakil and Goulden/Guay-Paquet/Novak formulas for the generating functions of classical and monotone Hurwitz numbers respectively, which suggests stronger links between these models. Our result strengthens recent results of Kazarian and Zograf, who studied the case where the number of faces is bounded, in the equivalent formalism of &lt;i&gt;dessins d’enfants&lt;/i&gt;. Our proofs borrow some ideas from Eynard’s “topological recursion” that he applied in particular to even-faced maps (unconventionally called “bipartite maps” in his work). However, the present paper requires no previous knowledge of this topic and comes with elementary (complex-analysis-free) proofs written in the perspective of formal power series. Nous calculons, pour chaque genre $g$ &amp;ge; 0, la série génératrice $L$&lt;sub&gt;$g$&lt;/sub&gt; &amp;equiv; $L$&lt;sub&gt;$g$&lt;/sub&gt;($t$;$p$&lt;sub&gt;1&lt;/sub&gt;,$p$&lt;sub&gt;2&lt;/sub&gt;,...) des cartes bipartites (étiquetées) sur la surface orientable de genre $g$, avec contrôle des degrés des faces. On exhibe un changement de variable explicite tel que pour tout $g$, $L$&lt;sub&gt;$g$&lt;/sub&gt; est une fonction rationnelle des nouvelles variables, calculable par une récurrence explicite sur le genre. La même chose est vraie de la série génératrice $L$&lt;sub&gt;$g$&lt;/sub&gt; des cartes biparties &lt;i&gt;enracinées&lt;/i&gt;. La forme du résultat est similaire aux formules de Goulden/Jackson/Vakil et Goulden/Guay-Paquet/Novak pour les séries génératrices de nombres de Hurwitz classiques et monotones, respectivement, ce qui suggère des liens plus forts entre ces modèles. Notre résultat renforce des résultats récents de Kazarian et Zograf, qui étudient le cas où le nombre de faces est borné, dans le formalisme équivalent des &lt;i&gt;dessins d’enfants&lt;/i&gt;. Nos démonstrations utilisent deux idées de la “récurrence topologique” d’Eynard, qu’il a appliquée notamment aux cartes paires (appelées de manière non-standard “cartes biparties” dans son travail). Cela dit, ce papier ne requiert pas de connaissance préliminaire sur ce sujet, et nos démonstrations (sans analyse complexe) sont écrites dans le language des séries formelles.

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of Km and 77% of kcat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.

How (not) to teach Lorentz covariance of the Dirac equation

In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties.

A Brachytherapy Plan Evaluation Tool for Interstitial Applications

Radiobiological metrics such as tumor control probability (TCP) and normal tissue complication probability (NTCP) help in assessing the quality of brachytherapy plans. Application of such metrics in clinics as well as research is still inadequate. This study presents the implementation of two indigenously designed plan evaluation modules: Brachy_TCP and Brachy_NTCP. Evaluation tools were constructed to compute TCP and NTCP from dose volume histograms (DVHs) of any interstitial brachytherapy treatment plan. The computation module was employed to estimate probabilities of tumor control and normal tissue complications in ten cervical cancer patients based on biologically effective equivalent uniform dose (BEEUD). The tumor control and normal tissue morbidity were assessed with clinical followup and were scored. The acute toxicity was graded using common terminology criteria for adverse events (CTCAE) version 4.0. Outcome score was found to be correlated with the TCP/NTCP estimates. Thus, the predictive ability of the estimates was quantified with the clinical outcomes. Biologically effective equivalent uniform dose-based formalism was found to be effective in predicting the complexities and disease control.

Ion‐conductivity study and anomalous diffusion analysis of plasticized gelatin films

ABSTRACTIn this article, we report a study on ion conduction in gelatin films with different concentrations of glycerol as a plasticizer; these films might be a candidate for electrolyte materials in solid polymer batteries. The ion conductivity was appreciable, showing a maximum of about 9.14 × 10−3 S/m at room temperature without the addition of any ionic salt. Analysis of the impedance measurements was done with a model based on material properties instead of the usual equivalent circuit formalism, where circuit elements are difficult to interpret. Generalized calculus was used to model the anomalous diffusion in the system. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3018–3024, 2013

Notes on quantitative structure–property relationships (QSPR), part 3: Density functions origin shift as a source of quantum QSPR algorithms in molecular spaces

A general algorithm implementing a useful variant of quantum quantitative structure-property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed.