Simple Theory Research Articles

Non-Hermitian guided modes and exceptional points using loss-free negative-index materials.

We analyze the guided modes in coupled waveguides made of negative-index materials without gain or loss. We show that it supports non-Hermitian phenomenon on the existence of guided mode versus geometric parameters of the structure. The non-Hermitian effect is different from parity-time (P T) symmetry, and can be explained by a simple coupled-mode theory with an anti-P T symmetry. The existence of exceptional points and slow-light effect are discussed. This work highlights the potential of loss-free negative-index materials in the study of non-Hermitian optics.

Non-invertible defects in 5d, boundaries and holography

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible codimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become codimension one non-invertible defects of a boundary theory with an ABJ anomaly.

Iron(II) Complexes with Porphyrin and Tetrabenzoporphyrin: CASSCF/MCQDPT2 Study of the Electronic Structures and UV-Vis Spectra by sTD-DFT.

The geometry and electronic structures of iron(II) complexes with porphyrin (FeP) and tetrabenzoporphyrin (FeTBP) in ground and low-lying excited electronic states are determined by DFT (PBE0/def2-TZVP) calculations and the complete active space self-consistent field (CASSCF) method, followed by the multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2) approach to determine the dynamic electron correlation. The minima on the potential energy surfaces (PESs) of the ground (3A2g) and low-lying, high-spin (5A1g) electronic states correspond to the planar structures of FeP and FeTBP with D4h symmetry. According to the results of the MCQDPT2 calculations, the wave functions of the 3A2g and 5A1g electronic states are single determinant. The electronic absorption (UV-Vis) spectra of FeP and FeTBP are simulated within the framework of the simplified time-dependent density functional theory (sTDDFT) approach with the use of the long-range corrected CAM-B3LYP function. The most intensive bands of the UV-Vis spectra of FeP and FeTBP occur in the Soret near-UV region of 370-390 nm.

Semi-analytical solution for the Lamb’s problem in second gradient elastodynamics

In the present paper, we consider the Lamb-type problem of the dynamic response of isotropic half-space subjected to the time-harmonic vertical point load within the simplified strain gradient elasticity theory (SGET). The classical elastodynamics solution of this problem predicts singular displacements and stresses at the point of the load application. In the present study, we use the technique of Lamé potentials and Hankel transform to solve the high-order motion equations of SGET. An explicit solution accounting for traction and double traction boundary conditions is obtained in the transformed domain. The inverse transformation is performed numerically with accurate capturing of the solution behavior around the Rayleigh pole, which position is defined by the modified scale-dependent Rayleigh equation. Based on obtained results, it is shown that SGET solution is bounded at the epicenter of the load, and that it takes into account the spatial dispersion effects for the propagated waves. These effects are important for the analysis of the high-frequency processes in the structured materials. The intensity of non-classical effects in the solution is controlled by the length scale parameters of gradient model. Based on numerical calculations, we derive the universal non-dimensional relations between the amplitudes of the applied load and maximum displacements on the surface, which can be used to identify the length scale parameters of SGET based on the atomistic calculations or experimental data.

Reaction calorimetry: Main types, simple theory, and application for kinetic study—A review

AbstractReaction calorimetry is a powerful experimental method widely used for reaction hazard assessment in chemical engineering for chemical process design and in other fields. Currently, several types of reaction calorimeters are available, each with its own features. Many articles and several monographs have been published dealing with various aspects of reaction calorimetry, but it is difficult to find an overview of different types of instruments and the theoretical basis of reaction calorimetry in one review in a compact form. The purpose of this article is to fill this gap as much as possible and to help in understanding the principles of this useful experimental method and in choosing the type of instrument most suitable for the purposes of a particular study. The review concludes with some recommendations for the proper organization of an experiment in reaction calorimetry, with an emphasis on the kinetic study. The usefulness of kinetics based on reaction calorimetry data is illustrated by an example of using kinetics to design an industrial process.

The Continued Forecasting Effectiveness of a Real Earnings Model of the Equity Premium

This article empirically demonstrates the continued forecasting effectiveness of a simple theory modeling expected stock returns as the sum of the earnings yield on the S&P 500 (measured as the highest past annual earnings on the index divided by the current index value) and a market-based forecast of the inflation rate. Besides having retained its significant one-to-one relationship with subsequent excess annual stock returns, this model’s estimate of the equity premium is discovered to have a correlation of 0.85 with S&P 500 excess returns over subsequent five-year intervals ever since market data for the estimator became available in 1997.

Modelling density surfaces of intraspecific classes using camera trap distance sampling

AbstractSpatially explicit densities of wildlife are important for understanding environmental drivers of populations, and density surfaces of intraspecific classes allow exploration of links between demographic ratios and environmental conditions. Although spatially explicit densities and class densities are valuable, conventional design‐based estimators remain prevalent when using camera‐trapping methods for unmarked populations.We developed a density surface model that utilized camera trap distance sampling data within a hierarchical generalized additive modelling framework. We estimated density surfaces of intraspecific classes of a common ungulate, white‐tailed deerOdocoileus virginianus, across three large management regions in Indiana, United States. We then extended simple statistical theory to test for differences in two ratios of density.Deer density was influenced by landscape fragmentation, wetlands and anthropogenic development. We documented class‐specific responses of density to availability of concealment cover, and found strong evidence that increased recruitment of young was tied to increased resource availability from anthropogenic agricultural land use. The coefficients of variation of the total density estimates within the three regions we surveyed were 0.11, 0.10 and 0.06.Synthesis and applications. Our strategy extends camera trap distance sampling and enables managers to use camera traps to better understand spatial predictors of density. Our density estimates were more precise than previous estimates from camera trap distance sampling. Population managers can use our methods to detect finer spatiotemporal changes in density or ratios of intraspecific‐class densities. Such changes in density can be linked to land use, or to management regimes on habitat and harvest limits of game species.

A simplified deformation gradient theory and its experimental verification

A simplified deformation gradient theory and its experimental verification

English

The present paper is devoted to study some completeness properties of transitive binary relational set, i.e., a set together with a transitive binary relation (so called t-set). We hope that the results of our paper will be a starting point for a sufficiently general but simple theory of objects that are suitable for modelling various aspects of computation and useful in modern applications of domain theory to general topology and mathematical analysis.

Analog Raychaudhuri Equation in Mechanics

Usually, in mechanics, we obtain the trajectory of a particle in a given force field by solving Newton’s second law with chosen initial conditions. In contrast, through our work here, we first demonstrate how one may analyze the behaviour of a suitably defined family of trajectories of a given mechanical system. Such an approach leads us to develop a mechanics analogue following the well-known Raychaudhuri equation largely studied in Riemannian geometry and general relativity. The idea of geodesic focusing, which is more familiar to a relativist, appears to be analogous to the meeting of trajectories of a mechanical system within a finite time. Applying our general results to the case of simple pendula, we obtain relevant quantitative consequences. Thereafter, we set up and perform a straightforward experiment based on a system with two pendula. The experimental results of this system are found to tally well with our proposed theoretical model. In summary, the simple theory and the related experiment provide us with a way to understand the essence of a fairly involved concept in advanced physics from an elementary standpoint.

Holographic open quantum systems: toy models and analytic properties of thermal correlators

We present a unified picture of open quantum systems, the theory of a system probing a noisy thermal environment, distilling lessons learnt from previous holographic analyses. Our treatment is applicable both when the system is coupled to short-lived (Markovian), and long-lived (non-Markovian) environmental degrees of freedom. The thermal environment is modeled using an asymptotically AdS black hole, and the systems of interest are simple probe field theories. The effective stochastic dynamics of the system is governed by real-time thermal correlators, which we compute using the gravitational Schwinger-Keldysh (grSK) geometry. We describe the structure of arbitrary tree-level contact and exchange Witten diagrams in the grSK geometry. In particular, we argue, that all such diagrams reduce to integrals supported on a single copy of the exterior of the black hole. The integrand is obtained as a multiple discontinuity of a function comprising ingoing boundary-bulk propagators, monodromy functions which appear as radial Boltzmann weights, and vertex factors. These results allow us to deduce the analytic structure of real-time thermal n-point functions in holographic CFTs. We illustrate the general statements by a two-dimensional toy model, dual to fields in the BTZ background, which we argue captures many of the essential features of generic open holographic QFTs.

Prediction and validation of the profiles of the top and mixed loading surfaces during discharge from multiple-outlet silos

One of the problems for the efficient operation of large industrial silos is that it is difficult to check the volume of the materials that remain inside the silo at any given time. This problem is more pronounced when materials from two or more sources are stored in a multiple-outlet silo, so that the profile of the mixed loading surface, i.e., the interface between materials from different sources, is not visible. To date, no research addressing this problem has been conducted. Therefore, this study proposes a model to predict the profiles of the top and mixed loading surfaces using the simple kinematic theory and considering the effect of the angle of repose on the shape of the top surface. The accuracy of the proposed prediction model was verified by comparing actual profiles of the top and mixed loading surfaces with those predicted by the model when materials were discharged from a multiple-outlet hopper with discharge sequences varying from the left, central, and right outlets. The results showed that the proposed model adequately predicted the profiles with relatively negligible errors.

Theoretical Advances in the Ecology and Evolution of Mutualistic Interactions – Review of a Symposium (SYMP 14) Organized at ESA + CSEE 2022 Joint Meeting

Theoretical Advances in the Ecology and Evolution of Mutualistic Interactions – Review of a Symposium (<scp>SYMP</scp> 14) Organized at <scp>ESA</scp> + <scp>CSEE</scp> 2022 Joint Meeting

Quantum critical dynamics in the two-dimensional transverse Ising model

In the vicinity of the quantum critical point (QCP), thermodynamic properties diverge toward zero temperature governed by universal exponents. Although this fact is well known, how it is reflected in quantum dynamics has not been addressed. The QCP of the transverse Ising model on a triangular lattice is an ideal platform to test the issue, since it has an experimental realization, the dielectrics being realized in an organic dimer Mott insulator, $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{ET}}_{2}X$, where a quantum electric dipole represents the Ising degrees of freedom. We track the Glauber-type dynamics of the model by constructing a kinetic protocol based on the quantum Monte Carlo method. The dynamical susceptibility takes the form of the Debye function and shows a significant peak narrowing in approaching a QCP due to the divergence of the relaxation timescale. It explains the anomaly of dielectric constants observed in the organic materials, indicating that the material is very near the ferroelectric QCP. We disclose how the dynamical and other critical exponents develop near QCP beyond the simple field theory.

The appropriacy of the analytical models for calculating the shear capacity of cross-laminated timber (CLT) under out-of-plane bending

Rolling shear, an inherent property of cross-laminated timber (CLT) due to the weak shear strength of cross layers, is always the determinant of load-bearing capacity for short-span CLT members subjected to out-of-plane bending. Many analytical models were developed to calculate the shear capacity of CLT members. Because of the difficulty to precisely model the complicated shear failure mechanisms, however, no model was universally accepted. This paper aims to study the appropriacy of the commonly used analytical models, namely, composite beam theory, shear analogy method, Gamma method, and simple beam theory, by tests and analytical calculations. A composite beam theory-based simplified method was proposed. Three-point loading tests for the short-span CLT panels with 3 and 5 layers were conducted, and the shear capacities of the test specimens were calculated using the above-mentioned analytical methods. Shear strength and modulus of cross layers of the test specimens, which were used as the inputs for calculating the shear capacities, were tested by modified planar shear method. By comparing the calculation results obtained from different analytical models and the test results as well, it can be concluded that: (1) composite beam theory, shear analogy method, and the proposed simplified method give almost the same calculation results, therefore, the proposed simplified method can be used as the replacement for the other models; (2) Gamma method is more appropriate for calculating the shear capacity in case the input shear strength is determined by planar shear test; (3) the simple beam theory that is used in CSA O86 provides significantly lower shear capacity predictions than those obtained by the other methods.

Determination of supply conditions, scenarios and pay-off for industrial machinery supplier selection post economic and engineering considerations

Supply conditions after economics and engineering considerations is important for consideration because machinery and equipment procurement is a tripod of which supply conditions is one. This study identified the attributes of supply conditions, different ways of combining the attributes using simple permutation and combination theories and determined the pay-off as well as the opportunity lost to every scenario used by method of Expected Decision Value (EDV). The attributes were identified as: Due Date of the Supply (A); Technical Capability of Vendor (B); After Sales Services (C); and Vendor’s Experience (D). Total number of scenarios were 15 of four (4) options. The pay-off with the opportunity lost to each selected option are: Option1 (25% against 75%); Option2 (50% against 50%); Option3 (75% against 25%); and Option4, 100% where the four (4) strategic decisions were all considered for selecting the supplier turns out to be optimum and in favour of purchaser. Further research in the area of development of a Surrogate Model for Industrial Machinery Supplier Selection Post Economics and Engineering Considerations is recommended.

Modeling extracellular stimulation of retinal ganglion cells: theoretical and practical aspects

Objective. Retinal prostheses use electric current to activate inner retinal neurons, providing artificial vision for blind people. Epiretinal stimulation primarily targets retinal ganglion cells (RGCs), which can be modeled with cable equations. Computational models provide a tool to investigate the mechanisms of retinal activation, and improve stimulation paradigms. However, documentation of RGC model structure and parameters is limited, and model implementation can influence model predictions. Approach. We created a functional guide for building a mammalian RGC multi-compartment cable model and applying extracellular stimuli. Next, we investigated how the neuron’s three-dimensional shape will influence model predictions. Finally, we tested several strategies to maximize computational efficiency. Main results. We conducted sensitivity analyses to examine how dendrite representation, axon trajectory, and axon diameter influence membrane dynamics and corresponding activation thresholds. We optimized the spatial and temporal discretization of our multi-compartment cable model. We also implemented several simplified threshold prediction theories based on activating function, but these did not match the prediction accuracy achieved by the cable equations. Significance. Through this work, we provide practical guidance for modeling the extracellular stimulation of RGCs to produce reliable and meaningful predictions. Robust computational models lay the groundwork for improving the performance of retinal prostheses.

Koszul duality in quantum field theory

In this article, we introduce basic aspects of the algebraic notion of Koszul duality for a physics audience. We then review its appearance in the physical problem of coupling QFTs to topological line defects, and illustrate the concept with some examples drawn from twists of various simple supersymmetric theories. Though much of the content of this article is well-known to experts, the presentation and examples have not, to our knowledge, appeared in the literature before. Our aim is to provide an elementary introduction for those interested in the appearance of Koszul duality in supersymmetric gauge theories with line defects and, ultimately, its generalizations to higher-dimensional defects and twisted holography.

Composite Quantum Coriolis Forces

In a consistent quantum theory known as “non-Hermitian interaction picture” (NIP), the standard quantum Coriolis operator Σ(t) emerges whenever the observables of a unitary system are given in their quasi-Hermitian and non-stationary rather than “usual” representations. With Σ(t) needed, in NIP, in both the Schrödinger-like and Heisenberg-like dynamical evolution equations we show that another, amended and potentially simplified theory can be based on an auxiliary N−term factorization of the Dyson’s Hermitization map Ω(t). The knowledge of this factorization is shown to lead to a multiplet of alternative eligible Coriolis forces Σn(t) with n=0,1,…,N. The related formulae for the measurable predictions constitute a new formalism refered to as “factorization-based non-Hermitian interaction picture” (FNIP). The conventional NIP formalism (where N=1) becomes complemented by an (N−1)-plet of its innovative “hybrid” alternatives. Some of the respective ad hoc adaptations of observables may result in an optimal representation of quantum dynamics.

Far-field blast responses of sandwich arbitrary polygonal reinforced plate system

This paper presents a spectral element model for investigating the dynamic response characteristics of the arbitrary polygonal built-up reinforced plate system subjected to far-field blast load. In the researched system, the plate elements are made of sandwich materials with functionally graded carbon nanotube reinforced (FG-CNTRC) panels and three-dimensional graphene foam (3D-GrF) core. The stiffness matrix assembly method is incorporated into the spectral element method (SEM) for establishing the overall dynamic formulas of arbitrary assembled plates. Thereinto, the governing equations of motion of plate elements are derived by the Hamilton's principle based on the simple first-order shear deformation theory (S-FSDT) retaining only four displacement variables, which provides an advantage to maintain interelement continuity conditions completely. After that, the natural frequencies and transient responses of the systems with different built-up forms are solved by introducing a golden section search algorithm and Fourier series expansion of the blast load. The admirable predictive accuracy of the present model is verified by comparing the obtained results and the reference solution from finite element method (FEM). Moreover, the effects of the CNT distribution form, CNT volume fraction, 3D-GrF pore distribution form, 3D-GrF porosity, the thickness ratio of the sandwich panel, TNT mass and explosion radius on the transient vibration properties of the system are revealed through a detailed parametric study.