Analytical Representation Research Articles

Three-phase lag model for thermal conductivity of a thermo-viscoelastic porous medium

This paper investigates the propagation of waves and the thermal behavior in a thermo-viscoelastic porous medium using the three-phase-lag (TPL) model which accounts for phase lags in the heat flux vector, temperature gradient and thermal displacement gradient. The study aims to capture the interactions between thermal, mechanical, and structural properties of the thermo-viscoelastic porous, isotropic, homogeneous medium. The governing equations, incorporating the TPL heat conduction law and constitutive relations for the viscoelastic porous material, are derived and analyzed. The impact of relaxation times, porosity, and viscoelastic parameters on heat propagation is investigated through analytical solutions by normal modal analysis. Analytical representations of various physical quantities (stresses components, displacements, temperature,…) in the material's domain are derived. These expressions are then assessed numerically for a specific material, with the outcomes depicted graphically. A comparison is made between the predictions of the three-phase-lag (TPL), the dual-phase-lag (DPL) and Lord–Shulman (L–S) theories in the absence and presence of voids.

Computational Fluid Dynamics Modeling of Pressure-Retarded Osmosis: Towards a Virtual Lab for Osmotic-Driven Process Simulations

Pressure-Retarded Osmosis (PRO) is an osmotically driven membrane-based process that has recently garnered significant attention from researchers due to its potential for clean energy harvesting from salinity gradients. The complex interactions between mixed-mode channel flows and osmotic fluxes in real PRO membrane modules necessitate high-fidelity modeling approaches. In this work, an efficient CFD framework is developed for the 3D simulation of osmotically driven membrane processes. This approach is based on a two-way coupling between a CFD solver, which captures external concentration polarization (ECP) effects, and an analytical representation of internal concentration polarization (ICP). Consequently, the osmotic water flux and reverse salt flux (RSF) can be accurately determined, accounting for all CP effects without any limitations on the geometrical complexity of the membrane chamber or its flow mode/regime. The proposed model is validated against experimental data, showing good agreement across various PRO case studies. Additionally, the model’s flexibility to simulate other types of osmotically driven processes such as forward osmosis (FO) is examined. Thus, the contributions of ECP and ICP effects in local osmotic pressure drop along the membrane chamber are comprehensively compared for FO and PRO modes. Finally, the capability of the CFD model to simulate a lab-scale PRO module is demonstrated across a range of Reynolds numbers from low-speed laminar up to turbulent flow regimes.

Sizing of energy storage for hybrid power plants aiming for turbine stress reduction under FCR-N requirements

This paper examines the storage sizing for hybrid power plants providing the Frequency Containment Reserve (FCR) for power grid balancing, where the hybridization of a turbine with energy storage system aims to decrease turbine stress under the most recent Nordic FCR requirements. This objective is addressed via the formulation of a hybrid plant optimal control problem, focusing on the achievable stress reduction as a function of storage energy capacity. The analysis of the optimization problem provided an analytical representation of the least upper bound for the best attainable turbine stress reduction, which was used to derive sizing recommendations for energy capacity. The obtained results imply that the hybrid plant’s control policy has a significant impact on the achievable stress reduction, as relatively small energy capacity can provide a high-stress reduction with “well–designed” control.

Fast and Compact Partial Differential Equation (PDE)-Based Dynamic Reconstruction of Extended Position-Based Dynamics (XPBD) Deformation Simulation

Dynamic simulation is widely applied in the real-time and realistic physical simulation field. How to achieve natural dynamic simulation results in real-time with small data sizes is an important and long-standing topic. In this paper, we propose a dynamic reconstruction and interpolation method grounded in physical principles for simulating dynamic deformations. This method replaces the deformation forces of the widely used eXtended Position-Based Dynamics (XPBD), which are traditionally derived from the gradient of the energy potential defined by the constraint function, with the elastic beam bending forces to more accurately represent the underlying deformation physics. By doing so, it establishes a mathematical model based on dynamic partial differential equations (PDE) for reconstruction, which are the differential equations involving both the parametric variable u and the time variable t. This model also considers the inertia forces caused by acceleration. The analytical solution to this model is then integrated with the XPBD framework, built upon Newton’s equations of motion. This integration reduces the number of design variables and data sizes, enhances simulation efficiency, achieves good reconstruction accuracy, and makes deformation simulation more capable. The experiment carried out in this paper demonstrates that deformed shapes at about half of the keyframes simulated by XPBD can be reconstructed by the proposed PDE-based dynamic reconstruction algorithm quickly and accurately with a compact and analytical representation, which outperforms static B-spline-based representation and interpolation, greatly shortens the XPBD simulation time, and represents deformed shapes with much smaller data sizes while maintaining good accuracy. Furthermore, the proposed PDE-based dynamic reconstruction algorithm can generate continuous deformation shapes, which cannot be generated by XPBD, to raise the capacity of deformation simulation.

Scintillator-SiPM detector for tracking and energy deposition measurements

An innovative particle detector that offers a compelling combination of cost-effectiveness and high accuracy is introduced. The detector features plastic scintillators paired with a sparse arrangement of SiPMs, strategically positioned within a unique opto-mechanical framework. This configuration delivers precise measurements of spatial impact position and energy deposition of impinging particles. The manuscript describes the detector’s physical model complemented by an analytical representation. These calculations underpin a numerical algorithm, facilitating the estimation of particle impingement position and energy deposition. The results of the numerical calculations are compared with the output of GEANT4 simulations and evaluated by rigorous laboratory testing. An array of these detectors, intended for deployment in a spaceborne experiment, underwent detailed design, manufacturing, and testing. Their performance and alignment with the physical model were validated through meticulously conducted ground-based laboratory experiments, conclusively affirming the detector’s properties.

The asymptotic-numerical method for the post-buckling response of curvilinearly stiffened panels

Abstract In the present work, the asymptotic-numerical method is applied in conjunction with the Ritz method as a powerful mean for analysing the post-buckling response of panels with variable stiffness skin and curvilinear stringers. Main advantage of the proposed approach is the reduced computational time. The Ritz method guarantees an excellent ratio between accuracy and required degrees of freedom; the asymptotic-numerical method requires just one matrix inversion throughout the solution process. Moreover, the complete analytical representation of the non-linear equilibrium path is obtained, as opposed to the point-by-point representation of predictor-corrector algorithms. Several test cases are presented and compared with standard Newton-Raphson computations and commercial finite element simulations. The results show noticeable saving of computational time. For the test cases investigated, the asymptotic-numerical method requires about one third of the time required by a standard Newton-Raphson routine. These results demonstrate that the combination between Ritz and the asymptotic-numerical method is an excellent strategy for investigating the post-buckling response of innovative curvilinearly stiffened panels.

On the classical approach to describing the diffusion of cosmic rays in a turbulent medium

The inhomogeneous structure of the interstellar medium (ISM) is characterized by largescale fluctuations that significantly affect the cosmic ray propagation process. Accounting for this influence can not only lead to adjustments in the diffusion process parameters but even to pass from differential operators to integral ones. The most crucial characteristics of a turbulent medium is its power spectrum. Including appropriate approximations of this spectrum allows us to consider this problem in the framework of the traditional diffusion approach [1, 2]. This article explores the analytical representations of this spectrum applied in the cosmic ray transfer theory, including the four-parameter Uchaikin—Zolotarev approximation, derived from the generalized Ornstein—Zernike equation. Testing of the latter revealed that, with carefully chosen parameters, it accurately replicates numerical modeling results both in the inertial interval and beyond. Therefore, it can be effectively employed in addressing cosmic ray transfer issues within a turbulent interstellar medium.

Constructing potential energy surface for carbon-chain containing systems using the radial angular network with gradual expansion method.

Investigating molecular excitation induced by collisions requires the prior determination of accurate analytical potential energy surfaces for the colliding partners. For carbon-chain molecules, such as cyanopolyynes, this has been a longstanding challenge, resulting in the absence of rate coefficients for HC5N, HC7N, HC9N, and others, induced by collisions with He. To overcome this bottleneck, we introduce a new approach: the Radial Angular Network with Gradual Expansion (RANGE). This method jointly connects the construction of abinitio interaction potentials with the determination of their analytical forms. We use the HC3N-He molecular complex as a reference to assess the reliability of our method, given that its analytical potential has been derived using various methods. Additionally, we apply the RANGE approach to construct the analytical representation of the interaction potential for HC5N-He and HC7N-He. The analysis of the analytical potentials reveals three systematic trends: (i) the anisotropy increases with the length of the carbon chain, (ii) the number of local minima correlates with the number of carbon atoms, and (iii) the shallowest local minimum is consistently located at ∼30 cm-1 below the dissociation limit of the complex. Using the time-independent quantum mechanical close-coupling formalism, we briefly estimate the propensity rules governing the excitation of HC3N, HC5N, and HC7N induced by collisions with He. Consequently, the three collisional systems exhibit the same propensity rule, favoring Δj = 2 transitions.

Qualitative Outcomes on Monotone Iterative Technique and Quasilinearization Method on Time Scale

In this paper, a nonlinear dynamic equation with an initial value problem (IVP) on a time scale is considered. First, applying comparison results with a coupled lower solution (LS) and an upper solution (US), we improved the quasilinearization method (QLM) for the IVP. Unlike other studies, we consider the LS and US pair of the seventh type instead of the natural type. It was determined that the solutions of the dynamic equation converge uniformly and monotonically to the unique solution of the IVP, and the convergence is quadratic. Moreover, we will use the delta derivative (Δγ) instead of the classical derivative (dγ) in the proof because it studies a time scale. In the second part of the paper, we applied the monotone iterative technique (MIT) coupled with the LS and US, which is an effective method, proving a clear analytical representation for the solution of the equation when the relevant functions are monotonically non-decreasing and non-increasing. Then an example is given to illustrate the results obtained.

Determination of Coefficients of Decomposition of a Nonlinear Characteristic into a Power Series

The problem of monitoring the parameters of nonlinear elements included in various electrical devices is considered. A new algorithm for reproducing the nonlinear current-voltage characteristic of a device based on the measurement results has been proposed and investigated, which has several advantages over the known ones, allowing, in particular, to obtain an analytical representation of the current-voltage characteristic in real time. The proposed algorithm is based on the direct determination of the coefficients of the polynomial approximation of the current-voltage characteristic. A review of scientific research done to date by other authors dealing with this problem has also been carried out. Formulas for determining the amplitudes of current harmonics through power series coefficients and voltage amplitudes on a nonlinear element are obtained. Binomial coefficients are used to facilitate intermediate calculations. The relations for the zero, odd and even harmonics of the current are obtained, as well as analytical expressions for the coefficients of the polynomial approximation. An experimental study of the proposed method was carried out, according to the results of which an assessment of its accuracy was made. The use of the proposed method significantly simplifies the processing and reduces the measurement time of nonlinear VAC.

A versatile analytical representation of the different aircraft wings

A versatile analytical representation of the different aircraft wings

From de Sitter to de Sitter: A Thermal Approach to Running Vacuum Cosmology and the Non-Canonical Scalar Field Description

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein’s equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale, which is equal or smaller than the reduced Planck mass. It is structurally unstable, and all of the continuous created matter, energy, and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be a step-by-step a faithful analytical representation of the thermal running vacuum cosmology.

Low‐Cost Surrogate Modeling for Expedited Data Acquisition of Reconfigurable Metasurfaces

AbstractIn recent years, machine learning (ML) and deep learning (DL) have been widely used to break the metasurface’s performance ceiling. However, the existing data‐driven ML and DL methods usually require the availability of vast amounts of training data to ensure their stable and accurate performance. The process of acquiring these data is high‐cost due to the need for numerous full‐wave electromagnetic (EM) simulations. Here, we propose a low‐cost surrogate model to generate these data efficiently. The proposed model employs microwave network theory to separate meta‐elements into four independent components. Through integration with transmission line theory, we derive the EM responses of meta‐elements using analytical representation with the active device equivalent impedance and dielectric as design variables. Two typical phase‐modulation active meta‐elements are employed to verify the accuracy of our macromodel in comparison with full‐wave EM simulations. Based on the developed macromodel, the superior prediction ability is further presented to illustrate the performance of meta‐elements with various active devices and dielectric substrates. The proposed macromodel is a feasible and general method to rapidly obtain the necessary training data of active meta‐elements, which holds a great potential to significantly reduce the designing time of ML and DL models for the active metasurfaces.

Energy spectrum and magnetic susceptibility of the improved Pöschl-Teller potential

This study presents an analytical representation of the internal motion of a diatomic system using the improved Pöschl-Teller potential. The ro-vibrational energy spectrum is derived by solving the radial Schrödinger time independent wave equation (STIWE) under a 2D electromagnetic potential field. Additionally, an explicit equation for magnetic susceptibility is formulated from the internal partition function. The analytical models are used to investigate physical properties of CO (X1∑+), K2 (a3∑u+), BCl (X1∑+), and NaK (c3∑+) molecules. Average percentage absolute deviations (APAD) for the ro-vibrational energy spectrum are calculated as 0.1001 %, 0.5306 %, 1.2070 %, and 0.9779 %, respectively, compared to observed data. Numerical results are consistent with existing literature. Furthermore, the study reveals that the magnetic susceptibility of the system increases with temperature and decreases with an increase in magnetic field intensity, indicating its paramagnetic nature.

Novel Analytic Representations for Caps, Floors, Collars, and Exchange Options on Continuous Flows, Arbitrage‐Free Relations, and Optimal Investments

ABSTRACTWe offer analytic formulae for valuing finite maturity profit caps and floors that are contingent on continuous flows without the need for subtracting the risk‐neutral expectation of the forward starting perpetual solution from the corresponding perpetual solution. The related price caps, floors, and collars are easily obtained from any analytic representation of profit caps and floors using some arbitrage‐free relations. Finally, we offer two novel methods for calculating the optimal triggers of investment projects in the presence of price floors and collars regimes in a way that is much simpler than the ones currently used.

Marshaling a Triumph: The Park Chung Hee Era, Developmental State Theory, and the Meaning of Success in South Korea

South Korea has long been looked to as a model of developmental success. Undoubtedly, South Korean society has experienced a remarkable expansion of wealth, social well-being, and technological capacity over the last half-century. The central turning point in this momentous transformation coincided with the authoritarian rule of Park Chung Hee (1961-1979). As such, scholars of political economy and development have paid close attention to the various facets of his regime to glean the primary causes underpinning South Korea's developmental feats. The most significant of these efforts have emerged from works emphasizing the role of the South Korean developmental state. This paper critically explores the theoretical foundations of developmental state theory to consider intellectual architecture of the success narrative widely appended to the era. The analysis builds from a premise that, given its widespread use of political violence and surveillance, framing the Park regime as a success carries significant ethical undertones. As such, the paper centers the interplay of ethics and empirics in the theoretical engagement with this crucial site in both Korean and development history. As such, it demonstrates that developmental state theory's reluctance to engage with these significant ethical questions systematically corresponds to distorted analytical and empirical representations of the case.

Translation functors for locally analytic representations

Let [Formula: see text] be a [Formula: see text]-adic Lie group with reductive Lie algebra [Formula: see text]. In analogy to the translation functors introduced by Bernstein and Gelfand on the categories of [Formula: see text]-modules, we consider similarly defined functors on the category of modules over the locally analytic distribution algebra [Formula: see text] on which the center of [Formula: see text] acts locally finitely. These functors induce equivalences between certain subcategories of the latter category. Furthermore, these translation functors are naturally related to those on category [Formula: see text] via the functors from category [Formula: see text] to the category of coadmissible modules. We also investigate the effect of the translation functors on locally analytic representations [Formula: see text]la associated by the [Formula: see text]-adic Langlands correspondence for [Formula: see text] to two-dimensional Galois representations [Formula: see text].

Correction to: Analysis of Numerical Estimations of the Yarkovsky Effect Parameter and Their Comparison with an Analytical Representation on the Example of Near-Sun Asteroids

Correction to: Analysis of Numerical Estimations of the Yarkovsky Effect Parameter and Their Comparison with an Analytical Representation on the Example of Near-Sun Asteroids

Convergence of the Two Point Flux Approximation method and the fitted Two Point Flux Approximation method for options pricing with local volatility function

In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for which analytical representations of the exact solution is known for European Call options, there is no analytical solution for local volatility. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called Fitted Two-Point Flux Approximation (FTPFA). The Fitted Two-Point Flux Approximation (FTPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero with the goal to handle the degeneracy of the PDE while the TPFA method is used on the rest of space domain. This combination yields our fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support theoretical results are provided.

Efficient generation of barrier crossing trajectories using approximate Brownian bridges.

We examine continuous random walks that are conditioned to reach one region before another. These conditioned processes are used to generate stochastic trajectories for barrier crossing events, which are generally rare and difficult to sample. The processes are generated using a Brownian bridge technique, resulting in near perfect sampling efficiency without accruing error in the conditional statistics of the process. The construction requires the hitting probability or committer function, which is a solution to the backward Fokker-Planck equation, a partial-differential equationthat can be difficult to solve through general means. Therefore, we derive a one-dimensional approximation through asymptotic methods for barrier crossing trajectories. We show that this approximation has a simple analytical representation and approaches the true solution as the barrier height increases. Brownian bridge trajectories generated with this approximate solution are then shown to result in accurate conditional statistics when used in conjunction with importance sampling, even in the case when potential energy barriers are not large. We show this idea's effectiveness by simulating rare events in a stochastic chemical reaction network (Schögl reaction) with multiple steady states. This methodology shows great promise for future implementation to simulate rare barrier crossing events for a wide variety of physical processes.