Analytical Counterpart Research Articles

Method of characteristics for transient, planar, cylindrical flows

Cylindrical radiation of individual pulses is studied and strong differences from spherical radiation are highlighted. Prior to this study, the class of available analytical solutions for cylindrical radiation was rather limited. It included (i) a well-known solution for a steady-state, time-harmonic line source and (ii) the solution for a delta-pulse line source. The first of these has no analytical counterpart for individual pulses. By means of the second (actually the Green's function) a more general class of line source solutions can be formulated, but each one is in the form of an integral that has to be evaluated numerically and requires tedious preparation of a singular integrand, making it difficult to achieve perfect accuracy. In the present paper, use is made instead of a particular family of analytically-exact (linear) solutions that has been developed recently. It is used to assess the accuracy of solutions obtained numerically by the method of characteristics (MoC), which is then applied to more general sources than those amenable to analytical treatment. The MoC analysis is specially formulated to reduce the influence of terms involving the reciprocal of the radius (such terms are numerically unmanageable close to the origin). It is found that the qualitative behaviour of waves radiating from the surface of a cylinder of finite radius can depend strongly on the duration of the initiating disturbance and that this can be interpreted in a convolution-like manner. After validation, the numerical method is coupled with a conventional MoC analysis of planar wave propagation and is used to simulate the reflection and radiation of an initially planar wavefront arriving at a flanged duct exit. The numerical representation is one-dimensional in both domains – (x,t) inside the duct and (r,t) outside it. Although its use implies identical behaviour in all radial directions in the external domain, the solution is found to be in close agreement with circumferential-average values from a CFD solution that simulates azimuthal variations as well as radial variations. Whilst being less comprehensive than the CFD simulation, the MoC analysis has the important practical benefit of making highly efficient use of human and computational resources. By comparing the MoC and CFD solutions, it is found that the nominally-cylindrical radiation from the duct approximates closely to radiation from a line source a small distance inside the duct (not at the exit plane). An approximate location of the effective source is quantified.

Analytical response and Markovianity of systems governed by fractional differential equations driven by [formula omitted]-stable white noise processes

This paper investigates the probabilistic response of systems governed by fractional differential equations and forced by α-stable white noise processes. The response in terms of scale of the response process is built starting from a finite differences version of the governing equation. An efficient formulation in terms of scale of the response process is obtained for both non-stationary and stationary white noise input process. Remarkably, the proposed numerical scheme has an analytical counterpart in terms of time evolution of the scale that is a generalization of the well known Duhamel integral. This analytical formulation permits to find closed form solutions in terms of the time evolution of the scale of the response process. Further, when the input white noise process is stationary, it is demonstrated that the system remains Markovian of order one also in presence of fractional operators in the governing equation. This is a very interesting result that makes the proposed numerical procedure very efficient from a computational point of view and that can be very useful for future developments. Numerical applications demonstrate the accuracy of the proposed numerical scheme and the validity of the analytical solution for some systems of interest in engineering.

210Pb-based dating of recent sediments with χ-mapping versions of the CFCS, CIC, CF and TERESA models

The 210Pb-based method allows for absolute age determination in recent sediments on the centennial scale. The most common sedimentary scenarios involve ideal deposition without any further redistribution. The conventional models apply to such conditions by adding specific assumptions that allow analytical formulations: constant flux (CF), constant initial concentration (CIC), and constant flux with constant sedimentation (CFCS). The χ-mapping models are presented as a novel methodological approach. They generate a large number (105 to 106) of potential solvers, consisting of sets of n (the number of slices in the core) values of initial activity concentrations, A0, and sedimentation rates, w. Empirical data serve to attract the solver that minimizes a χ function after encountering the best sorting along the core of the A0 and w values. The specific assumptions of the above models are reformulated in terms of the statistical distributions of A0 and w. The performance of the χ-mapping versions is demonstrated with a set of cores from the literature with independent chronologies. The main advantages compared to known analytical formulations are: i) χ-mapping provides a more robust fitting method. ii) It overcomes the problem of age reversals often found in the CIC model. iii) The CF model successfully applies to cores with unsteady and/or incomplete inventories. iv) The TERESA model (time estimates from random entries of sediments and activities), without analytical counterpart, is the only model that can manage continuous trends of change in the fluxes of unsupported 210Pb. The work discusses the conditions for compensating model errors in the chronologies, and the use of the palaeorecords of fluxes, A0 and w. The methodology can be extended to other assumptions (models) and provides novel and insightful views on the 210Pb-based dating of recent sediments.

Characterization of the iPhone LiDAR-Based Sensing System for Vibration Measurement and Modal Analysis.

Portable depth sensing using time-of-flight LiDAR principles is available on iPhone 13 Pro and similar Apple mobile devices. This study sought to characterize the LiDAR sensing system for measuring full-field vibrations to support modal analysis. A vibrating target was employed to identify the limits and quality of the sensor in terms of noise, frequency, and range, and the results were compared to a laser displacement transducer. In addition, properties such as phone-to-target distance and lighting conditions were investigated. It was determined that the optimal phone-to-target distance range is between 0.30 m and 2.00 m. Despite an indicated sampling frequency equal to the 60 Hz framerate of the RGB camera, the LiDAR depth map sampling rate is actually 15 Hz, limiting the utility of this sensor for vibration measurement and presenting challenges if the depth map time series is not downsampled to 15 Hz before further processing. Depth maps were processed with Stochastic Subspace Identification in a Monte Carlo manner for stochastic modal parameter identification of a flexible steel cantilever. Despite significant noise and distortion, the natural frequencies were identified with an average difference of 1.9% in comparison to the laser displacement transducer data, and high-resolution mode shapes including uncertainty ranges were obtained and compared to an analytical solution counterpart. Our findings indicate that mobile LiDAR measurements can be a powerful tool in modal identification if used in combination with prior knowledge of the structural system. The technology has significant potential for applications in structural health monitoring and diagnostics, particularly where non-contact vibration sensing is useful, such as in flexible scaled laboratory models or field scenarios where access to place physical sensors is challenging.

Recovery of fluoride from spent cathode carbon block by combustion combined with water leaching process

Spent cathode carbon blocks (SCCBs) is a kind of hazardous waste that can be harmful to the environment. In this study, a process of high-temperature combustion combined with water leaching was explored to dissociate toxic substances from SCCB and recover valuable components. Combustible components in SCCB can be converted into useable heat energy. The combustion parameters and water leaching process were optimized, and the transformation trend of important components was explained. According to the experimental findings, under optimal conditions, the combustion weight loss rate of SCCB reaches 81.5%, and the defluorination rate reached 88.2%. The toxic leaching concentration of fluoride from the treated residue was reduced to 49 mg L−1, in line with the safe discharge standard. The characterization results showed that the final recovered product was highly similar to its analytical reagent counterpart. This treatment process has the environmental benefits of secondary resource recycling and can effectively reduce the negative impact of SCCB on the environment.

Trapping array-based preparative two-dimensional liquid chromatography for the purification of four components in tobacco leaves

Two-dimensional liquid chromatography (2D-LC) has gained increased attention because of its high peak capacity for separating complex samples. However, preparative 2D-LC aimed at isolating compounds is significantly different compared with one-dimensional liquid chromatography (1D-LC) in terms of method development and system configuration; thus, it is less developed than its analytical counterpart. The use of 2D-LC in large-scale product preparation has rarely been reported. Hence, a preparative 2D-LC system was developed in this study. The system was composed of one set of preparative LC modules as a separation system, with a dilution pump, switch valves, and trap column array as the interface, to enable the simultaneous isolation of several compounds. Tobacco was used as a sample, and the developed system was applied to isolate nicotine, chlorogenic acid, rutin, and solanesol. The chromatographic conditions were developed by investigating the trapping efficiency of different types of trap column packings, and chromatographic behaviors under different overload conditions. The four compounds were isolated in one 2D-LC run with high purity. The developed system features low cost because it employs medium-pressure isolation, excellent automation owing to its use of an online column switch, high stability, and capability for large-scale production. The isolation of chemicals from tobacco leaves as pharmaceutical raw materials could aid in the development of the tobacco industry and promote the local agricultural economy.

DeepLux: A data-driven method and benchmark for 3D illuminance maps estimation

In this paper, we propose a pipeline and benchmark, called DeepLux, for predicting illuminance on 3D point clouds. Classic algorithms for computing photometrically accurate illumination are based on numerical and analytical models which are generally computationally expensive, especially in scenarios with complex geometries. Unlike existing approaches, our algorithm is the first learning-based method that is able to predict accurate illuminance map information that could be used for real-time smart lighting applications. We also evaluate our approach on two complementary tasks, that is, light position and intensity estimation, which are important aspects in the field of lighting design. Additionally, we provide an extensive novel photometrically correct dataset, which we use for training and evaluating our approach. Experiments show that the proposed algorithm produces results on par with or even better than the state of the art (+8% average error in real tests) while achieving faster simulation timings than its analytical counterpart, especially in complex synthetic and real-world scenarios.

Emergence of Raman Spectroscopy as a Probing Tool for Theranostics.

Although medical advances have increased our grasp of the amazing morphological, genetic, and phenotypic diversity of diseases, there are still significant technological barriers to understanding their complex and dynamic character. Specifically, the complexities of the biological systems throw a diverse set of challenges in developing efficient theranostic tools and methodologies that can probe and treat pathologies. Among several emerging theranostic techniques such as photodynamic therapy, photothermal therapy, magnetic resonance imaging, and computed tomography, Raman spectroscopy (RS) is emerging as a promising tool that is a label-free, cost-effective, and non-destructive technique. It can also provide real-time diagnostic information and can employ multimodal probes for detection and therapy. These attributes make it a perfect candidate for the analytical counterpart of the existing theranostic probes. The use of biocompatible nanomaterials for the fabrication of Raman probes provides rich structural information about the biological molecules, cells, and tissues and highly sensitive information down to single-molecule levels when integrated with advanced RS tools. This review discusses the fundamentals of Raman spectroscopic tools such as surface-enhanced Raman spectroscopy and Resonance Raman spectroscopy, their variants, and the associated theranostic applications. Besides the advantages, the current limitations, and future challenges of using RS in disease diagnosis and therapy have also been discussed.

Data-driven Enhancement of the Time-domain First-order Regular Perturbation Model

A normalized batch gradient descent optimizer is proposed to improve the first-order regular perturbation coefficients of the Manakov equation, often referred to as kernels. The optimization is based on the linear parameterization offered by the first-order regular perturbation and targets enhanced low-complexity models for the fiber channel. We demonstrate that the optimized model outperforms the analytical counterpart where the kernels are numerically evaluated via their integral form. The enhanced model provides the same accuracy with a reduced number of kernels while operating over an extended power range covering both the nonlinear and highly nonlinear regimes. A $6-7$~dB gain, depending on the metric used, is obtained with respect to the conventional first-order regular perturbation.

Finite difference solver for simulating leaching process in bounded porous media: Development and application

This work, for the first time, developed an unconditionally stable, implicit numerical solution of a one-sided spatial fractional advection-dispersion equation (s-FADE) on a bounded domain to model contaminant transport through porous media during a leaching process. We used the zero-value Robin and Neumann conditions with a fractional-order derivative as the inlet and outlet boundaries, respectively, and a constant initial concentration of the contaminant in the whole domain as an initial condition. By conducting numerical analyses, we found that there is a good agreement between the results of the numerical solution and of its analytical counterpart, validating the accuracy of the numerical solution. In the case of the α variations meaningfully altered the heterogeneity degree of the porous medium, these variations significantly affected the results of the numerical solution, especially at intermediate times. Contrary to the α parameter, the numerical solution was insensitive to the spatial node number. The noisy observational data led to the maximum uncertainty in the estimated fractional dispersion coefficient. The application of the developed numerical solution to simulate sodium chloride (NaCl) leaching curves (LCs) at a laboratory scale revealed that the numerical solution described the leaching process in the homogeneous and heterogeneous sands better than COMSOL Multiphysics®, a commercial finite element software package. According to the fitting results of the developed numerical solution to the experimental data, the mean α values were 1.876 and 1.379 for the homogeneous and heterogeneous sands, respectively. The α values correctly represented the heterogeneity degrees of the used sands and the deviation rate of the transport process from the Fickian transport. Overall, the proposed numerical solution is a reliable numerical model to simulate the leaching process in homogeneous and heterogeneous porous media with bounded domains.

Domain Structure in Ferroelectric Thin Films

At low temperatures, uniaxial perovskites exhibit a spontaneous polarization with a permanent dipole moment. The broken symmetry state involves an order parameter and dielectric properties of the materials which are strongly dominated by a one-dimensional physics. For the last sixty years there has been growing interest in these crystals for potential applications in communication technology. Very recently, renewed interest to ferroelectric memory devices has been remarkable with particular emphasis on miniaturized devices. This new perspective comes along with great challenges, one of which is the critical size for stable domains in thin ferroelectric crystals. Since the polarization switching involves a pre-existing spontaneous polarization, it is of fundamental importance to address the question of conditions under which polarized domains can develop in a ferroelectric thin film. From previous articles, it has been observed that most studies focus on numerical simulations which is a good approach but for the fact that numerical simulations involve approximation of physical quantities, which is limitation to comparing experimental with theoretical studies. This motivated the authors to look purely at an analytical approach taking advantage of the new mathematical approach in the study of nonlinear systems. In this work, the authors have considered the question from an analytical point of view, focusing on an interesting model introduced by Lu and Cao. We propose an analytical counterpart of the numerical simulations done in this previous study.

Management of invasive cells in soft biological tissues through modulated nonlinear excitations: Long-range effects

In the present paper, we investigate the contribution of long-range diffusion and diffusive stresses on cellular waves generated during an invasion in soft biological tissues. To that end, we consider a set of three coupled nonlinear partial differential equations describing spatiotemporal evolutions of cell density, extracellular matrix (ECM), and spatial displacements of a material point taken in the ECM. In addition to long-range diffusion, diffusive stresses, and proliferation, the model also accounts for ECM production-degradation. The linear stability analysis reveals that in presence of temporal perturbations, there is no stability-instability transition in the system. In presence of spatiotemporal perturbations, instability dominates but the stability-instability transition is controlled by proliferation rate and long-range diffusion of cells. Analytical solutions are constructed as well as their existence conditions provided. Amongst the structures recovered, breathers are associated with the transport of a high number of cells. Long-range diffusive stresses, saturation, and ECM depletion rate significantly modify the wave structure as well as the number of cells carried. On the other hand, Proliferation, ECM production rate, long-range haptotaxis, diffusion, and traction affect both spatial rearrangement and the number of cells carried by the wave. Through our analysis, numerical solutions remain positive, do not diverge from their analytical counterpart, meaning that the solutions proposed are stable and may be used to probe the inherent biological realities of the model considered.

On the analytical and meshless numerical approaches to mixture stress gradient functionally graded nano-bar in tension

The mixture stress gradient theory of elasticity is conceived via consistent unification of the classical elasticity theory and the stress gradient theory within a stationary variational framework. The boundary-value problem associated with a functionally graded nano-bar is rigorously formulated. The constitutive law of the axial force field is determined and equipped with proper non-standard boundary conditions. Evidences of well-posedness of the mixture stress gradient problems, defined on finite structural domains, are demonstrated by analytical analysis of the axial displacement field of structural schemes of practical interest in nano-mechanics. An effective meshless numerical approach is, moreover, introduced based on the proposed stationary variational principle while employing autonomous series solution of the kinematic and kinetic field variables. Suitable mathematical forms of the coordinate functions are set forth in terms of the modified Chebyshev polynomials, satisfying the required classical and non-standard boundary conditions. An excellent agreement between the numerical results of the axial displacement field of the functionally graded nano-bar and the analytical solution counterpart is confirmed on the entire span of the nano-sized bar, in terms of the mixture parameter and the stress gradient characteristic parameter. The effectiveness of the established meshless numerical approach, demonstrating a fast convergence rate and an admissible convergence region, is hence ensured. The established mixture stress gradient theory can effectively characterize the peculiar size-dependent response of functionally graded structural elements of advanced ultra-small systems.

The influence of autotoxicity on the dynamics of vegetation spots

Plant autotoxicity has proved to play an essential role in the behaviour of local vegetation. We analyse a reaction–diffusion-ODE model describing the interactions between vegetation, water, and autotoxicity. The presence of autotoxicity is seen to induce movement and deformation of spot patterns in some parameter regimes, a phenomenon which does not occur in classical biomass–water models. We aim to analytically quantify this novel feature, by studying travelling wave solutions in one spatial dimension. We use geometric singular perturbation theory to prove the existence of symmetric, stationary and non-symmetric, travelling pulse solutions, by constructing appropriate homoclinic orbits in the associated 5-dimensional dynamical system. In the singularly perturbed context, we perform an extensive scaling analysis of the dynamical system, identifying multiple asymptotic scaling regimes where (travelling) pulses may or may not be constructed. We show that, while the analytically constructed stationary pulse corresponds to its numerical counterpart, there is a discrepancy between the numerically observed travelling pulse and its analytical counterpart. Our findings indicate how the inclusion of an additional ODE may significantly influence the properties of classical biomass–water models of Klausmeier/Gray–Scott type.

Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors

Abstract Johansen’s (2000. “A Bartlett Correction Factor for Tests of on the Cointegrating Relations.” Econometric Theory 16: 740–78) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables is fat-tailed and often skewed; there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using the non-parametric bootstrap to approximate a Bartlett-type correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than it’s analytical counterpart. The procedure involves calculating a number of bootstrap values of the LR test statistic and estimating the expected value of the test statistic by the average value of the bootstrapped LR statistic. Simulation results suggest that the inference procedure has good finite sample property and is less dependent on the parameter space of the data generating process.

Analytical signatures and proper actions

We compare Mishchenko's definition of non-commutative signature for an oriented manifold with an orientation preserving proper action of a discrete, countable group $G$ with the (more analytical) counterpart defined by Higson and Roe in the series of articles ``Mapping surgery to analysis''. A generalization of the bordism invariance of the coarse index is also addressed.

Chitosan/tripolyphosphate nanoformulation carrying paraquat: insights on its enhanced herbicidal activity

A paraquat-nanoherbicide presented distinct electroactivity behavior compared to its analytical counterpart, which may explain its greater herbicidal activity on plants.

Discrete differential operators on a class of lattices

Lattice differential operators are known to preserve key properties of their analytical counterpart, such as isotropy, fundamental vector identities due to the symmetries of the discrete kinetic lattice. Here, we present the idea of discrete lattice operators derived on a body-centered-cubic (BCC) lattice. These operators show quite a high degree of accuracy and isotropy as compared to the earlier simple cubic (SC) representations of the same while maintaining a relatively smaller stencil. To illustrate the usefulness of these schemes, we have considered a couple of examples, such as passive scalar transport and fluctuating hydrodynamics.

분석적으로 미분 가능한 시스템 동역학을 이용한 온라인 동작 합성 기법

In physics-based character animation, trajectory optimization has been widely adopted for automatic motion synthesis, through the prediction of an optimal sequence of future states of the character based on its system dynamics model. In general, the system dynamics model is neither in a closed form nor differentiable when it handles the contact dynamics between a character and the environment with rigid body collisions. Employing smoothed contact dynamics, researchers have suggested efficient trajectory optimization techniques based on numerical differentiation of the resulting system dynamics. However, the numerical derivative of the system dynamics model could be inaccurate unlike its analytical counterpart, which may affect the stability of trajectory optimization. In this paper, we propose a novel method to derive the closed-form derivative for the system dynamics by properly approximating the contact model. Based on the resulting derivatives of the system dynamics model, we also present a model predictive control (MPC)-based motion synthesis framework to robustly control the motion of a biped character according to on-line user input without any example motion data.

Static Watson-Crick regular grammar

DNA computing, or more generally, molecular computing, is a recent development at the interface of computer science and molecular biology. In DNA computing, many computational models have been proposed in the framework of formal language theory and automata such as Watson-Crick grammars and sticker systems. A Watson-Crick grammar is a grammar model that generates double stranded strings, whereas a sticker system is a DNA computing model of the ligation and annealing operations over DNA strands using the Watson-Crick complementarity to form a complete double stranded DNA sequence. Most of the proposed DNA computing models make use of this concept, including the Watson-Crick grammars and sticker systems. Watson-Crick grammars and their variants can be explored using formal language theory which allows the development of new concepts of Watson-Crick grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick regular grammar is introduced as an analytical counterpart of sticker systems. The computation of a sticker system starts from a given set of incomplete double stranded sequence to form a complete double stranded sequence. Here, a static Watson-Crick regular grammar differs from a dynamic Watson-Crick regular grammar in generating double stranded strings: the latter grammar produces each strand string “independently” and only check for the Watson-Crick complementarity of a generated complete double stranded string at the end, while the former grammar generates both strand strings “dependently”, i.e., checking for the Watson-Crick complementarity for each complete substring. In this paper, computational properties of static Watson-Crick regular grammars are investigated to correlate with the Chomsky hierarchy and hierarchy of the families of dynamic Watson-Crick regular languages. The relationship between families of languages generated by static Watson-Crick regular grammars with several variants of sticker systems, Watson-Crick regular grammars and Chomsky grammars are presented by showing the hierarchy.