Analytical Results Research Articles

Large Deflections, Loss of Stability and Over-Critical Behavior of Sloping Panels and Arches of Variable Thickness on an Elastic Base

The problem of large deflections of a flat arch in its plane (or an infinitely long panel) loaded with transverse loads is considered. A variational approach has been applied to solve it. The resolving nonlinear equations are reduced to finding the deflection and longitudinal force, which is considered constant along the length of the arch due to its flatness. An approximate solution method is proposed by decomposing the displacements into a Fourier series. The peculiarity of the approach used is that in order to pass the limit points, it is not necessary to use special algorithms such as the continuation method by parameter. It also allows you to trace the process of supercritical deformation of the arch. The proposed approach allows us to consider problems for arches of variable thicknesses, located on elastic supports, on an elastic base with a variable bed coefficient and various loads. Therefore, it is also convenient in problems of finding, for example, the optimal thickness distribution under restrictions on critical loads, on rigidity stiffness and on maximum compression or tension stresses. The results of numerical calculations are presented. The convergence is studied of the solution depending on the number of terms of the series, into which the desired deflection decomposes. A good agreement with the known analytical results is obtained earlier by solving the equilibrium equations of the arch element and panel in the case of simple types of loading. At the same time, even in more complex cases of loading and supercritical bending of an arch without an elastic base, the results are obtained when holding three, four and five members of the Fourier series, the maximum deflections and critical loads differed by no more than 2.5%. On the basis of numerical experiments, the features of the arch behavior caused by the rearrangement of geometry during loading are revealed. The processes of stability loss of the arch and its supercritical behavior are investigated. The effect of symmetric deformation in the case of kinematic loading is found, namely, it is revealed that at a certain value of the concentrated force, an infinite number of equilibrium forms are possible. Arches on an elastic base, as well as with variable thickness are considered (the results are presented in the form of load–displacement diagrams and in the form of pictures of deformed arch shapes). An interesting effect has been revealed based on numerical experiments. It turned out that the increase in thickness when moving away from the supports does not change the nature of the load–displacement diagram, i.e., with some load, a slap occurs. On the contrary, a decrease in thickness when moving away from the supports leads to a flattening of the diagram, and after a certain thickness value in the center, its further decrease leads to the fact that the arch does not occur.

Analytical Investigation of Time-Dependent Two-Dimensional Non-Newtonian Boundary Layer Equations

In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated with the self-similar Ansatz, including external magnetic field effects. The power-law, the Casson fluid, the Oldroyd-B model, the Walter fluid B model, and the Williamson fluid are analyzed. For the first two models, analytical results are given for the velocity and pressure distributions, which can be expressed by different types of hypergeometric functions. Depending on the parameters involved in the analytical solutions of the nonlinear ordinary differential equation obtained by the similarity transformation, a vast range of solution types is presented. It turned out that the last three models lack self-similar symmetry; therefore, no analytic solutions can be derived.

Tuning planar transverse domain wall dynamics in bilayer nanostructures using transverse magnetic fields, Rashba, and spin-Hall effects

Abstract This work deals with the tunability of a planar transverse domain wall with an arbitrary azimuthal angle, achieved by applying a transverse magnetic field of tunable strength and fixed orientation. To be precise, we investigate the static and dynamic features of a planar transverse domain wall within a bilayer nanostructure consisting of a ferromagnetic layer and a non-magnetic heavy metal layer, employing the Landau-Lifshitz-Gilbert equation as our theoretical framework. The domain wall dynamics are analyzed through the collective coordinate method and regular perturbation asymptotic approach, accounting for the combined effects of axial and transverse magnetic fields, spin-polarized electric currents, Rashba effect, and spin-Hall effect. Our study comprehensively analyses the planar transverse domain wall profile, characterized by sharply defined boundaries between adjacent domains and a precise distribution of the transverse magnetic field. In addition, we detail the linear polar angle distribution within the domain wall region, the capability to freely tune the domain wall width, and the enhanced domain wall velocity in steady-state regime. The analytical results are further numerically illustrated, offering valuable insights into manipulating and controlling domain wall dynamics.

On the relation between the velocity- and position-Verlet integrators.

The difference and similarity between the velocity- and position-Verlet integrators are discussed from the viewpoint of their Hamiltonian representations for both linear and nonlinear systems. For a harmonic oscillator, the exact Hamiltonians reveal that positional trajectories generated by the two integrators follow an identical second-order differential equation and thus can be matched by adjusting initial conditions. In contrast, the series expansion of the Hamiltonians for the nonlinear discrete dynamics clearly indicates that the two integrators differ fundamentally. These analytical results are confirmed by simple numerical simulations of harmonic and anharmonic oscillators.

Effective radius of a contact diffusion-controlled reaction between small solutes and a polymer chain.

The aim of this study was to develop a formula for estimating the effective radius of a diffusion-controlled irreversible contact reaction between diffusing solutes and a nonlinear immobile polymer molecule. Analytical expressions for the reaction radius were obtained that took into account averaging over conformations for chains with arbitrary segment-to-segment angles and distributions of dihedral angles. A comparison of the analytical results with the results of computer stochastic modeling of the reaction showed good agreement over a wide range of parameters. Based on an analysis of these expressions, parameter ranges were established in which it was possible to use either the linear chain or Gaussian coil approximation to describe the reaction kinetics. A comparison of several distributions over chain lengths showed that, as a first approximation, the radius of reaction can be estimated as that for a chain corresponding to the number-averaged molecular weight. Results of earlier experimental studies on charge scavenging by polymer molecules have been explained.

Observation of an Inverse Turbulent-Wave Cascade in a Driven Quantum Gas

We observe an inverse turbulent-wave cascade, from small to large length scales, in a driven homogeneous 2D Bose gas. Starting with an equilibrium condensate, we drive the gas isotropically on a length scale much smaller than its size, and observe a nonthermal population of modes with wavelengths larger than the drive one. At long drive times, the gas exhibits a steady nonthermal momentum distribution. At length scales increasing from the drive one to the system size, this distribution features in turn: (i) a power-law spectrum with an exponent close to the analytical result for a particle cascade in weak-wave turbulence, and (ii) a spectrum reminiscent of a nonthermal fixed point associated with universal coarsening in an isolated 2D gas. In further experiments, based on anisotropic driving, we reveal the complete qualitative picture of how the steady-state cascade forms. Published by the American Physical Society 2024

Ultrafast Joule Heating Modification of Methane-Pyrolyzed Carbon Black for Supercapacitor Application.

Carbon black from methane pyrolysis for hydrogen is an alternative resource and can be improved for conductive material supplication. Our current work uses an ultrafast Joule heating technique to modify the methane-pyrolyzed carbon black and prepare nanoparticles of electrode material for supercapacitor application, coupled with density functional theory, structural, and electrochemical analyses. Evolution rules of the carbon and pore structures of the modified sample with an increase in temperature reveal good structure improvements. The graphitization degree of modified carbon black nanoparticles increases, and the particle morphology changes from a smooth surface, disordered structure removal, and pore formation to graphite crystallization. Band structure and state density analytical results show that the modified carbon black with a defect-free structure possesses metallic properties and exhibits good electrical conductivity. A temperature around 1576 °C to the initial graphitization was defined based on the critical point of the evolution of ordered and disordered structures, while the electrical conductivity of the carbon black nanoparticles at 2000 °C reaches 2300 S/m. The modified carbon black performed with stable charge/discharge characteristics, exhibiting a 4.31% capacitance drop at a current load of 2 A/g and a 18.31% capacitance drop at a current load of 20 A/g.

Engineering Zn/Fe Mixed Metal Oxides with Tunable Structural and Magnetic Properties for Magnetic Particle Imaging.

Engineering magnetic nanoparticles with tunable structural properties and magnetism is critical to develop desirable magnetic particle imaging (MPI) tracers for biomedical applications. Here we present a new superparamagnetic metal oxide nanoparticle with a controllable chemical composition and magnetism for imaging tumor xenografts in living mice. Superparamagnetic Zn/Fe mixed metal oxide (ZnFe-MMO) nanoparticles are fabricated via a facile one-pot co-precipitation method in water followed by thermal decomposition with tunable Zn/Fe ratios and at various calcination temperatures. This work, for the first time, presented LDH-derived metal oxides for an MPI application. The metal composition is tunable to present an optimized MPI performance. The analytical results demonstrate that ZnFe-MMO nanoparticles at the designed molar ratio of Zn/Fe = 2:1 after 650 °C calcination demonstrate a higher saturation magnetization (MS) value and optimal MPI signal than the samples presented with other conditions. The excellent biocompatibility of ZnFe-MMO is demonstrated in both breast cancer cells and fibroblast cell cultures. In vivo imaging of 4T1 tumor xenografts in mice using ZnFe-MMO as a tracer showed that the mean signal intensity is 1.27-fold higher than the commercial tracer VivoTrax at 72 h post-injection, indicating ZnFe-MMO's promise for prolonged MPI imaging applications.

Elementary econometric and strategic analysis of curling matches

PurposeWe develop a Markov model of curling matches. This enables strategic and econometric analyses to be performed alongside computer simulation work.Design/methodology/approachWe develop a Markov model of curling matches, parametrised by the probability of winning an end and the probability distribution of scoring ends. In practical applications, these end-winning probabilities can be estimated econometrically and are shown to depend on which team holds the hammer as well as the offensive and defensive strengths of the respective teams. Using a maximum entropy argument, based on the idea of characteristic scoring patterns in curling, we predict that the points distribution of scoring ends should follow a constrained geometric distribution.FindingsWe provide analytical results detailing when it is optimal to blank the end in preference to scoring one point and losing possession of the hammer. Statistical and simulation analysis of international curling matches is also performed.Originality/valueOur work adds to the theory and application of sports analytics, especially Markov models, and to the econometric and strategic analysis of curling matches.

Spinning waveforms in cubic effective field theories of gravity

We derive analytic all-order-in-spin expressions for the leading-order time-domain waveforms generated in the scattering of two Kerr black holes with arbitrary masses and spin vectors in the presence of all independent cubic deformations of Einstein-Hilbert gravity. These are the two parity-even interactions I1 and G3, and the parity-odd ones Ĩ1 and G~3. Our results are obtained using three independent methods: a particularly efficient direct integration and tensor reduction approach; integration by parts combined with the method of differential equations; and finally a residue computation. For the case of the G3 and G~3 deformations we can express the spinning waveform in terms of the scalar waveform with appropriately shifted impact parameters, which are reminiscent of Newman-Janis shifts. For I1 and Ĩ1 similar shifts occur, but are accompanied by additional contributions that cannot be captured by simply shifting the scalar I1 and Ĩ1 waveforms. We also show the absence of leading-order corrections to gravitational memory. Our analytic results are notably compact, and we compare the effectiveness of the three methods used to obtain them. We also briefly comment on the magnitude of the corrections to observables due to cubic deformations.

The efficacy and safety of radiofrequency ablation for allergic rhinitis: a systematic review and meta-analysis.

This systematic review aims to synthesise findings from randomised, controlled trials and assess the efficacy and safety of radiofrequency ablation in treating allergic rhinitis. A thorough search was conducted across PubMed, the Cochrane Library, Embase, Web of Science, China National Knowledge Infrastructure, WanFang, Chinese Scientific Journal, and Chinese Biomedical Literature databases from their inception until October 2023. The primary outcome measure was the total effective rate, with secondary outcomes including adverse events. This review included 15 randomised, controlled trials involving 1430 patients. The pooled analysis revealed a statistically significant effect on the total effective rate (odds ratio = 3.27, 95 per cent confidence interval = 2.37 to ~4.51). However, no statistical significance was observed in adverse events (odds ratio = 1.18, 95 per cent confidence interval = 0.67 to ~2.08). Based on the analytical results, radiofrequency ablation emerges as an efficacious and safe treatment modality for allergic rhinitis. Given the constraints posed by a limited sample size, it is imperative that forthcoming clinical trials adhere rigorously to the gold standard of randomised, controlled trials for the purpose of corroborating these conclusions.

Analysis of the dynamic responses of a piezothermoelastic microbeam resonator under dual-phase-lag heat conduction

Thermoelastic vibration responses of a piezothermoelastic (PTE) microbeam resonator have been investigated in the present work under simply supported boundary conditions. The basic governing equations for a transversely isotropic piezothermoelastic solid are formulated by assuming the Euler–Bernoulli beam theory with hyperbolic dual-phase-lag (DPL) heat conduction model. Later on, non-dimensionalization of the variables have been carried out for simplicity to obtain the set of coupled governing equations for thermal deflection, electric field, and thermal moment. Initial and boundary conditions are defined to solve for the non-dimensional thermal deflection and thermal moment by using Laplace transform technique along with the finite Fourier sine transform. Closed-form solutions of the problem are obtained. Moreover, an attempt is made to illustrate the analytical results through numerical simulations by taking a PTE material of Lead Zirconate Titanate (PZT-5A). The influence of the quadratic term of the phase-lag parameter of heal flux in the DPL model is investigated to compare the effects of phase-lags under parabolic and hyperbolic DPL models. In addition, the long-term and short-term vibration responses of thermal moment and thermal deflection are analyzed in detail to observe the impact of different factors which characterize the piezoelectric phenomena and dual-phase-lag effects. Comparative analysis of different well-known models for responses of thermal moment and thermal deflection is also presented for short- and long-time ranges. Some important observations about how piezoelectric parameters, dual-phase-lag parameters, and beam parameters affect the behavior of piezothermoelastic vibrations have been highlighted.

The State of the Art in Post-Mortem Redistribution and Stability of New Psychoactive Substances in Fatal Cases: A Review of the Literature

In post-mortem (PM) investigations, forensic toxicologists attempt to identify legal or illegal substances present before death and determine how they contributed to the cause of death. A critical challenge is ensuring that PM sample concentrations accurately reflect those at the time of death, as postmortem redistribution (PMR) can alter these levels due to anatomical and physiological changes. The PMR phenomenon is called a ‘toxicological nightmare’. PMR significantly affects post-mortem drug concentrations, particularly for lipophilic drugs and those with a high volume of distribution. The emergence of new psychoactive substances (NPSs) has led to a growing recognition of their role as a significant public health concern, frequently associated with fatalities related to polydrug use. These substances are renowned for their ability to induce intoxication at low doses, which has led to the continuous updating of toxicological and forensic methods to improve detection and adopt new analytical standards. The comprehensive detection of NPS metabolites, some of which are still undiscovered, presents an additional analytical challenge, as do their metabolic pathways. This complicates their identification in fatal cases using standard analytical methods, potentially leading to an underestimation of their actual prevalence in toxicological results. Furthermore, the interpretation of analytical results is hindered by the absence of data on PM blood levels and the specific contributions of NPS to causes of death, exacerbated by the lack of knowledge of whether the PMR phenomenon influences them. This paper presents a comprehensive review of the literature on post-mortem cases involving various NPS, categorized according to classifications by the United Nations Office on Drugs and Crime (UNODC) and the European Union Drugs Agency (EUDA). These categories include cathinones, phenylethylamines, arylalkylamines, phencyclidine-type substances, phenmetrazines, piperazines, phenidates, aminoindanes, LSD-like NPSs, tryptamines, fentanyl analogs, designer benzodiazepines, synthetic cannabinoids, and nitazenes. This review covers not only postmortem blood levels but also the stability of the substances studied, the methods of analysis, and attempts to shed some light on the PMR phenomenon. This review used various key terms, such as PMR, NPS, and the names of previously categorized substances and drug analyses across multiple peer-reviewed journals and databases, including Scopus, Google Schoolar, Springer, PubMed, and Wiley Online Library. In addition, references from retrieved articles were examined to identify additional relevant research. Interpreting post-mortem toxicological results is complex and lacks definitive guidelines, requiring a nuanced understanding of its challenges and potential pitfalls. As a result, post-mortem toxicology is often regarded as an art. The primary aim of this review is to provide forensic toxicologists with a comprehensive framework to assist in the evaluation and interpretation of NPS analysis. This guide is intended to complement the existing knowledge and practices applied in forensic laboratories within the toxicological analysis of post-mortem cases.

Effect of sewing on the mechanical characteristics of composite sandwich materials

Sandwich composite are used in numerous structural applications, with demonstrated weight savings over conventional metals and solid composite materials. The increasing use of sandwich composites in defense structures, particularly those which may be exposed to shock loading, demands for a thorough understanding of their response to suc highly transient loadings. The present work is a comparative study of the mechanical characteristics of the presence of reinforced transverse seams sewn at an angle of 45 ° and without seams on the Behavior of sandwich structures subjected to mechanical stresses. The experimental results show an improvement in performance in terms of the energy required for crack initiation and propagation. In addition, the presence of the seams results in atypical behavior that results in a series of characteristic damage and, on the other hand, the seamless structure exhibits a delamination phenomenon. Finally, a comparison of the analytical results with the experiment is carried out.

Operating policies for robotic cellular warehousing systems

Robotic Cellular Warehousing Systems provide an innovative robot-to-goods picking approach designed to improve robot transportation efficiency, where robots move to pick items and transport the picked items to workstations. In this study, we investigate the optimal operating policies for such a system by comparing two picking strategies (pick-while-sort and pick-then-sort) and three robot-to-workstation assignment rules (random, closest, and dedicated). Specifically, we develop dedicated closed queuing networks to model robot-to-goods picking and estimate warehouse throughput under different policies through single-class and multi-class models. The effectiveness of these analytical models is validated through numerical simulations, with an average gap of 5.53% between simulation and analytical results. Additionally, we conduct a series of numerical experiments to examine the impact of various factors on warehouse performance, including the numbers of robots and workstations, robot capacity, order size, and sorting efficiency. Based on the experimental findings, we provide managerial implications that offer insights into optimizing resource allocation and system configuration. These insights enable warehouse managers to improve operational efficiency and overall performance.

One‐Dimensional Fully Coupled Hydro‐Mechanical‐Chemical Model for Contaminant Transport Under Step‐Loading Condition and Its Analytical Solutions

ABSTRACTStepped dumpling of waste is the main operating method used in landfill engineering. For the liners located at the bottom of the landfill, the waste can be considered as a vertical loading due to its heavy weight, causing compressive deformation of the liners and, most importantly, tending to lose the effectiveness of the geomembrane with the differential deformation. However, most experiments or numerical models use transient‐loading and ignore the influence of variable step‐loading on liner performance. In this study, a one‐dimensional fully coupled hydro‐mechanical‐chemical (HMC) model for contaminant transport under the framework of small strain, taking into account the step‐loading effect, is proposed, and its analytical solutions are derived by using the separation of variables. The behavior of contaminant transport in a single‐layer clay liner is investigated under variable step‐loading conditions. Analytical results show that the step‐loading can significantly accelerate the transport of contaminants compared to the transient‐loading. Variation of the step‐loading rate from 2 to 4 times yields an increase of 6.1 and 15.2 years of the breakthrough time. At a step‐loading rate of 50 kPa/year, the breakthrough increases by 13.37 years, and the peak settlement reduces to half that under transient‐loading. Ignoring the influence of step‐loading on contaminant transport may overestimate the performance of clay liners.

Enhanced correlations due to ballistic transport

Abstract We investigate the nature of density-density correlations in a 1D gas of hard-core particles initially prepared at equilibrium (either at zero or finite temperature) on a semi-infinite line and subsequently let to expand into the other (initially empty) half of the system. Using a combination of analytical techniques based on exact methods and asymptotic hydrodynamic approaches, we discuss the behavior of the gas as its initial temperature varies, and back up our derivations with numerical exact diagonalization of the model. Our findings reveal that, irrespective of the initial temperature, the non-equilibrium behavior of density-density correlations at sufficiently large times is characterized by algebraic decay. Furthermore, we provide analytical results based on quantum generalized hydrodynamics that match with the numerical data both at zero and finite temperature.

On Existence of Heteroclinic Connections in Discontinuous Kurland–Levi Differential Equations with Slowly Varying Coefficients

We study the existence of heteroclinic solutions for discontinuous Kurland–Levi differential equations with slowly varying coefficients. Our main results follow from our recent general theorem concerning heteroclinic solutions in singularly perturbed discontinuous differential equations. We apply the new analytical results to concrete examples and give numerical simulations.

Design and Failure Analysis of a Vacuum Pressure Vessel for Aerospace Applications using Finite Element Analysis (FEA)

This paper provides detailed insights into the external pressure vessels. External pressure vessels are designed to perform under extreme operating conditions, so the selection of material and geometry along with stress analysis are fundamental for their optimal efficiency. The objective of this research is to provide a case study of the material, design, and stress generated in the pressure vessel to make it suitable for thermal and load-bearing applications in the aerospace industry. An aluminum alloy was chosen as the design material due to its low density and high strength. The modeling geometry of the alloy was constructed using the ASME section-VIII division-I div code. After the performed Finite Element Analysis (FEA), modeling was carried out deploying the ANSYS design modeler to obtain the stress concentration and failure mode of the model. The present study demonstrates the behavior of a structure under applied load and identifies the weak areas of its geometry. Based on the external stress at the center of the structure, the maximum and minimum stresses computed are 0.763 MPa and 0.00803 MPa, respectively. It was also found that the maximum strain is generated at the center of the structure and is equal to 1.0834e-6 mm/mm, the maximum deformation is equal to 0.00109 mm and also occurred at the center, while the shells of the model are unable to undergo any deformation. FEA results agree with the analytical results, as the errors for hoop stress and equivalent strain are 4.8% and 1.8%, respectively. Thus, the proposed method can be applied to predict the equivalent stress, equivalent strain, total deformation, and stress intensity, which are required for the structural integrity analysis of pressure vessels.

Randomness and early termination: What makes a game exciting?

AbstractIn this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators? Our construction is based on the detailed study of a terminal-boundary value problem for the nonlinear parabolic PDE $$2\partial _t e(t,x)= \log (-\partial _{xx}e(t,x))$$ 2 ∂ t e ( t , x ) = log ( - ∂ xx e ( t , x ) ) derived by Aldous. We prove its wellposedness and regularity of its solution by combining PDE analysis and probabilistic tools, in particular the reformulation as a stochastic control problem with restricted control set, which allows us to deduce strict ellipticity. We establish key qualitative properties of the solution including concavity, monotonicity, convergence to a steady state for long remaining time and the asymptotic behaviour shortly before the terminal time. Moreover, we construct convergent numerical approximations. The analytical and numerical results allow us to characterise the max-entropy win-probability martingale and to highlight the behaviour of this process in the present case where the match may end early, in contrast to recent work by Backhoff-Veraguas and Beiglböck where the match always runs the full length.