Analytical Results Research Articles

Dimensional regularization and two-loop vacuum polarization operator: Master integrals, analytic results, and energy shifts

We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in D=4−2ε dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order ε, to be combined with the 1/ε divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for 1S, 2S, and 2P states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the Zα-expansion. We compare the results obtained to the existing literature. Published by the American Physical Society 2024

Five-parton scattering in QCD at two loops

We compute all helicity amplitudes for the scattering of five partons in two-loop QCD in all the relevant flavor configurations, retaining all contributing color structures. We employ tensor projection to obtain helicity amplitudes in the ’t Hooft-Veltman scheme starting from a set of primitive amplitudes. Our analytic results are expressed in terms of massless pentagon functions, and are easy to evaluate numerically. These amplitudes provide important input to investigations of soft-collinear factorization and to studies of the high-energy limit. Published by the American Physical Society 2024

Corruption dynamics: a mathematical model and analysis

This study proposes and analyzes a deterministic mathematical model to describe the dynamics of corruption transmission. We began by proving that the solution to the model is bounded and positive. The next-generation matrix approach is used to compute the basic reproduction number (R0) in relation to corruption-free equilibrium. The Jacobian and Lyapunov functions are used to show that corruption-free equilibrium is asymptotically stable in both locally and globally when R0<1, and otherwise, an endemic corruption equilibrium develops. Furthermore, the sensitivity of the model's parameters was investigated. The findings demonstrate that religious precepts govern public education. The two sectors most susceptible to corruption control are education and corrections. The study recommends investing more in the provision of public education to citizens by creating awareness among all and including it in the education curriculum and religious leaders to teach their followers seriously about the impact of corruption as well as the use of jail as punishment. The numerical simulation results agreed with the analytical results.

Quantum state engineering by steering in the presence of errors

Quantum state engineering plays a vital role in various applications in the field of quantum information. Different strategies, including drive-and-dissipation, adiabatic cooling, and measurement-based steering, have been proposed for state generation and manipulation, each with its upsides and downsides. Here, we address a class of measurement-based state engineering protocols where a sequence of generalized measurements is employed to steer a quantum system toward a desired (pure or mixed) target state. Previously studied measurement-based protocols relied on idealized procedures and avoided exploration of the effects of various errors stemming from imperfections of experimental realizations and external noise. We employ the quantum trajectory formalism to provide a detailed analysis of the robustness of these steering protocols against multiple classes of errors. We study a set of realistic errors that can be classified as dynamic or static, depending on whether they remain unchanged while running the protocol. More specifically, we investigate the impact of the erroneous choice of detector-system coupling, erroneous re-initialization of the detector state following a measurement step, fluctuating steering directions, and environmentally induced errors in the detector-system interaction. We show that the protocol remains fully robust against the erroneous choice of detector-system coupling parameters and presents reasonable robustness against other types of errors. Our analysis employs various quantifiers such as fidelity, trace distance, and linear entropy to characterize the protocol's robustness and provide analytical results for these quantifiers against various errors. We introduce averaging hierarchies of stochastic equations describing individual quantum trajectories associated with detector readouts. Subsequently, we demonstrate the commutation between the classical expectation value and the time-ordering operator of the exponential of a Hamiltonian with multiplicative white noise, as well as the commutation of the expectation value and the partial trace with respect to detector outcomes. Our ideas are implemented and demonstrated for a specific class of steering platforms, addressing a single qubit. Published by the American Physical Society 2024

Topological nano-switches in higher-order topological insulators

Abstract We consider multi-terminal transport through a flake of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field. This system has been shown to be a second-order topological insulator, thus exhibiting corner states at its boundaries. The position of the corner states and their decay length can be controlled by the direction of the magnetic field. In the leads we assume that the magnetic field is absent and therefore we have helical one-dimensional propagating states characteristic of the spin-Hall effect. Using a low-energy effective Hamiltonian we show analytically that, in a two-terminal setup, transport can be turned on and off by a rotation of the in-plane magnetic field. Similarly, in a three terminal configuration, the in-plane magnetic field can be used to turn on and off the transmission between neighbouring contacts, thus realising a directional switch. Analytical calculations are supplemented by a numerical finite-difference method. For small values of the Fermi energy and field strength, the analytical results agree exceptionally well with the numerics. The effect of disorder is also addressed in the numerical approach. We find that the switching functionality is remarkably robust to the presence of strong disorder stemming from the topological nature of the states contributing to the electron transport.

A subbands study on the resistivity of field-effect CNT-based piezoresistive nanocomposites.

In this paper, an analytical model based on the percolation theory has been developed to predict the subbands effect on the effective electrical resistivity of carbon nanotubes (CNT)-based polymer nanocomposites. The CNTs are considered as randomly distributed or aligned channel material in the polymer transmitting electrons through tunneling. The tunneling effect takes into account the electron transmission between each connected pair of CNTs to evaluate electrical resistivity. The modeling approach contains two steps of primary prediction of resistivity and further calculation of CNTs' displacements and subsequent change of the resistance. A good agreement is found between the analytical model predictions and experimental data when the tunneling behavior was considered in the percolation transition region. The effect of CNT diameter, orientation state, and subbands on the resistivity has been investigated. The results depict that subbands increment is a collateral benefit to the aspect ratio in decreasing the resistivity. The analytical results demonstrate that a random CNT dispersion leads to a decreased piezoresistivity, while an increased strain range depicts a more non-linear behavior.

Finite Element Analysis and Weight Optimization of Knuckle joint for different Materials by using CAE Tools

The current study involved the analysis of a knuckle joint using finite elements. A mechanical joint with two intersecting cylindrical rods whose axes are in the same plane is called a knuckle joint. Knuckle joint should be designed and manufactured in such a way that it can sustain more load without failure. The objective of the present study is to study knuckle joints made of different materials like aluminum, stainless steel, structural steel, magnesium, and gray cast iron using CAE tools. The CAD model of knuckle joint is made in CATIA V5 R20. The finite element analysis of this CAD model using ANSYS 15 has been carried out to investigate maximum stress and deformation. The CAE results compared with the analytical results using conventional approach. The CAE results have been found close to the analytical results, thus validating the model. The knuckle joint of aluminum is found to have highest factor of safety (1.641) at 50 KN load and is the most the most suitable material for knuckle joint. Weight of vehicle plays an important role in overall performance and fuel efficiency of vehicle. Knuckle joint is a part of vehicle. Hence weight optimization of knuckle joint made of aluminum has been performed using ANSYS 15 and it is observed that weight of knuckle joint made of aluminum can be reduced by 5.08% for 50 KN loading condition. Key Words: Knuckle joint, Finite element analysis, Mechanical joint, Load-bearing capacity, Material selection, CAE tools, Deformation analysis etc.

Experimental and analytical study on enhancing flexural strength of RC beams using post‐ tensioned heavy‐duty metal straps wrapped around anchored steel plates

AbstractThis paper addresses the challenge of enhancing the bending capacity of beams through a cost‐effective and practical approach. Current methods are often expensive, brittle, time‐intensive, or massive. In response, an alternative method is proposed that involves the utilization of post‐tensioned heavy‐duty metal straps wrapped around steel plates anchored to the beams. To evaluate the effectiveness of the method, six large‐scale normal reinforced concrete beams were constructed with a width of 160 mm and a depth of 240 mm, and a clear span of 1900 mm. The testing parameters were the position of the steel plates along the length of the beam and the position of the metal straps along the height of the steel plates. Quantitative results demonstrate a significant enhancement in the load‐carrying capacity of the beams. Compared to the control specimen, the method led to a minimum increase of 40% of load carrying capacity and a maximum increase of 66%. Key influencing factors include the location of the metal straps on the steel plates (120 or 90 mm away from the bottom of the beam) and the position of the steel plates on the face of the beam (650 mm or 350 away from the edge of the beam). Notably, the load‐carrying capacity increases when the metal straps are positioned lower on the steel plates and the plates are placed further away from the center of the beam. Finally, analytical results obtained using VecTor2 software align well with experimental findings.

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations

In this study, we propose coupled time-delayed fractional oscillators with dichotomous fluctuating frequencies and investigate the collective resonant behavior. Firstly, we obtain the condition of complete synchronization between the average behavior of the two oscillators. Subsequently, we derive the precise analytical expression of the output amplitude gain. Based on the analytical results, we observe the collective resonant behavior of the coupled time-delayed system and further study its dependence on various system parameters. The observed results underscore that the coupling strength, fractional order, and time delay play significant roles in controlling the collective resonant behavior by facilitating the occurrence and optimizing the intensity. Finally, numerical simulations are also conducted and verify the accuracy of the analytical results.

An Innovative Design to Enhance Osteoinductive Efficacy and Biomechanical Behavior of a Titanium Dental Implant

The present study investigated the in vivo bone-forming efficacy of an innovative titanium (Ti) dental implant combined with a collagen sponge containing recombinant human bone morphogenetic protein-2 (BMP-2) in a pig model. Two different concentrations of BMP-2 (20 and 40 µg/mL) were incorporated into collagen sponges and placed at the bottom of Ti dental implants. The investigated implants were inserted into the edentulous ridge at the canine–premolar regions of Lanyu small-ear pigs, which were then euthanized at weeks 1, 2, 4, 8, and 12 post-implantation. Specimens containing the implants and surrounding bone tissue were collected for histological evaluation of their bone-to-implant contact (BIC) ratios and calculation of maximum torques using removal torque measurement. Analytical results showed that the control and BMP-2-loaded implants presented good implant stability and bone healing for all testing durations. After 1 week of healing, the BMP-2-loaded implants with a concentration of 20 µg/mL exhibited the highest BIC ratios, ranging from 58% to 76%, among all groups (p = 0.034). Additionally, they also possessed the highest removal torque values (50.1 ± 1.3 N-cm) throughout the 8-week healing period. The BMP-2-loaded implants not only displayed excellent in vivo biocompatibility but also presented superior osteoinductive performance. Therefore, these findings demonstrate that BMP-2 delivered through a collagen sponge can potentially enhance the early-stage osseointegration of Ti dental implants.

Efficient semianalytical investigation of a fractional model describing human cornea shape

Purpose: This study presents a novel application of the semianalytical residual power series method to investigate a one-dimensional fractional anisotropic curvature equation describing the human cornea, the outermost layer of the eye. The fractional boundary value problem, involving the fractional derivative of curvature, poses challenges that conventional methods struggle to address. Methods: The analytical results are obtained by utilizing the simple and efficient residual power series method. The proposed method is accessible to researchers in all medical fields and is extendable to various models in disease spread and control. Results: The derived solution is a crucial outcome of this study. Through the application of the proposed method to the corneal shape model, an explicit formula for the curvature profile is obtained. To validate the solution, direct comparisons are made with numerical solutions for the integer case and other analytical solutions available in the literature for the fractional case. Conclusion: Our findings highlight the potential of the proposed method to significantly contribute to the diagnosis and treatment of various ophthalmological conditions.

Outdoor-to-Indoor mmWave Relaying with Massive MIMO: Impact of Imperfect Channel Estimation

Assuming incomplete knowledge of the channel state information (CSI), we investigate two scenarios involving millimeter wave (mmWave) relaying to support outdoor-to-indoor communications. We proceed to derive the average signal-to-noise ratio (SNR) expressions for two relaying scenarios and quantify the asymptotic SNR. The performance of the two relaying scenarios is evaluated using the outage probability—for which we have derived closed-form equations—the end-to-end channel capacity, and the energy efficiency. The obtained results are compared with those derived assuming complete knowledge of the CSI. The effect of the imperfect CSI is therefore assessed in relation to the reference of perfect CSI. In these scenarios, an outside base station (BS) in an urban cellular network serves several indoor users. In the context of a two-hop full-duplex (FD) relaying scheme, we initially suggest a method in which the base station (BS) utilizes zero-forcing (ZF) precoding, and we take into account the overall channel response. Furthermore, we make the assumption that the base station (BS) engages in precoding only depending on the response of the channel in the first hop; in this second design, the relay precodes (using the response of the second-hop channel), amplifies, and sends the signals. Both techniques utilize massive multiple-input–multiple-output (mMIMO) arrays to permit transmission. We also present Monte Carlo simulation results to assess the accuracy of our analytical results. Finally, the two systems are compared in terms of channel estimation and precoding complexity, the number of antennas, as well as the number of users. Practical deployment recommendations are formulated at the end of this work.

Lump Kink interactional and breather-type waves solutions of (3+1)-dimensional shallow water wave dynamical model and its stability with applications

The shallow water equations are used to describe the behavior of water waves in various shallow regions such as coastal areas, lakes, rivers, etc. These equations are derived by making simplifying assumptions about the water depth relative to the wavelength of the waves. In this paper, the generalized exponential rational function method (gERFM) is used to construct novel wave solutions of the (3+1)-dimensional shallow water wave ((3+1)-dSWW) dynamical model. These solutions encompass distinct kinds of waves, such as solitary waves, solitons, Kink and anti-kink solitons, lump Kink interactional waves, traveling breathers-type waves and multi-peak solitons. The dynamical behavior of these wave solutions is discussed, examining the influence of free parameters on the resulting wave shapes. Furthermore, to provide a scientific elucidation of the obtained results, the solutions are presented graphically, making it easy to distinguish the dynamical features, which have practical implications in different areas of applied sciences and engineering. The stability of this dynamical model is revealed via modulational instability analysis, signifying that all analytical results are stable. The obtained results show that the given technique is universal and efficient. Through comparing the projected technique with the existing techniques, the obtained results demonstrate that the given technique is universal, pithy and efficient.

Amplification in parametrically-driven resonators near instability based on Floquet theory and Green’s functions

Abstract Here we use Floquet theory to calculate the response of
parametrically-driven time-periodic systems near the onset of parametric
instability to an added external ac signal or white noise.
We provide new estimates, based on the Green's function method,
for the response of the system in the frequency domain.
Furthermore, we present novel expressions for the power and
noise spectral densities.
We validate our theoretical results by comparing our predictions for the
specific cases of a single degree of freedom parametric amplifier and of the
parametric amplifier coupled to a harmonic resonator with the
numerical integration results and with analytical approximate results obtained via
the averaging method up to second order.

Analytic Solution and Benchmark Results for the Free Vibrations of Thin Shallow Shells with Rectangular Planform

Analytic Solution and Benchmark Results for the Free Vibrations of Thin Shallow Shells with Rectangular Planform

Analysis of two interactive burning droplets with different temperatures

This paper presents a comprehensive theoretical analysis of the interaction between two quasi-steady burning droplets with differing temperatures, sizes and distances, building upon the mass-flux-potential model and flame-sheet assumption. In contrast to existing research, this study introduces a fresh perspective on droplet interactions by considering the different temperatures of the droplets. Utilizing the bispherical coordinate approach, theoretical solutions for the Stefan flow, scalar fields, droplet evaporation/burning rates, interaction coefficients and flame positions have been derived successfully. A comparison with extensive numerical simulations indicates a good agreement between the analytical and numerical results under a variety of conditions. It is revealed that proximity between the droplets causes non-uniform evaporation rates on their surfaces, and in some cases, leads to condensation on the cooler droplet. Notably, when the temperatures of the two droplets differ, this results in an uneven temperature distribution across the flame surface, and increasing the temperature of one droplet substantially elevates the temperature of the nearby flame. This study also establishes a criterion for the transition between different combustion modes, specifically between group and separated combustion. The findings of this study are crucial in deepening our understanding of evaporation and combustion processes, as well as the dynamics of flame spreading, local ignition, and extinction in systems involving multiple droplets.

Analytical Modeling and Validation of New Prismatic Compliant Joints Based on Zero Poisson’s Ratio Lattice Structures

Abstract The design and analysis of prismatic compliant joints have received less attention compared to that given to revolute compliant joints, thus limiting their implementation in compliant mechanisms beyond translational stages. Lattice structures have been used effectively to increase flexibility and stiffness ratios in compliant joints. Considering these, new prismatic compliant joints based on zero Poisson’s ratio lattice structures (ZP-PCJ) are proposed. Lattices with three different cell arrangements are considered: single cells, 2×2, and 3×3 lattices. Additionally, unit cells with three different geometries are studied: triangular, chamfer, and cosine. The compliance matrices of the ZP-PCJs are assembled analytically using Castigliano’s second theorem and compliance series–parallel simplification. The compliance ratios along the three orthogonal axes of the ZP-PCJs are computed varying their geometric parameters. Finite element models are constructed to validate the analytical results. Experimental tests are performed on additively manufactured ZP-PCJs to corroborate the compliance coefficients. Results showed that analytical models can predict the ZP-PCJ’s elastic properties accurately, differences less than 3% and 12% were obtained when compared to computational and experiments, respectively. Based on the compliance ratios obtained, the ZP-PCJs are suitable for two-dimensional applications. Finally, the ZP-PCJs are implemented in a compliant mechanism to evaluate their behavior, analytically and computationally. The ZP-PCJs have advantages such as eliminating axis drift and high flexibility in motion-direction while maintaining stiffness in other directions. The differences observed when comparing the analytically obtained estimations with simulations and experimental data suggest that ZP-PCJ analytical models are reliable for estimating their performance in compliant systems.

Three-Body Binary Formation in Clusters: Analytical Theory

Abstract Binary formation in clusters through triple encounters between three unbound stars, ‘three-body’ binary formation, is one of the main dynamical formation processes of binary systems in dense environments. In this paper, we use an analytical probabilistic approach to study the process for the equal mass case and calculate a probability distribution for the orbital parameters of three-body-formed binaries, as well as their formation rate. For the first time, we give closed-form analytical expressions to the full orbital parameter distribution, accounting for both energy and angular momentum conservation. This calculation relies on the sensitive dependence of the outcomes of three-body scatterings on the initial conditions: here we compute the rate of three-body binaries from ergodic interactions, which allow for an analytical derivation of the distribution of orbital parameters of the binaries thus created. We find that soft binaries are highly favoured in this process and that these binaries have a super-thermal eccentricity distribution, while the few hard three-body binaries have an eccentricity distribution much closer to thermal. The analytical results predict and reproduce simulation results of three-body scattering experiments in the literature well.

Gender differences in cardiogenic shock: characteristics and prognosis

Abstract Funding Acknowledgements Type of funding sources: Public hospital(s). Main funding source(s): Hospital Clinico San Carlos. Background Cardiogenic shock (CS) is a life-threatening condition caused by severe heart dysfunction. While significant advances have been made in the management and treatment of cardiogenic shock, there is growing recognition of the importance of considering gender-specific differences in the presentation and outcomes of this condition. Recent research highlights gender-related variations in how the condition is presented, managed, and its outcomes. Understanding these differences is crucial for tailored and effective treatment. Our goal is to identify potential gender differences in terms of the characteristics and prognosis of CS. Methods From 2013 to 2023, 142 consecutive patients diagnosed with CS in and admitted to an Acute Cardiac Care Unit in a tertiary care hospital were recruited. Demographic, clinical, and analytical variables were retrospectively collected. Patient were followed-up to November-2023 and clinical events were also recorded. For purposes of analysis, patients were classified in woman (N=95) and men (N=47). Success, in terms of IABP use, was defined as patient’s survival to the index event. Failure of IABP was defined as in-hospital death. A multivariate logistic regression analysis was performed to identify potential predictors of success. A descriptive analysis of clinical, analytical, and demographic parameters was performed in both groups, followed by a survival curve analysis to assess differences in prognosis between both sexes. Results Mean age was 67.3±12.2 years and 67.0% were females. There were no significant differences in cardiovascular risk factor and comorbidities between groups: hypertension (61.2% vs 38.8%, p 0.077), diabetes (65.9% vs 34.1%, p 0.866), chronic kidney disease (75% vs 25%, p 0.465), previous stroke (61.5% vs 38.5%, p 0.666) in woman vs men group respectively. STEMI was the most frequent cause of CS requiring an IABP in men (33.7%) but NSTEMI was in women (67.7%). Regarding the CS classification, both groups had a similar distribution of the severity and complexity of the shock (Figure 1). There were also no differences in hemodynamic parameters, analytical results, complete revascularization, and left ventricular ejection fraction (LVEF) between men and women (Figure 1). There were also no differences in hemodynamic parameters, analytical results, complete revascularization, and left ventricular ejection fraction (LVEF) between men and women (Figure 1). The complications, mortality (Figure 2), and long-term mortality were also similar in both groups. Conclusions In our observational study, there were no differences between genders in terms of characteristics, shock complexity, and prognosis.

Finite Element Analysis and weight Optimization of Knuckle joint for different materials by using CAE Tools

The current study involved the analysis of a knuckle joint using finite elements. A mechanical joint with two intersecting cylindrical rods whose axes are in the same plane is called a knuckle joint. Knuckle joint should be designed and manufactured in such a way that it can sustain more load without failure. The objective of the present study is to study knuckle joints made of different materials like aluminum, stainless steel, structural steel, magnesium, and gray cast iron using CAE tools. The CAD model of knuckle joint is made in CATIA V5 R20. The finite element analysis of this CAD model using ANSYS 15 has been carried out to investigate maximum stress and deformation. The CAE results compared with the analytical results using conventional approach. The CAE results have been found close to the analytical results, thus validating the model. The knuckle joint of aluminum is found to have highest factor of safety (1.641) at 50 KN load and is the most the most suitable material for knuckle joint. Weight of vehicle plays an important role in overall performance and fuel efficiency of vehicle. Knuckle joint is a part of vehicle. Hence weight optimization of knuckle joint made of aluminum has been performed using ANSYS 15 and it is observed that weight of knuckle joint made of aluminum can be reduced by 5.08% for 50 KN loading condition. Key Words: Knuckle joint, Finite element analysis, Mechanical joint, Load-bearing capacity, Material selection, CAE tools, Deformation analysis etc.