Quintic Research Articles

Application of the Green's function method for static analysis of nonlocal stress-driven and strain gradient elastic nanobeams

This paper focuses on the static analysis of a generally restrained Euler-Bernoulli nanobeam (GRNB), which is subjected to arbitrary distributed or concentrated loads. The small length scale effect is introduced through a strongly nonlocal integral elastic law called the stress-driven nonlocal Euler-Bernoulli beam model, and a weakly nonlocal elastic law called the strain-gradient Euler-Bernoulli beam model. The stress-driven nonlocal theory and the strain gradient elasticity theory are both employed, to formulate the differential equation governing the Euler-Bernoulli nanobeams. Both theories are ruled by a similar 6th order differential equation, with distinct higher-order boundary conditions. The paper demonstrates that the strain gradient theory can be also reformulated as a stress-driven nonlocal theory with unsymmetrical kernel, in contrast to the initial stress-driven nonlocal theory which has symmetrical exponential kernel. Additionally, some theoretical backgrounds about both nonlocal elasticity theorems are provided. Exact solutions for both nanobeam models are presented, using Green's function method. The parameters of the Green's functions are derived for each beam theory, and then utilized to establish the static displacement function of both nanobeam theories. Exact solutions are provided for the bending of both nanobeams with various end boundary conditions, that account for the small length scale effects. The paper also compares the responses of the stress-driven Euler-Bernoulli beam and the strain gradient Euler-Bernoulli beam, showing close deflections and similar effects of increasing the nonlocal parameter on beam stiffness. A major difference highlighted between the two theories is that the strain gradient theory predicts a homogeneous strain state for homogeneous stress state, as opposed to the stress-driven theory.

A trocar puncture robot for assisting venipuncture blood collection

AbstractThe venous blood test is a prevalent auxiliary medical diagnostic method. Venous blood collection equipment can improve blood collection’s success rate and stability, reduce the workload of medical staff, and improve the efficiency of diagnosis and treatment. This study proposed a rigid-flexible composite puncture (RFCP) strategy, based on which a small 7-degree-of-freedom (DOF) auxiliary venipuncture blood collection (VPBC) robot using a trocar needle was designed. The robot consists of a position and orientation adjustment mechanism and a RFCP end-effector, which can perform RFCP to avoid piercing the blood vessel’s lower wall during puncture. The inverse kinematics solution and validation of the robot were analyzed based on the differential evolution algorithm, after which the quintic polynomial interpolation algorithm was applied to achieve the robot trajectory planning control. Finally, the VPBC robot prototype was developed for experiments. The trajectory planning experiment verified the correctness of the inverse kinematics solution and trajectory planning, and the composite puncture blood collection experiment verified the feasibility of the RFCP strategy.

Efficient techniques for nonlinear dynamics: a study of fractional generalized quintic Ginzburg-Landau equation

In this research, we explore the solution of the fractional Generalized Quintic Complex Ginzburg-Landau equation (GQCGLE) using the Controlled Picard Transform Method. We solve the equation by incorporating the Laplace transform (LT) and the Caputo-Fabrizio fractional derivative (CF). The fractional GQCGLE is a complex-valued equation that exhibits intricate dynamics and plays a significant role in various physical phenomena, particularly in the realm of nonlinear optics. The suggested method can efficiently address a wide variety of differential equations, encompassing both integer and fractional-order equations. This is achieved by integrating an extra parameter that enhances convergence, making it especially suitable for non-linear differential equations. To confirm the precision and convergence of our approach, we validate it by comparing it with other methods, presenting graphical representations to clarify the effects of different parameters on the solution behaviour, and confirming its precision and convergence. The existence and uniqueness of the solutions are also examined.

Estimating the strong coupling from τ decay using accelerating series convergence

We apply the Euler transformation to accelerate the convergence of the QCD perturbative series with the aim to determine the strong coupling αs in terms of the total τ-decay rate rτ. The variation of the result with the order of the QCD perturbation theory is small and comparable with the uncertainties of rτ. We also present an estimate of a range of the yet unknown 5th and 6th order coefficients k5 and k6 of the Adler function.

Numerical illustration of diffusive flow of blood-based tri-hybrid nanofluid generated by a curved stretching sheet using law of porosity

The study of flow of blood through the blood vessels carries nanoparticles which opens new ways in the research. This study explores one such flow of trihybrid nanoparticles suspended in blood over a curved stretching surface which undergoes the Darcy-Forchheimer porosity model. The analysis employs Cattaneo-Christov heat flux model along with chemical reaction, linear heat source allowing the surface to slip with heat and mass convection. The trihybrid nanofluids consist of a mixture of titanium dioxide, iron oxide, and silica nanoparticles mixed with base fluid (blood) to generate TiO 2 - Fe 3 O 4 - SiO 2 /blood hybrid nanofluids. Runge-Kutta-Fehlberg 4th–5th order technique, a robust numerical technique, was employed to obtain mathematical solutions. Throughout the numerical process, all parameters, except those under examination, were kept at their default values. Additionally, various plots were generated based on numerical results to illustrate the obtained data. The findings indicate that an increase in the Forchheimer number and porosity results in a reduction in the velocity profile. Furthermore, an increase in the radiation parameter and thermal Biot number leads to an increase in the temperature profile, while the temperature profile decreases with an increase in the thermal relaxation parameter. Additionally, an increase in the chemical reaction parameter and concentration Biot number results in an increase in the concentration profile. Moreover, higher Brinkman and Prandtl numbers enhance the Nusselt number.

Enhancing Whole-Brain Magnetic Field Homogeneity for 3D-Magnetic Resonance Spectroscopic Imaging with a Novel Unified Coil: A Preliminary Study.

The spectral quality of magnetic resonance spectroscopic imaging (MRSI) can be affected by strong magnetic field inhomogeneities, posing a challenge for 3D-MRSI's widespread clinical use with standard scanner-equipped 2nd-order shim coils. To overcome this, we designed an empirical unified shim-RF head coil (32-ch RF receive and 51-ch shim) for 3D-MRSI improvement. We compared its shimming performance and 3D-MRSI brain coverages against the standard scanner shim (2nd-order spherical harmonic (SH) shim coils) and integrated parallel reception, excitation, and shimming (iPRES) 32-ch AC/DC head coil. We also simulated a theoretical 3rd-, 4th-, and 5th-order SH shim as a benchmark to assess the UNIfied shim-RF coil (UNIC) improvements. In this preliminary study, the whole-brain coverage was simulated by using B0 field maps of twenty-four healthy human subjects (n = 24). Our results demonstrated that UNIC substantially improves brain field homogeneity, reducing whole-brain frequency standard deviations by 27% compared to the standard 2nd-order scanner shim and 17% compared to the iPRES shim. Moreover, UNIC enhances whole-brain coverage of 3D-MRSI by up to 34% compared to the standard 2nd-order scanner shim and up to 13% compared to the iPRES shim. UNIC markedly increases coverage in the prefrontal cortex by 147% and 47% and in the medial temporal lobe and temporal pole by 29% and 13%, respectively, at voxel resolutions of 1.4 cc and 0.09 cc for 3D-MRSI. Furthermore, UNIC effectively reduces variations in shim quality and brain coverage among different subjects compared to scanner shim and iPRES shim. Anticipated advancements in higher-order shimming (beyond 6th order) are expected via optimized designs using dimensionality reduction methods.

Mathematical modelling of the emission characteristics of a field electron cathode in a scanning electron microscope under biosampling conditions

Currently, the use of electron microscopes in medicine is developing intensively, including scanning electron microscopes (SEM), which are designed to solve a huge number of problems in various fields with a wide range of electron accelerating voltages and electron beam energies. The development of an SEM with certain emission characteristics, with a range of lower beam energies for the study of biological samples, is an urgent task because modifying the SEM to solve problems in medicine, for example, would make it possible to obtain higher-quality images of biospecimens for diagnostics and monitoring the effectiveness of therapy. To develop new SEMs with certain characteristics, it is proposed to conduct less expensive research using numerical methods based on mathematical models of processes in electron-optical SEM systems. In this regard, this work sets the task of determining the size and shape of the beam, the main emission characteristics of the field electron cathode (FEC) of the SEM, which is under the influence of the electric field that excites electron emission and the external longitudinal magnetic field by studying the movement of the outermost electron of the beam, taking into account the influence of space charge beam electrons, external magnetic field. In the model, the FEC is approximated by a paraboloid of rotation, and the concept of a boundary “outermost” electron is introduced, the trajectory of which determines the shape and size of the beam. The problem of calculating the emission characteristics along the trajectory of the outermost electron of a FEC is solved using a mathematical model that includes the following equations: motion of the “outermost” electron, Maxwell outside and inside the beam, continuity of the current density, Fowler-Nordheim equation. As a result, a system of 18 first-order ordinary differential equations was obtained, the numerical calculation of which using the 4th order Runge-Kutta method allows us to obtain the emission characteristics of the FEC. As a result, it is suggested that it would be feasible to modify SEMs for more effective use in the medical field, taking into account their increasing use in disease diagnosis and the possible improvement of image quality through the development of FEC SEMs with more suitable characteristics.

Nonlinear dynamics of magnetically coupled double beam based piezoelectric energy harvester under galloping excitation

This paper presents a magnetically coupled double cantilever beam-based piezoelectric energy harvester. Two square-shaped bluff bodies are attached to the tip of the beams to induce galloping-based oscillation in the proposed system. Spatio-temporal electro-mechanical equations of motion are developed using the Lagrange principle and discretized to their temporal form using generalized Galerkin’s method. 4th order Runge-Kutta method-based MATLAB solver (ode45) is used to solve these equations of motion and obtain numerical results. A prototype of the system is developed and experimented in a wind tunnel to support the numerical findings. Three wind speed regions (light air, light breeze, and gentle breeze) based on the Beaufort wind force scale are considered for getting a detailed insight into the system dynamics. Periodic, quasi-periodic, and chaotic oscillations are observed depending on different coupling conditions and wind speeds. Typical hopf bifurcation, Torus 3 bifurcations occur in the system due to galloping and magnetic repulsive force. Parametric studies are conducted for each wind speed region considering the load resistances and distance between the permanent magnets. Significant improvement in power output can be found for light air and gentle breeze regions with the magnetically coupled system than the uncoupled system (without magnetic interaction), whereas the uncoupled system performs better in the light breeze region.

Performance of the Direct Sequence Spread Spectrum Underwater Acoustic Communication System with Differential Detection in Strong Multipath Propagation Conditions

The underwater acoustic communication (UAC) operating in very shallow-water should ensure reliable transmission in conditions of strong multipath propagation, significantly disturbing the received signal. One of the techniques to achieve this goal is the direct sequence spread spectrum (DSSS) technique, which consists in binary phase shift keying (BPSK) according to a pseudo-random spreading sequence. This paper describes the DSSS data transmission tests in the simulation and experimental environment, using different types of pseudo-noise sequences: m-sequences and Kasami codes of the order 6 and 8. The transmitted signals are of different bandwidth and the detection at the receiver side was performed using two detection methods: non-differential and differential. The performed experiments allowed to draw important conclusions for the designing of a physical layer of the shallow-water UAC system. Both, m-sequences and Kasami codes allow to achieve a similar bit error rate, which at best was less than 10 −3. At the same time, the 6th order sequences are not long enough to achieve an acceptable BER under strong multipath conditions. In the case of transmission of wideband signals the differential detection algorithm allows to achieve a significantly better BER (less than 10 −2) than nondifferential one (BER not less than 10 −1). In the case of narrowband signals the simulation tests have shown that the non-differential algorithm gives a better BER, but experimental tests under conditions of strong multipath propagation did not confirm it. The differential algorithm allowed to achieve a BER less than 10 −2 in experimental tests, while the second algorithm allowed to obtain, at best, a BER less than 10 −1. In addition, two indicators have been proposed for a rough assessment which of the detection algorithms under current propagation conditions in the channel will allow to obtain a better BER.

Shock wave induced by the collapse of a bubble cluster with each bubble distributed randomly

The phenomenon of bubble collapse is ubiquitous in both natural and industrial settings, often manifesting in the form of bubble clusters. Despite its prevalence, there has been limited research on the dynamics of bubble clusters. In order to gain a better understanding of shock wave emission, liquid jet propagation, and the resulting pressure loads during bubble cluster collapse, we have developed a high-fidelity numerical approach aimed at accurately capturing shock waves and phase interfaces. The interface compression technique is introduced into the compressible two-phase model to improve the sharpness of the phase interface. We solve the physical model using the BVD (Boundary Variation Diminishing) principle. Both the 5th order WENO (Weighted Essentially Non-Oscillatory) scheme and the interface capturing function THINC (Tangent of Hyperbola for INterface Capturing) are utilized to reconstruct primary variables at cell boundaries, effectively minimizing numerical dissipation. For further resolution improvement, we implement these numerical methods on the AMR (Adaptive Mesh Refinement) mesh. Our numerical results demonstrate that the distance between the wall and the bubble cluster, as well as the nearest bubble to the wall, significantly influence the wall peak pressure. However, they have a minimal impact on the overall evolution of the bubble cluster and the peak pressure induced in the flow field. Remarkably, the spatial distribution of bubbles and the total number of bubbles play a crucial role in shaping the dynamic behavior of the bubble cluster and the pressure loads exerted both on the solid wall and in the flow field. The crucial findings offer profound insights into a range of applications, including cavitation erosion, underwater explosions, and drug delivery.

Scattering spectra models for physics.

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a pointwise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multiscale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to fourth order. The scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

Cross element integration for superconvergent frequency computation with cubic isogeometric formulation

A superconvergent cross element integration technique is presented for the cubic isogeometric formulation referring to the frequency computation of wave equations. More specifically, a four-element integration cell with 11-point quadrature and an intermediate two-element integration cell with 6-point quadrature are developed in accordance with the optimization of discrete isogeometric frequency error. These cross-element quadrature rules stand in sharp contrast to the conventional 4-point element based integration for the cubic isogeometric formulation, which needs 16 quadrature points within four elements per spatial dimension, especially for multi-dimensional scenarios. Meanwhile, a superconvergence with two added accuracy orders upon the 6th order accurate standard cubic isogeometric approach is naturally embedded in the proposed cross element integration technique by construction. Consequently, both efficiency and accuracy advantages are simultaneously realized in the proposed cross element integration method for cubic isogeometric formulation. The efficacy of the proposed superconvergent methodology is consistently validated by several representative numerical examples.

Comparative study of CUDA-based parallel programming in C and Python for GPU acceleration of the 4th order Runge-Kutta method

In this paper, a comparative study is presented on the application of General-purpose Computing on Graphics Processing Units for solving the point reactor kinetics equations through the utilization of the 4th Order Runge-Kutta (RK4) method using the programming languages C and Python. Sequential and parallel algorithms of the RK4 method were developed in C/C++ and Python, with parallel algorithms specifically designed to operate on Graphics Processing Units (GPUs) utilizing the NVIDIA Compute Unified Device Architecture (CUDA) as the programming platform. As an experiment, the execution time for the sequential and parallel algorithms were compared for a reactivity value of ρ = 0.003 and a simulation time of t = 100 s. The parallel C and Python algorithms achieved, respectively, speedups of 9.33 and 409.7 when comparing the execution time on the best GPU utilized (RTX 3070Ti) with the best CPU (3600XT), while still maintaining numerical precision.

Longitudinally continuous varying high-order cylindrical vector fields enabled by spin-decoupled metasurfaces

Abstract The manipulation of vector optical fields in three-dimensional (3D) space plays a vital role in both fundamental research and practical implementations of polarization optics. However, existing studies mostly focus on 3D vector optical fields with limited modes. Here, an approach of spin-decoupled spatial partitioning is proposed to generate complex 3D vector optical fields with a customizable number of modes on demand. The crosstalk among different modes is effectively suppressed by the decoupling capability of asymmetric photonic spin–orbit interactions (PSOIs) and the design of region displacement for opposite spin states. As a proof-of-concept demonstration, a metasurface is designed to generate longitudinally varying high-order cylindrical vector fields, ranging from the 2nd to the 10th order in even sequences along the propagation direction. The experimental results demonstrate the effectiveness and potential of our approach to enabling precise control of 3D vector optical fields with arbitrary mode combinations. This work holds promising applications in biophotonics, quantum optics, and communications.

Exploring landscape and geologic controls on spatial patterning of streambank groundwater discharge in a mixed land use watershed

AbstractPreferential groundwater discharge features along stream corridors are ecologically important at local and stream network scales, yet we lack quantification of the multiscale controls on the spatial patterning of groundwater discharge. Here we identify physical attributes that best explain variation in the presence and lateral extent of preferential groundwater discharges along two 5th order streams, the Housatonic and Farmington Rivers, and 32 1st to 4th order reaches across the Farmington River network. We mapped locations of preferential groundwater discharge exposed along streambanks using handheld thermal infrared cameras paired with high‐resolution topographic and land use land cover datasets, surficial soil characteristic maps, and depth‐to‐bedrock geophysical measurements. The unconfined Housatonic River, MA, USA (12 km) had fewer discharge locations and less lateral extent (41 discharge locations with 38 m of active discharge/km of river) compared to the partially confined Farmington River, CT, USA (26 km; 169 discharge locations with 129 m of active discharge/km of river). Using a moving window analysis, we found along both rivers that discharge was more likely to occur where bank slopes were steeper, floodplain extent was narrower, and degree of confinement was higher. Along the Farmington River, groundwater discharge was more likely to occur where saturated hydraulic conductivity was higher and depth‐to‐bedrock was shallower. Among the 32 stream reaches surveyed (33.2 km of total stream length) within the Farmington River watershed, preferential discharge was observed in all but two stream reaches, varied from 0 to 25% of lateral extent along stream banks (mean = 6%), and was more likely to occur where stream reach slopes were steep, saturated hydraulic conductivity was high, and watershed urbanization was low. Our results show that, though both surface (e.g., topographic, land use land cover) and subsurface (e.g., soil characteristics, bedrock depth) factors control the prevalence of streambank preferential groundwater discharge, the dominant controls vary across valley settings and stream sizes.

A gradient reproducing kernel based stabilized collocation method for the 5th order Korteweg–de Vries equations

This paper presents a gradient reproducing kernel based stabilized collocation method (GRK-SCM) to solve the generalized nonlinear 5th order Korteweg–de Vries (KdV) equations. By introducing gradient reproducing kernel (GRK) approximations, one can circumvent the intricacy of high-order derivatives in RK approximations, while still satisfying high-order consistency requirements. This leads to the high accuracy and efficiency. GRKs are very good approximation candidates for addressing high order partial differential equations that require higher order derivatives formulated as strong form. The stabilized collocation method (SCM) effectively meets high-order integration constraints which can achieve accurate integration in the subdomains. This ensures both high precision and optimal convergence. Von Neumann analysis is utilized to establish the stability criteria for GRK-SCM when combined with forward difference temporal discretization. Numerical solutions for Sawada–Kotera (SK) equation and Kaup-Kupershmidt (KK) equation are studied where the solitary wave migration and collision, and periodic waves are represented. A fifth order forced KdV equation is also considered. The presented method's high accuracy and convergence are demonstrated through comparative studies with analytical solutions, and investigations of invariants and corresponding errors determine the good conservation properties of this algorithm.

Effects of tree size and organ age on variations in carbon, nitrogen, and phosphorus stoichiometry in Pinus koraiensis

Carbon (C), nitrogen (N), and phosphorus (P) are of fundamental importance for growth and nutrient dynamics within plant organs and deserve more attention at regional to global scales. However, our knowledge of how these nutrients vary with tree size, organ age, or root order at the individual level remains limited. We determined C, N, and P contents and their stoichiometric ratios (i.e., nutrient traits) in needles, branches, and fine roots at different organ ages (0–3-year-old needles and branches) and root orders (1st–4th order roots) from 64 Pinus koraiensis of varying size (Diameter at breast height ranged from 0.3 to 100 cm) in northeast China. Soil factors were also measured. The results show that nutrient traits were regulated by tree size, organ age, or root order rather than soil factors. At a whole-plant level, nutrient traits decreased in needles and fine roots but increased in branches with tree size. At the organ level, age or root order had a negative effect on C, N, and P and a positive effect on stoichiometric ratios. Our results demonstrate that nutrient variations are closely related to organ-specific functions and ecophysiological processes at an individual level. It is suggested that the nutrient acquisition strategy by younger trees and organ fractions with higher nutrient content is for survival. Conversely, nutrient storage strategy in older trees and organ fractions are mainly for steady growth. Our results clarified the nutrient utilization strategies during tree and organ ontogeny and suggest that tree size and organ age or root order should be simultaneously considered to understand the complexities of nutrient variations.

Comparison of modal and zonal wavefront measurements of refractive extended depth of focus intraocular lenses.

Extended depth-of-focus (EDoF) intraocular lenses (IOLs) are typically evaluated using commercially available aberrometers. Given the intricate optical design of these IOLs, employing an appropriate wavefront reconstruction method with a sufficient sampling resolution of the aberrometer is crucial. A high-resolution Shack-Hartmann wavefront sensor was developed by magnifying the pupil aperture by a factor of five onto a lenslet array (pitch: 133 µm) and utilizing a full-frame CMOS sensor (24 by 36 mm), resulting in a 26.6 µm sampling resolution. Zonal wavefront reconstruction was used and compared with Zernike-based modal wavefront reconstruction to retain detailed local slope irregularities. Four refractive EDoF IOLs with a power of 20D were examined, and the wavefront difference between the zonal and modal methods, expressed as the root mean squared error (RMSE), remained significant for two of the IOLs up to the 16th-order Zernike spherical aberrations (SAs). Conversely, a negligibly small RMSE was observed for the other two IOLs, as long as the Zernike SAs were higher than the 6th order. The raytracing simulation results from the zonal wavefronts exhibited a stronger correlation with the results of recent optical bench studies than those from the modal wavefronts. The study suggests that certain recent refractive EDoF IOLs possess a complex optical profile that cannot be adequately characterized by limited orders of SAs.

Flow separation and stability analysis for aligned magnetic field in a porous medium saturated by a titanium alloy nanofluid

ABSTRACT This article examines Joule heating and aligned magnetic field in a porous medium saturated by Ti-alloy nanofluid. The heat generation and first-order velocity slip towards an exponentially permeable shrinking surface are taken. Non-dimensional forms of the resulting flow equations are solved numerically for multiple solutions using the shooting technique along with the Runge–Kutta method of 4th order in MATLAB(R2021a). The stability of the resultant system of equations is verified through the smallest eigenvalue approach. Both the first and second solutions of correlation streamline profiles are extracted for appropriate values of physical parameters. By stability analysis, the first solution is unquestionably more stable than the second solution. The major outcome is that the Joule heating raises the fluid’s temperature. The presence of flow separation is identified in the shrinking regions and the delay of boundary layer separation is pointed out. These analyses play a significant role in the fields of aerodynamics, medicine, and space sciences.

Dissipative MHD flow of ternary‐hybrid nanofluid over an inclined stretching sheet with heat source and mass flux due to temperature gradient

AbstractAn analysis has been made to illuminate the unsteady MHD slip flow of ternary‐hybrid nanofluid of water conveying spherical Cu, cylindrical Al2O3, and platelet Ag nanoparticles over an inclined stretching sheet. The above complex scenario explores how the presence of a magnetic field affects the behavior of ternary‐hybrid nanofluid over an inclined stretching surface. Understanding this interaction is crucial in advanced thermal systems like cooling mechanisms and energy generation technologies. The study can provide insights into optimizing heat transfer rates, enhancing thermal conductivity and improving efficiency in practical applications by manipulating the flow characteristics and temperature distribution in the system. The heat transfer has been analyzed incorporating Darcy dissipation and heat source in the presence of 1st order velocity slip. The presence of Soret effect makes the study more congenial. Using similarity transformation technique, the governing partial differential equations are converted into a system of ordinary differential equations. The reduced system is dealt with 4th order Runge–Kutta method with shooting technique. The comparison with earlier results gives a reliability of present results. The important findings are: velocity of the flow decelerates for higher values of 1st order slip parameter, velocity of the flow increases with increase in Soret number, increasing values of chemical reaction parameter lead to lower concentration in both the cases, that is, with or without velocity slip.