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This study introduces a novel approach to achieving nonreciprocal transmission by implementing time modulation to the bianisotropic metasurface. For the first time, we present the analytical solution of the excitation of anti-symmetric surface waves on penetrable metasurfaces depending on the excitation direction. Exploiting this finding, we numerically demonstrate asymmetric control of the transmission coefficient under a fast-time scale by employing solely time modulation. This approach lowers the complexity of the modulation scheme and implementation encountered in the space-time modulation technique. We develop and simulate a 3D unit cell model in the microwave domain, which forms a surface cavity that incorporates time-varying capacitors. The impedance transfer matrix method and harmonic balance numerical solutions are applied to the retrieved equivalent circuit for the numerical simulations. The results reveal optimized phase-coherent and incoherent nonreciprocal transmission at the significant isolation level (≥ 40 dB) for forward and backward transmissions. We discuss the consistency and discrepancies between numerical methods and consider the impact of the losses and nonlinearity on the metastructure performance. [ABSTRACT FROM AUTHOR]

In this paper, an exact analytical solution is presented for achieving coherent population transfer and creating arbitrary coherent superposition states in a five-state chainwise system by a train of coincident pulses. We show that the solution of a five-state chainwise system can be reduced to an equivalent three-state Λ-type one with the simplest resonant coupling under the assumption of adiabatic elimination together with a requirement of the relation among the four coincident pulses. In this method, the four coincident pulses at each step all have the same time dependence, but with specific magnitudes. The results show that, by using a train of appropriately coincident pulses, this technique not only enables complete population transfer, but also creates any desired coherent superposition between the initial and final states, while the population in all intermediate states is effectively suppressed. Furthermore, this technique can also exhibit a one-way population transfer behavior. The results are of potential interest in applications where high-fidelity multi-state quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, nuclear coherent population transfer, and light transfer in waveguide arrays. [ABSTRACT FROM AUTHOR]

An analytical linearized mean-field theory is presented to describe the adsorption behavior of polyelectrolytes near charged colloidal surfaces with additional short-ranged non-electrostatic interactions. The coupling between the polyelectrolyte segment density and electrostatic potential is explicitly accounted for in a self-consistent manner. This coupling gives rise to highly non-linear behavior, such as oscillations of the electrostatic potential. We derive analytical expressions for the critical surface charge density σc, after which adsorption takes place, and recover the well-known σ c ∼ n s 3 / 2 scaling regime, where ns is the salt concentration. In addition, the theory yields a new n s 1 scaling regime if the surface is hard and a unified n s 1 scaling regime if the surface also possesses some short-ranged attraction with the polyelectrolyte. Furthermore, we derive an analytical expression to describe the critical polyelectrolyte concentration φc to achieve complete charge reversal, which is found to scale as φc ∼ σ2/(f2c2), where c is related to the magnitude of short-ranged interactions and f is the average charge per monomer of the polyelectrolyte. It is observed that within our theory, complete charge reversal can only take place if the short-ranged interactions are sufficiently strong to completely compensate for the entropy loss of adsorption. [ABSTRACT FROM AUTHOR]

Narrow escape theory deals with the first passage of a particle diffusing in a cavity with small circular windows on the cavity wall to one of the windows. Assuming that (i) the cavity has no size anisotropy and (ii) all windows are sufficiently far away from each other, the theory provides an analytical expression for the particle mean first-passage time (MFPT) to one of the windows. This expression shows that the MFPT depends on the only global parameter of the cavity, its volume, independent of the cavity shape, and is inversely proportional to the product of the particle diffusivity and the sum of the window radii. Amazing simplicity and universality of this result raises the question of the range of its applicability. To shed some light on this issue, we study the narrow escape problem in a cylindrical cavity of arbitrary size anisotropy with two small windows arbitrarily located on the cavity side wall. We derive an approximate analytical solution for the MFPT, which smoothly goes from the conventional narrow escape solution in an isotropic cavity when the windows are sufficiently far away from each other to a qualitatively different solution in a long cylindrical cavity (the cavity length significantly exceeds its radius). Our solution demonstrates the mutual influence of the windows on the MFPT and shows how it depends on the inter-window distance. A key step in finding the solution is an approximate replacement of the initial three-dimensional problem by an equivalent one-dimensional one, where the particle diffuses along the cavity axis and the small absorbing windows are modeled by delta-function sinks. Brownian dynamics simulations are used to establish the range of applicability of our approximate approach and to learn what it means that the two windows are far away from each other. [ABSTRACT FROM AUTHOR]

Inventory planning in fashion markets is highly challenging, owing to uncertain demand; yet, in making inventory decisions, retailers may be able to capitalise on high substitutability between products. This research develops single-period inventory-management models describing a market with two substitutable products, under stockout-based substitution; i.e. when a customer's preferred product is out-of-stock, s/he may choose to purchase the substitute. Two settings are considered: centralised (a single retailer who sells both products) and competitive (two retailers, each selling one product). For each setting, we derive closed-form analytical solutions for the inventory levels that maximise expected profit. The model is further enriched with sales data from an online apparel retailer offering substitutable products (a sneaker in different colours), and we analyse the sensitivity of the optimal inventory levels and profits to parameter values. Key findings include the following: (i) Under competitive conditions, both retailers always order positive inventory so as not to lose customers. However, in a single-retailer setting, there are situations in which the retailer orders inventory for only one product. (ii) The optimal inventory levels and corresponding profits are highly sensitive to consumers' willingness to substitute between products. These findings provide concrete insights that can guide fashion brands' inventory-management decisions. [ABSTRACT FROM AUTHOR]

This paper presents a new conformal mapping method to solve 2D Laplace and Poisson equations in MOS devices. More specifically, it consists of an analytical solution of the 2D Laplace equation in a rectangular domain with Dirichlet boundary conditions, with arbitrary values on the boundaries. The advantages of the new method are that all four edges of the rectangle are taken into account and the solution consists of closed-form analytical expressions, which make it fast and suitable for compact modeling. The new model was validated against other similar methods. It was found that the new model is much faster, easier to implement, and avoids many numerical issues, especially near the boundaries, at the cost of a very small loss in accuracy. [ABSTRACT FROM AUTHOR]

The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled Fick-type partial differential equations and a mass exchange term connecting the diffusivities, is a paradigm in modeling mass transport in inhomogeneous media, e.g., fissures or fractures. Uncoupling of these equations led to a higher order partial differential equation that reproduced the non-classical transport terms, analyzed independently through Barenblatt's pseudoparabolic equation and the Cahn–Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction–diffusion (R–D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models. [ABSTRACT FROM AUTHOR]

This study looked for a way to evaluate the validity of previously suggested models for describing the spin-selective recombination of radical pairs. As an example, for analysis, we used the conventional model, the model by Jones and Hore [Chem. Phys. Lett. 488, 90 (2010)], and the model by Salikhov [Am. J. Phys. Chem. 11, 67 (2022)]. To do this, analytical solutions to the evolution of the radical pair density matrix due to a radical pair's spin-selective recombination and singlet–triplet transitions in a strong magnetic field were obtained for the conventional model and the Jones and Hore model. Spin interactions included in the Hamiltonian were time-independent exchange interactions as well as Zeeman and hyperfine interactions. The most striking difference between the models' predictions appeared when considering the fraction of singlet pairs among all currently existing ones. In the Jones and Hore model, this ratio has the form of damped oscillations for any values of the spin-hamiltonian parameters. The conventional model and the Salikhov model both predicted that this ratio had the form of undamped oscillations in the absence of exchange interaction and at a sufficiently low recombination rate. Besides, the conventional model predicts the possibility of a resonance-like behavior of this ratio when singlet–triplet transitions in a part of the radical pair ensemble are completely suppressed by tuning the magnetic field strength. Possible experimental conditions in which distinguishing between the models seems to be most straightforward were suggested. [ABSTRACT FROM AUTHOR]

The classical three-stage model of stochastic gene expression predicts the statistics of single cell mRNA and protein number fluctuations as a function of the rates of promoter switching, transcription, translation, degradation and dilution. While this model is easily simulated, its analytical solution remains an unsolved problem. Here we modify this model to explicitly include cell-cycle dynamics and then derive an exact solution for the time-dependent joint distribution of mRNA and protein numbers. We show large differences between this model and the classical model which captures cell-cycle effects implicitly via effective first-order dilution reactions. In particular we find that the Fano factor of protein numbers calculated from a population snapshot measurement are underestimated by the classical model whereas the correlation between mRNA and protein can be either over- or underestimated, depending on the timescales of mRNA degradation and promoter switching relative to the mean cell-cycle duration time. [ABSTRACT FROM AUTHOR]

The aim of this study is to suggest a novel approach for estimating the intramolecular mobility of a charge carrier that migrates within a polymer chain and is involved in a pair reaction with a particle located on the same chain. The approach is based on the effect of an external electric field on the migration rate and, consequently, the kinetics of the reaction. As a first step, this problem is considered a stochastic one-step process with absorbing and reflecting boundaries, and an analytical solution is obtained in the case that the second reactant is immobile. With the use of computer simulations of stochastic migration, the effect of the mobility of both reactants and the influence of the Coulomb interaction between them are considered. It is found that the ratio of the pair reaction rates with and without an external field is relatively little dependent on these factors and that the analytical expressions derived can be applied to estimate the relative mobility of recombining particles with accuracy better than a factor of two in many realistic situations. [ABSTRACT FROM AUTHOR]

This paper proposes analytical solutions for the resonant radiation performance of bending-mode magnetoelectric (ME) antennas. The strain-mediated Converse ME (CME) coupling model of bending-mode ME antennas is first established by solving nonlinear constitutive equations and bending governing equations using the elastic mechanics method. Then, the calculated magnetic flux and electric displacement are employed to propose a resonant radiation field model based on the dipole method. The numerical results for the CME coefficient show a good agreement with the experimental data. It can be observed that the volume fraction ratio of the piezoelectric layer can control the CME coefficient and radiation efficiency with the same variation trend since it can determine the bending strain via changing the location of the neutral layer of the ME antennas, which also demonstrates the strain-mediated essence of the ME antennas. In addition, the volume fraction ratio can tune the resonant frequency within a wide range. The gain of the ME antenna is stable and higher than −168 dB with the volume fraction ratio ranging from 0.2 to 0.7. The tensile stress and compressive stress have the opposite effect on the resonant frequency at low and high bias magnetic fields. Meanwhile, the tensile (compressive) stress is beneficial for both the radiation and gain in the low (high) bias field region. This model may facilitate the understanding of the bending-mode radiation mechanism of ME antennas and provide a basis for designing asymmetric ME antennas. [ABSTRACT FROM AUTHOR]

While characterizing space-charge-limited current (SCLC) is important for numerous applications, no analytical solutions for SCLC with monoenergetic initial velocity exist for two-dimensional (2D) geometries. Here, we derive approximate closed-form solutions for uniform SCLC with monoenergetic emission of electrons in a 2D planar diode, where emission is restricted to a long patch of width W for electrodes separated by a distance D. We also derive a semiempirical approach for estimating the SCLC for these cases by treating the geometric and velocity correction factors as multiplicative corrections to the SCLC for a one-dimensional vacuum diode given by the Child–Langmuir (CL) law. We show that the SCLC for a finite patch with nonzero velocity can exceed the CL law by three orders of magnitude. The theoretically calculated SCLCs for various emission widths and initial velocities in the 2D diode agree well with particle-in-cell simulations using the over-injection method in XOOPIC; they agree with the semiempirical relationship for lower initial velocities. In the limit of high initial velocity, the geometry and velocity corrections to the CL law cannot be decoupled, invalidating the assumption of the semiempirical approach and causing it to diverge from the theoretical solution and XOOPIC simulations. These results provide valuable estimates for determining the onset of virtual cathode formation for photocathodes and thermionic cathodes, which operate in the over-injection regime to avoid beam quality degradation. [ABSTRACT FROM AUTHOR]

Solid–liquid friction plays a key role in nanofluidic systems. Following the pioneering work of Bocquet and Barrat, who proposed to extract the friction coefficient (FC) from the plateau of the Green–Kubo (GK) integral of the solid–liquid shear force autocorrelation, the so-called plateau problem has been identified when applying the method to finite-sized molecular dynamics simulations, e.g., with a liquid confined between parallel solid walls. A variety of approaches have been developed to overcome this problem. Here, we propose another method that is easy to implement, makes no assumptions about the time dependence of the friction kernel, does not require the hydrodynamic system width as an input, and is applicable to a wide range of interfaces. In this method, the FC is evaluated by fitting the GK integral for the timescale range where it slowly decays with time. The fitting function was derived based on an analytical solution of the hydrodynamics equations [Oga et al., Phys. Rev. Res. 3, L032019 (2021)], assuming that the timescales related to the friction kernel and the bulk viscous dissipation can be separated. By comparing the results with those of other GK-based methods and non-equilibrium molecular dynamics, we show that the FC is extracted with excellent accuracy by the present method, even in wettability regimes where other GK-based methods suffer from the plateau problem. Finally, the method is also applicable to grooved solid walls, where the GK integral displays complex behavior at short times. [ABSTRACT FROM AUTHOR]

The important character of the applied moment with a fixed line of direction as implied in deriving the governing differential equations of LTB for elastic beams, however, is not represented in stating the boundary conditions based on conventional energy approaches. This paper sets out to consider the boundary conditions derived by conventional potentials in order to identify the ignored second-order moments that need to be added for maintaining the initial direction of the applied moment during LTB. By taking into account the non-zero work done by these ignored moments for modifying original potentials, the nonconservative nature of the elastic LTB of beam under external moments is clarified in two aspects — by discovering the path-dependent property of the non-zero work and by demonstrating that only trivial solution of LTB mode is expected from the analytical solution of the governing differential equations. Using the concept of dynamic instability, an analysis procedure combining the numerical solution of an eigen-value problem and the bisection method is proposed to identify the first appearance of imaginary or conjugate complex frequencies and to determine the value of the critical moment. Demonstrative examples are considered for illuminating the elastic LTB behavior using conventional energy methods and revised virtual work equation. It has been found that the critical moments given by conventional potentials are generally not consistent with each other unless the work done by the ignored second-order moments vanishes. However, consistent critical moment, under which the free vibrating amplitude of elastic beam is increased unboundedly with time, can be obtained by the kinetic approach based on any revised virtual work equation, indicating the necessity of considering the nonconservative nature of non-follower applied moment. [ABSTRACT FROM AUTHOR]

This article proposes the use of the Karhunen Loève expansion in the design of computer experiments when the Gaussian Process (GP) model is used to model the output, Y(x). We start by finding the K-L expansion in the case of the univariate and multivariate processes. When the analytical solution does not exist, we apply several methods of approximation, such as Haar wavelet functions and Fourier expansions. Numerical examples are presented to illustrate the idea of the approximations. We use the approximated model to select the maximum entropy sampling design. [ABSTRACT FROM AUTHOR]

Modeling underground temperatures provides a practical application of the one-dimensional heat equation. In this work, the one-dimensional heat equation in surface soil is extended to include heat carried by the vertical flow of rainwater through the soil. Analytical solutions, with and without water flow, illustrate the influence of rainwater circulation on the sub-surface propagation of seasonal temperature variations, an important effect that is generally neglected in textbooks. The surface temperature variations are damped by the soil, and this effect was used by the Troglodytae in Egypt or the Petra in South Jordan to insulate against extreme temperatures. For a realistic case of horizontally layered geology, a finite volume Python code was developed for the same purpose. Subsurface temperatures were also measured over a full year at depths up to 1.8 m and used to estimate the thermal skin depth and thermal wavelength. This study provides students with a practical example of how a textbook physics problem can be modified to extract information of contemporary importance in geophysics and global warming. Editor's Note: Frequently, modeling the three-dimensional world is too challenging for a class exercise, and we instead teach students using unrealistic one-dimensional problems. So it is wonderful when a one-dimensional model turns out not only to be fairly accurate, but also to have real world implications. That is the case with heat flow through the soil, which can be treated with a one-dimensional model, and which is important to energy-efficient solutions such as underground housing and ground-source heat pumps. This paper finds the underground temperature as a function of depth through measurements, analytical solutions, and computational solutions. These solutions can form the basis for a very interesting class assignment. In addition to considering heat transport through conduction, the model also includes heat transport through the flow of rain water. [ABSTRACT FROM AUTHOR]

Drawing upon the fundamental principles of mixture continuum and thermodynamics, planar S-wave incident model for layered unsaturated soil is formulated. Employing the Helmholtz vector decomposition principle, the wave field within the layered unsaturated soil is analyzed using the transfer matrix method, accounting for the influence of thermal effects. An analytical solution is obtained for the seismic response in layered unsaturated soil under the action of thermal effect. The results of the numerical analyses show that the thermo-physical parameters such as relative heat of solid, temperature, and thermal expansion coefficient have a notable effect on the seismic response of the site. [ABSTRACT FROM AUTHOR]

An extensive investigation into the bending behavior of nanoshells made of coated functionally graded (FG) carbon nanotubes reinforced composites has been conducted, employing a novel spatial variation in material properties. The study explored Hardcore and Softcore of coated FG nanoshells. The examination includes five distribution patterns: a fully coated tri-directional, two bidirectional patterns, a transverse unidirectional, and an axial unidirectional distribution. The shell is resting on an orthotropic Winkler, Pasternak and Kerr foundations. Galerkin method is employed to establish an analytical solution for the equilibrium equations. This approach is designed to accommodate a variety of different boundary conditions. A comprehensive examination is undertaken to demonstrate the effects of various geometric and material parameters on the deflection and stresses of nanoshells. [ABSTRACT FROM AUTHOR]

Analytical solutions for functionally graded (FG) rotating disks are limited due to the functional representation of the cross-sectional geometry, the density, and the modulus of elasticity which lead to a governing differental equation with variable coefficients. Analytical solutions for such disks are limited according to the functional form chosen for the variation of the property. Hence, analytical approximation approaches gain importance for such problems. In this study, two analytical approximation approaches are proposed for the analysis FG rotating disks. The methods used are the Improved Adomian decomposition method (IADM) and the optimal homotopy asymptotic method (OHAM). The resulting solution is an analytical solution in power series form. It is assumed that the disks considered are subjected to constant angular velocity. Material properties such as modulus of elasticity, density and yield strength are assumed to vary along the radial direction according to the power law function. Stresses are obtained for different values of the gradient parameters to investigate the effects of the parameters. Von Mises yield criterion is used to determine elastic limit angular velocities. The results from this study are in very good agreement with previous results available in the literature. In addition, it is observed that OHAM converges to results much faster than IADM. [ABSTRACT FROM AUTHOR]

Stone column technology is a method used to reduce liquefaction in saturated sediments. By using materials with greater permeability than the surrounding soil, stone columns can help drain excess pore water pressure and mitigate liquefaction potential during seismic loading. In this study, analytical solutions are proposed to address the liquefaction problem in saturated soils during earthquakes, taking into account the influence of stone columns and the surrounding soil. These solutions consider the excess pore water pressure at the boundary of the zones and analyze the vertical and horizontal drainages. The study also includes centrifuge tests on sandy soils improved with stone columns, calculating the total seepage flow and converting it into settlement based on the relationship between drainage flow rate and volumetric changes in the soil. The calculated settlement aligns well with the measured value in the centrifuge test, confirming the accuracy of the analytical formula for calculating settlement in stone column foundations. The study also evaluates the combined effects of radial and vertical drainages in stone column foundations using the derived analytical solutions. [ABSTRACT FROM AUTHOR]

Vertical drains installed in soft clay deposits enhance the rate of consolidation in preloading projects. Using a mandrel to install the prefabricated vertical drains, its insertion and withdrawal will result in the remoulding of the soil zone surrounding it, called the smear zone. The extent of the smear zone is an important parameter that characterises the smearing effect. This paper describes this effect in terms of smear ratio (i.e. the ratio of the diameter of smear zone ds to the diameter of drain, dw) on the consolidation characteristics of soil with radial drainage. A series of radial consolidation tests with a predetermined smear zone in a model unit cell was conducted by varying the diameter of the smear zone. The experimental results show that beyond a smear ratio of 4, the soil behaves as if it is in a fully remoulded condition. The results were compared with some of the theoretical approaches reported in the literature. The analytical solution that predicts the time–settlement curve in a better way is identified. Also, it is observed that the gain in undrained shear strength due to the consolidation of soft clay decreases with the increase in the diameter of the smear. [ABSTRACT FROM AUTHOR]

In this work, a finite element-meshless coupling method for modeling the inhomogeneous structures composed of functionally graded materials is presented. Coupling the two methods is usually based on the continuity and equilibrium conditions at the finite element-meshless interface. In the proposed hybrid method, the equilibrium condition is satisfied by the action-reaction principle to ensure the coupling between the finite element method and the strong-form meshless method. The idea is to satisfy the equilibrium condition by calculating the interface force vector in the finite element formulation using a strong-form meshless technique. In the weak formulation the forces are modeled by the interface force functional. This hybrid method has been used to study the behavior of functionally graded materials in small deformations, with a comparison between the results of other numerical methods and those of analytical solutions. Following this validation, the hybrid numerical approach is adapted to the simulation of static computational problems for inhomogeneous functionally graded materials with geometric nonlinearity. In this context, a high-order algorithm has been developed by associating a high-order development, continuation procedure and hybrid method. Numerical analysis is performed to prove the accuracy and efficiency of the present approach, through a comparative study with solutions provided by high-order algorithms derived from the finite element method and strong-form meshless methods. In addition, the good qualities of the solution are controlled by the residues, which do not exceed 10 − 6. [ABSTRACT FROM AUTHOR]

In the process of lightweight design, there will be problems such as stress concentration and structural weakening. In order to improve the design defect of serious insufficient life caused by the bending failure of worm gear, the bending stress of worm gear tooth root was analyzed by solution method and finite element simulation method. The main research contents include: firstly, the bending stress of worm gear is calculated by analytical solution method; Secondly, CAD is used to reconstruct the model; Finally, HyperMesh is used for analysis of the structure. The maximum bending stress obtained from theoretical calculation is 34.56Mpa, and the maximum stress from simulation is 39.3Mpa, 29.6Mpa and 26.3Mpa respectively in the three areas of gear root A, B and C (figure 7). Compared with the finite element, the maximum stress difference between them is 4.74Mpa. The stress concentration point is determined, and the structure optimization is carried out; CAE analysis of the optimized model shows that stresses in A, B and C regions of the worm gear root are 33.4 MPa, 22.5 MPa and 5.9 MPa, respectively. After optimization, the maximum stress difference between the two is 1.16Mpa.The above analysis results provide theoretical support for the design of worm gear reducer. [ABSTRACT FROM AUTHOR]

Droplet evaporation occurs in many natural phenomena and industrial processes; hence, several studies have been conducted on droplet evaporation. In many applications, a group of droplets evaporate and the interaction between them affects the evaporation process. In this paper, the front-tracking method is used to simulate the droplets groups evaporation. Since the front-tracking method uses a Lagrangian grid for each droplet, this method offers good accuracy in predicting the shape, the displacement and the evaporation rate of droplets. The numerical method has been developed to simulate the evaporation of binary droplets. The fluid surrounding the droplets is modeled as a gas mixture, so the numerical method can be used to simulate multiphase-multicomponent problems. The front-tracking method requires very fine grid resolution to simulate flows at high-density ratios; therefore, the method is rarely used at high-density ratios. In this paper, a two-step method is used to move the front at high-density ratios without requiring a very fine grid resolution. First, a static droplet evaporation is simulated, and the results are compared with the analytical solutions; evaporation of a Decane droplet is then simulated, and the results are compared with the experimental data. Subsequently, the evaporation of a binary droplet is modeled. The evaporation of a group of static droplets is also simulated, and the effect of droplets interaction is investigated. Next, the evaporation of three injected droplets is simulated, and the effect of some parameters on droplets interaction is probed. The evaporation rate and displacement of each droplet are calculated and compared with the single droplet. Finally, the evaporation of the groups of droplets is simulated, and the effect of different arrangements of droplets on the evaporation rate is studied. Understanding the droplets interactions is helpful in predicting droplet spray behavior and developing numerical methods. Thus, the presented results are useful to achieve a better understanding of the droplets interaction phenomenon, its outcomes, and the parameters affecting evaporation rate. [ABSTRACT FROM AUTHOR]

Uneven settlement of the strata induced by ground fissure activity trigger great damage to a shield tunnel crossing a ground fissure zone. It is of great significance for the safe maintenance of tunnels to accurately predict the mechanical response of the tunnel structure under the dislocation of a ground fissure. In this paper, an analytical solution of mechanical behaviors of a shield tunnel crossing an active ground fissure zone is proposed. The shield tunnel-strata interaction in a ground fissure site is simplified as a Timoshenko beam placed on a Vlasov foundation. The governing differential equation and the closed-form solution for an equivalent shield tunnel subjected to additional load induced by the dislocation of ground fissure are derived. The proposed solution is adopted to analyze the mechanical behaviors of a shield tunnel, including tunnel displacement, rotation, bending moment, and shear force. The results of a model test and a numerical model are provided to verify the rationality of the proposed analytical solutions. Finally, a parameter sensitivity analysis about the additional load forms, the compression and shear modulus of the foundation, and the shear stiffness coefficients of the tunnel are conducted. The result shows that the form and value of the additional load has a large impact on the deformation and a slight impact on the internal forces of the tunnel. The foundation compression modulus determines the constraint effect of the strata, and the deformation and internal force response of a tunnel decrease with the increasing foundation shear modulus. In addition, the increase of shear coefficient enhances the shear stiffness of a tunnel, but largely increases the internal force as well. [ABSTRACT FROM AUTHOR]

Rainfall erosion can cause environmental and economic damage by decreasing the storage capacity of water reservoirs because of the detachment of soil particles. The purpose of this study was to develop a one-dimensional physicomathematical model that can help predict the effects of rainfall erosion on the banks of water reservoirs. The model was developed using the Mein–Larson model to describe water infiltration, the kinematic wave approximation to represent overland flow generation, and the steady state sediment continuity equation to estimate sediment transport. The model was validated using rainfall simulator tests and lateritic soil samples with a bimodal soil–water retention curve. The results showed conformity with the experimental data, identifying a threshold in the models for discharge per unit area and sediment yield rate, as well as a linear increase in the models for total runoff and sediment load per unit area. However, the model failed to capture the peak in sediment yield rate owing to raindrop impact during the initial minutes of rainfall. Parametric analysis highlighted the impact of increasing the calibration constant of splash erosion, erodibility coefficient, and critical shear stress on the slope of the sediment load per unit area model. Despite its limitations, the model demonstrates satisfactory predictive capability for sediment load per unit area under high-intensity rainfalls, achieving an R2 greater than 0.92 in five of the six cases examined. [ABSTRACT FROM AUTHOR]

Buried pipelines subjected to permanent ground deformations (through, e.g., earthquake-induced liquefaction or fault rupture) often experience widespread damage. Regardless of the direction of ground movement, pipelines tend to respond and experience damage axially due to their directional stiffness characteristics. In addition, case studies and previous testing have shown that damage is concentrated at the pipe joints due to their lower strength compared with a pipe barrel. Previous testing has also shown that axial forces increase significantly when pipe connections have jointing mechanisms, such as coupling restraints, with larger diameters than the pipe barrel alone. These enlarged joints act as anchors along the pipe, increasing the soil resistance at these locations. Current methods for predicting the axial force along a pipe underpredict the force demands and oversimplify the mechanics of soil resistance on the joint face. This study conducts a series of 12 pipe-pull tests in a centrifuge, varying joint diameter and burial depth, to quantify the axial forces developed. A strong linear correlation was observed between the soil resistance on a joint face and the joint surface area and burial depth. The study also proposes an analytical solution based on pullout capacity design equations for vertical anchor plates as a function of soil and pipe joint properties. The proposed solution to calculate joint resistance is in good agreement with the centrifuge tests performed for this study and previous full- and model-scale experiments. The proposed prediction equation is anticipated to have future applications to other buried structures because it is based on mechanisms of passive resistance commonly encountered in underground structures and lifelines. [ABSTRACT FROM AUTHOR]

Rapid launching is a crucial technology for the digitalization and regularization of space transportation systems. This paper focuses on the fast trajectory prediction of the launch-vehicle boost phase. A high-precision and high-efficiency analytical solution of the whole boost phase dynamics model of the rocket is obtained by adopting one of the regular perturbation methods called the state-space perturbation method in the launch rotated coordinate system. An analytical framework known as the perturbation expansion framework is proposed by first figuring out the correlation with the state variables/independent variables and then performing the approximate expansion. This framework can successfully address the issue of analytically solving the transfer matrix and integral term caused by the coupling and time-varying properties among state variables of the affine equations of the boost phase. The analytical solution developed in this paper has great fidelity and takes into account the combined effects of various factors, including thrust, aerodynamic force, Earth's gravity, oblateness, and rotation. It can serve as a theoretical guide for the rapid launch requirements and iterative design processes for early rocket demonstrations in engineering. [ABSTRACT FROM AUTHOR]

This article studied a general analytical method for dynamical behaviors of various FG-GPLRC non-rectangular plates with a piezoelectric layer. For the first time, classical plate theory and Galerkin's method are used to scrutinize the nonlinear vibration of plates with many different shapes. Profiles of new plates are defined by four edges, specifically two parallel opposite edges, and others are assumed to horizontal change according to arbitrary functions. Linear and nonlinear vibration of plates are confirmed with results obtained by Finite Element Method. Effects of environment, material, and geometrical parameters are studied. Besides, periodic and chaotic motions of plates are investigated. [ABSTRACT FROM AUTHOR]

The DTM-Pade approximation is used in the current work to analyze the thermal behavior and thermal stresses of an annular fin while accounting for temperature-dependent thermal conductivity and internal heat generation. The energy problem is converted into a nonlinear ordinary differential equation (ODE) using non-dimensional parameters, and the DTM-Pade approximation is then utilized to provide an approximate analytical solution. The impacts of various settings on the temperature field are also graphically analyzed. It has been found that increasing the heat generation parameter causes the temperature distribution to improve. The growing thermo-geometric parameter values lead to an improvement in fin efficiency. [ABSTRACT FROM AUTHOR]

In this study, we have investigated a diabetes model and its complication using the Katugampola fractional derivative in Caputo sense. We studied a deterministic mathematical model that uses non integer derivatives to precisely depict the dynamics of diabetes mellitus. We have employed q-homotopy analysis generalized transform method (q-HAGTM) to find analytical approximate solution for presented model. Furthermore, the fixed-point theorem is employed to present the existence as well as uniqueness analysis of obtained solution for the discussed model. The obtained results are further complemented by conducting numerical simulations, providing graphical demonstrations that support and illustrate the findings. This approach enables us to understand and develop efficient ways to cure these diseases. [ABSTRACT FROM AUTHOR]

Due to the great success of hypergeometric functions, we provide the analytical solutions of certain definite logarithmic integrals and Nielsen-type integrals in terms of multi-variable Kampé de Fériet functions with suitable convergence conditions and higher harmonic sums by using series rearrangement technique and incomplete Gamma function. Further we also obtain the solution of other related logarithmic integrals in terms of generalized hypergeometric functions and Kummer’s confluent hypergeometric functions by using series rearrangement technique. The results presented in the paper and comparable outcomes are hoped to be supplied by the use of computer-aid programs, for example, Mathematica. [ABSTRACT FROM AUTHOR]

This study delves into the investigation of exact analytical solutions for the plane stress and displacement fields within linear homogeneous anisotropic nano-beam models of gradient elasticity. It focuses on solving the Helmholtz equation, which encompasses a second-order non-homogeneous linear partial differential equation in plane gradient elasticity theory, utilizing polynomial series-type solutions. The analysis centers on the utilization of gradient Airy stress functions to derive stress fields in the gradient theory. The research yields closed-form analytical solutions for Airy stress functions, stress, and strain fields in both classical and gradient theories. The study considers five distinct types of two-dimensional functionally graded cantilever beams with various boundary conditions: a cantilever anisotropic nano-beam subjected to a concentrated force at the free end, a cantilever anisotropic nano-beam under a uniform load, a simple anisotropic nano-beam under a uniform load, a propped cantilever anisotropic nano-beam under a uniform load, and a fixed end cantilever anisotropic nano-beam under a uniform load. General analytical solutions for the gradient stress and displacement fields of two-dimensional and one-dimensional anisotropic nano-beams under different boundary conditions are provided. The study showcases significant strain gradient size effects at the nano-scale through the derived analytical solutions for anisotropic beams. Additionally, it demonstrates that the strain gradient theory results for the limit case of the gradient coefficient c precisely align with results for isotropic and anisotropic materials in elasticity theory and classical theory. Furthermore, real-world applications are discussed, considering stress and displacement fields in real anisotropic materials such as TiSi 2 single crystals and orthotropic materials, which are special cases of anisotropic materials like wood and epoxy as documented in the literature. • Exact solutions for stress/displacement in gradient elasticity models for anisotropic functionally graded nano-beams. • Analysis focuses on constructing stress fields using "gradient Airy stress function" notation. • Solutions reveal significant strain gradient effects in anisotropic nano-beams. • Literature solutions for CT beams match findings by taking gradient coefficient c to zero. • Gradient stress fields vanish except in y-direction as c approaches infinity. [ABSTRACT FROM AUTHOR]

Introduction. Designing electrical substations involves analyzing the horizontal tensile force in flexible tension conductors under varying temperatures. These temperature changes affect the conductor’s length and forces. Problem. Existing methods for calculating horizontal tensile force in conductors often focus on symmetric spans or require complex finite element modeling (FEM), which is impractical for routine substation design. Asymmetric spans with tension insulators present a more complex challenge that current solutions do not adequately address. Purpose. Universal analytical solution and algorithm for calculating the horizontal tensile forces in conductors in asymmetric spans with tension insulators used in power substations or short overhead power line spans. The solution is designed to be easily implementable in software without requiring complex tools or extensive FEM. Methodology. The methodology involves deriving an analytical solution based on the catenary curve formed by the conductor between attachment points at different heights. The analysis includes calculating the conductor’s length for a given tensile force and using a state change equation to determine forces under new temperature conditions. Validation is performed using FEM calculations. Results. The proposed solution was validated against FEM models with varying height differences (5 m and 15 m) and conductor temperatures (–30 °C, –5 °C, +80 °C). The results showed a minimal error (less than 0.15 %) between the analytical solution and FEM results, demonstrating high accuracy. Originality. This paper presents a novel analytical solution to the problem of calculating tensile forces in asymmetric spans with tension insulators. Unlike existing methods, our solution is straightforward and easily implementable in any programming language. Practical value. The solution is practical for routine design tasks in electrical substations or short overhead power lines. Especially in power substations, accurate tensile forces are needed not only for mechanical design and sag calculations but also for calculating the dynamic effects of short-circuit currents. References 23, tables 4, figures 3. [ABSTRACT FROM AUTHOR]

Direct and two inverse problems for a Legendre equation involving integral convolution in time are studied. The inverse problems are ill-posed in the sense of Hadamard. The analytical series solutions of the problems are constructed by using method of variable separation. The determination of only u(x, y) is studied in the direct problem, the recovery of a pair of functions, i.e., { u (x , y) , f (x) } with appropriate addition data at some T is investigated in the 1st inverse problem while the identification of a pair of functions, i.e., { u (x , y) , q (y) } with an integral type data is considered in the 2nd inverse problem. By imposing certain regularity conditions, the unique existence of series solutions is developed. We provided some numerical examples to illustrate our results for the inverse problems. [ABSTRACT FROM AUTHOR]

Fractional derivatives are suitable for describing several physical phenomena. The construction of efficient analytical and numerical methods for the solutions of ordinary and partial fractional differential equations is an active research area and it is of great interest to the researchers. The Caputo fractional derivative is of great use in the modelling and simulation of phenomena where consideration is given to the interactions within the past and problems with nonlocal properties. This study considers the use of a hybrid of the Sumudu Transform method for constructing the solution of nonlinear equations that describe the processes in the functional and structural materials. This study considers the models that are given by the integer-order derivatives, Caputo derivatives of fractional variable orders and Caputo derivatives of fractional variable orders that are associated with delays. The study applies a hybrid of Sumudu Transform to present solutions for each considered model and makes use of graphs to show the correlation among the models. The study is of great importance in the numerical and experimental characterization of the decay properties of functional and structural materials. [ABSTRACT FROM AUTHOR]

Summary This paper contributes to the study of a new model called the q$$ \mathfrak{q} $$‐deformed equation or the q$$ \mathfrak{q} $$‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the G′kG′+G+r$$ \left(\frac{{\mathcal{G}}^{\prime }}{k{\mathcal{G}}^{\prime }+\mathcal{G}+r}\right) $$‐expansion approach to solve the q$$ \mathfrak{q} $$‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the q$$ \mathfrak{q} $$‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The q$$ \mathfrak{q} $$‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the q$$ \mathfrak{q} $$‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of q$$ \mathfrak{q} $$‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations appear in various branches of physics, including fluid dynamics, solid mechanics, quantum mechanics, and other fields. They are essential for describing systems where interactions and nonlinearity play a significant role, providing a more accurate representation of real-world phenomena than linear equations in certain cases. The study of nonlinear evolution equations involves exploring their solutions, stability properties, and the behavior of the systems they describe over time. In this study, we provide plenty of analytical solutions to a very recently proposed water wave model using the modified generalized exponential rational function, modified extended tanh-function, and the exp(−φ(ξ))-expansion methods. To examine the dynamic characteristics of these results, we displayed three-dimensional (3D), contour, and two-dimensional (2D) visual representations of specific solutions. The outcomes reveal a multitude of novel solutions, emphasizing the robustness and effectiveness of the applied methodologies. It is important to note that all the solutions derived in this study are original and have not been previously documented in the existing literature. These novel solutions hold significant value for researchers in the realms of fluids and plasma physics, providing insights into the dynamics of nonlinear waves within various physical systems. Furthermore, this research contributes to a deeper understanding of the nature of nonlinear waves prevalent in seas and oceans, offering valuable knowledge for the broader study of such phenomena. [ABSTRACT FROM AUTHOR]

Electrokinetic flows driven by electro-osmotic forces are especially relevant in micro and nano-devices, presenting specific applications in medicine, biochemistry, and miniaturized industrial processes. In this work, we integrate analytical solutions with numerical methodologies to explore the fluid dynamics of viscoelastic electro-osmotic/pressure-driven fluid flows (described by the generalized Phan–Thien–Tanner (gPTT) constitutive equation) in a microchannel under asymmetric zeta potential conditions. The constitutive equation incorporates the Mittag–Leffler function with two parameters (α and β ), which regulate the rate of destruction of junctions in a network model. We analyze the impact of the various model parameters on the velocity profile and observe that our newly proposed model provides a more comprehensive depiction of flow behavior compared to traditional models, rendering it suitable for modeling complex viscoelastic flows. [ABSTRACT FROM AUTHOR]

Fractional calculus is a method to predict processes mathematically. This study uses fractional order models to determine whether starch hydration is governed by Fickian or anomalous diffusion. Native and modified starches are compared and classified based on their diffusive characteristics and the type of diffusion observed. The study aims to adjust the equation of the analytical solution of the diffusion model to study the hydration of both native and modified starches. The fractional order diffusion model is generalized to compare the two models and identify whether anomalous mechanisms exist in native and modified starches. The results show that water absorption by native and modified starch granules is characterized by anomalous diffusion. This is due to the temperature conditions and differences in the chemical potential of the starches. It is verified that the diffusive characteristics of native and modified starches differ under the same hydration conditions. [ABSTRACT FROM AUTHOR]

The capacity of the circumferential joint of the precast concrete segmental tunnel lining (PCTL) structure in terms of shear performance principally includes the dowel action by connector/bolt as well as friction force, and it is a vital parameter to assess the mechanical response of the circumferential joint. Further, as there was no analytical model available for precise estimation of a circumferential joint in terms of the shear‐bearing capacity considering the dowel action of the bolt in the presence of axial/normal force, therefore in this investigation, an analytical model has been proposed to estimate the shear‐bearing capacity of the circumferential joint. Furthermore, the analytical model's precision and accuracy were validated via large‐scale experimental investigation on a circumferential joint of PCTL. Upon comparing analytical model outcomes with experimental results, absolute error varied between +5% and −9%, with an average value of the coefficient of friction at the yield point of the bolt. Moreover, the formation of hinges on the side of the bolt within the segment was considered a failure of the circumferential joint. Additionally, the parametric investigation revealed that with just a 1% change in axial force, the diameter, pre‐tightening, and yield strength of the bolt and concrete strength improved by 2.85%, 1%, 0.27%, 0.26% and 0.17% shear‐bearing capacity of the circumferential joint respectively. Axial force variation greatly influences the shear‐bearing capacity of circumferential joint followed by diameter, pre‐tightening, yield strength of the bolt, and concrete strength. Conclusively, with analysis of axial force distribution around the ring for the tunnel, the proposed model has been applied to a full ring to estimate shear bearing capacity. [ABSTRACT FROM AUTHOR]

Based on Biot's dynamic wave theory and Novak's plane strain model (PSM), an analytical model for the horizontal vibration of a partially embedded pipe pile group (PEPPG) in layered saturated soil (LSS) that considers the soil‐plugging effect was established: First, the frequency‐domain analytical expressions of the saturated surrounding soil (SSS) and soil plug were obtained by introducing operator decomposition theory and the variable separation method. Second, the analytical solution of the horizontal impedance of a partially embedded pipe pile in the LSS is derived using the coupled condition of the pile–soil interface and transfer matrix method. Finally, an analytical solution for the horizontal impedance of PEPPG in LSS was derived by introducing the horizontal dynamic interaction factor of piles and the superposition method. The derived solution is then reduced and compared with existing theoretical solutions to verify its rationality. In addition, further parametric analysis was conducted to investigate the influences of pile spacing, embedment ratio, properties of layered SSS, and soil‐plugging on the horizontal vibration characteristics (HVCs) of PEPPG. [ABSTRACT FROM AUTHOR]

Many of the most intriguing features, including spirals and cavities, in the current disc observations are found in binary systems like GG Tau, HD 142527, or HD 100453. Such features are evidence of the dynamic interactions between binary stars and the viscous disc. Understanding these dynamic interactions and how they result in the structure and growth of asymmetric circumbinary discs is a difficult problem, for which there is no complete analytical solution, that predicts the shape of the observed disc accurately. We use numerical simulations to evolve circumbinary discs with varying disc viscosities and investigate the size and shape of the inner cavities in such protoplanetary discs. We have simulated over 140 locally isothermal 2D grid-based disc models for |$\ge$| 3 × 104 binary orbits each and mapped out the parameter space relevant for protoplanetary discs. With this, it becomes possible to create parametrized profiles for individual discs to compare to observations and find limits to their binary eccentricity or internal viscosity from the simulation data. In the long-term simulations, larger cavity sizes than previously considered are possible within the parameter space (⁠|$\le$| 6 binary separations). As an example, we find that the eccentricity of the disc around HD 142527 suggests the impact of the binary dynamics on the disc. However, even considering the larger cavity sizes, the large size of the cavity in HD 142527 remains unexplained by the simulations considering the most recent orbital constraints. [ABSTRACT FROM AUTHOR]

Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between g Y M 2 (generalized two-dimensional Yang–Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang–Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, g Y M 2 (for G (z) = z m + λ z n ; m = 4 , 6 ; n < m ) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained. [ABSTRACT FROM AUTHOR]

Complex and nonlinear fractal equations are ubiquitous in natural phenomena. This research employs the fractal Euler−Lagrange and semi-inverse methods to derive the nonlinear space–time fractal Fornberg–Whitham equation. This derivation provides an in-depth comprehension of traveling wave propagation. Consequently, the nonlinear space–time fractal Fornberg–Whitham equation is pivotal in elucidating fundamental phenomena across applied sciences. A novel analytical technique, the generalized Kudryashov method, is presented to address the space–time fractal Fornberg–Whitham equation. This method combines the fractional complex approach with the modified Kudryashov method to enhance its effectiveness. We derive an analytical solution for the space–time fractal Fornberg–Whitham equation to elucidate how various parameters influence the propagation of new traveling wave solutions. Furthermore, Figures 1 through 6 analyze the impact of parameters α , β , b 1 , and k on these new traveling wave solutions. Our results show that the solitary wave solutions remain intact for both case 1 and case 2, regardless of the time fractional orders β . At the end, the manuscript discusses the implications of these findings for understanding complex wave phenomena, paving the way for further exploration and applications in wave propagation studies. [ABSTRACT FROM AUTHOR]

The article highlights the growing importance of computational mathematics in tackling intricate real-world phenomena governed by distributed order fractional dynamics. These dynamics, characterized by memory effects and non-local interactions, are pervasive in various fields such as physics, biology, finance, and engineering. Despite their prevalence, analytical solutions for distributed order fractional differential equations remain difficult to find, necessitating the development of robust numerical methods. The paper explores the effectiveness of Romanovski–Jacobi spectral collocation techniques in this context and provides a thorough analysis of how to use them to solve distributed order fractional differential equations. By leveraging these schemes, researchers gain valuable insights into efficiently analyzing and simulating fractional systems, thereby advancing our understanding of complex dynamics across diverse domains. It provides precise numerical findings by using finite expansion to evaluate residuals. The precision of the approach is illustrated by numerical simulations, especially in distributed order fractional differential equations. Additionally, we provide a few numerical tests to demonstrate the method's ability to preserve the underlying problem's non-smooth solution. [ABSTRACT FROM AUTHOR]