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The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.

Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.

Failed deliveries (i.e. deliveries not accomplished due to the absence of customers) represent a critical issue in B2C (Business-to-consumer) e-commerce last-mile deliveries, implying high costs for e-commerce players and negatively affecting customer satisfaction. A promising option to reduce them would be scheduling deliveries based on the probability to find customers at home. This work proposes a solution based on presence data (gathered through Internet of Things [IoT] devices) to organise the delivery tours, which aims to both minimise the travelled distance and maximise the probability to find customers at home.

The adopted methodology is a multi-method approach, based on interviews with practitioners. A model is developed and applied to Milan (Italy) to compare the performance of the proposed innovative solution with traditional home deliveries (both in terms of cost and delivery success rate).

The proposed solution implies a significant reduction of missed deliveries if compared to the traditional operating mode. Accordingly, even if allocating the customers to time windows based on their availability profiles (APs) entails an increase in the total travel time, the average delivery cost per parcel decreases.

On the academic side, this work proposes and evaluates an innovative last-mile delivery (LMD) solution that exploits new AI (Artificial Intelligence)-based technological trends. On the managerial side, it proposes an efficient and effective novel option for scheduling last-mile deliveries based on the use of smart home devices, which has a significant impact in reducing costs and increasing the service level.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

There are a number of different approaches for calculating creep-fatigue (CF) damage for design, such as the French nuclear code RCC-MRx, the American ASME III NH and the British R5 assessment code. To acquire estimates for the CF damage, that are not overly conservative, both the cyclic material softening/hardening and the potential changes in relaxation behavior have to be considered. The data presented here and models are an initial glimpse of the ongoing European FP7 project MATISSE effort to model the softening and relaxation behavior of Grade 91 steel under CF loading. The resulting models are used for calculating the relaxed stress at arbitrary location in the material cyclic softening curve. The initial test results show that softening of the material is not always detrimental. The initial model development and the pre-assessment of the MATISSE data show that the relaxed stress can be robustly predicted with hold time, strain range and the cyclic life fraction as the main input parameters. The paper aims to discuss these issues.

Engineering models have been developed for predicting cyclic softening and relaxation for Gr. 91 steel at 550 and 600°C.

A simple engineering model can adequately predict the low cycle fatigue (LCF) and CF softening rates of Gr. 91 steel. Also a simple relaxation model was successfully defined for predicting relaxed stress of both virgin and cyclically softened material.

The data are not yet complete and the models will be updated when the complete set of data in the MATISSE project is available.

The models described can be used for predicting P91 material softening in an arbitrary location (n/N_f0) of the LCF and CF cyclic life. Also the relaxed stress in the softened material can be estimated.

The models are simple in nature but are able to estimate both material softening and relaxation in arbitrary location of the softening curve. This is the first time the Wilshire methodology has been applied on cyclic relaxation data.

This study aims to propose an offline exploratory method that consists of two stages: first, the authors focus on completing the kinematics model of the system by analyzing the Jacobians in the vicinity of the starting point and deducing a virtual input to effectively navigate the system along the non-holonomic constraint. Second, the authors explore the sensorimotor space in a predetermined pattern and obtain an approximate mapping from sensor space to chained form that facilitates controllability.

In this paper, the authors tackle the controller acquisition problem of unknown sensorimotor model in non-holonomic driftless systems. This feature is interesting to simplify and speed up the process of setting up industrial mobile robots with feedback controllers.

The authors validate the approach for the test case of the unicycle by controlling the system with time-state control policy. The authors present simulated and experimental results that show the effectiveness of the proposed method, and a comparison with the proximal policy optimization algorithm.

This research indicates clearly that feedback control of non-holonomic systems with uncertain kinematics and unknown sensor configuration is possible.