Transition from Discrete to Continuous Media: The Impact of Symmetry Changes on Asymptotic Behavior of Waves

This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete case, Schrödinger’s analytical solution of the initial-value problem for the Lagrange lattice is used. Various continuous approximations are proposed to approximate the lattice. They are based on Debye’s concept of quasicontinuum. The asymptotics of the initial motion and the behavior of the systems in the vicinity of the quasifront and at large times are compared. The approximations of phase and group velocities is analyzed. The merits and limitations of the described approaches are discussed.

A Computational Framework for Design and Optimization of Flexoelectric Materials

We combine isogeometric analysis (IGA), level set (LS) and pointwise density-mapping techniques for design and topology optimization of piezoelectric/flexoelectric materials. We use B-spline elements to discretize the fourth-order partial differential equations of flexoelectricity, which require at least [Formula: see text] continuous approximations. We adopt the multiphase vector LS model which easily copes with various numbers of material phases and multiple constraints. In case studies, we first confirm the accuracy of the IGA model and then provide numerical examples for both pure and composite flexoelectric structures. The results demonstrate the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization and particularly by multi-material topology optimization for flexoelectric composites.

NIGHT DELIVERIES AND CARRIER-LED CONSOLIDATION STRATEGIES TO IMPROVE URBAN GOODS DISTRIBUTION

Night distribution and consolidation strategies have been proposed in many cities to increase the efficiency of the urban goods distribution system and to reduce the external effects that it causes in terms of emissions. However, the deployment of these initiatives presents a new reallocation of costs and incomes among collaborative stakeholders that take part in. In this paper, an analytical model to estimate the new economic effects caused by these strategies on the involved agents is presented, based on continuous approximations. This model allows decision makers to estimate the transportation cost and emissions savings that will be obtained by each strategy as well as the range of retailer demand in which these strategies are not economically feasible. The results show that night distribution generally outperforms the carrier cost reduction and emissions savings, especially when large vehicles are used in night periods.

On Numerical Integration of Discontinuous Dynamical Systems

This paper addresses an important issue in numerical integration of dynamical systems, integer- or fractional-order, with discontinuous vector fields. It is shown that these systems cannot be solved using numerical methods designed for ODEs with continuous functions on the right-hand side, therefore we have to resort to special schemes and procedures in numerical integrations such as continuous approximations of the right-hand sides of the ODEs.

Fitting mechanistic epidemic models to data: a comparison of simple Markov chain Monte Carlo approaches

BackgroundSimple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).ResultsModels incorporating at least one source of population-level variation (i.e., dispersion in either the transmission process or the observation process) provide reasonably good forecasts and parameter estimates, while models that incorporate only individual-level variation can lead to inaccurate (or overconfident) results. Models using continuous approximations to the transmission process showed improved computational efficiency without loss of accuracy.ConclusionSimple models of disease transmission and observation can be fitted reliably to simple simulations, as long as population-level variation is taken into account. Continuous approximations can improve computational efficiency using more advanced MCMC techniques.

Numerical Determination of Pseudobreathers of a Three-Dimensional Spherically Symmetric Wave Equation

A numerical method for finding spherically symmetric pseudobreathers of a nonlinear wave equation is presented. The algorithm, based on pseudospectral methods, is applied to find quasi-periodic solutions with force terms being continuous approximations of the signum function. The obtained pseudobreathers slowly radiate energy and decay after some (usually long) time depending on the period that characterizes (unambiguously) the initial configuration.