2063 research outputs found
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The role of the particle aspect ratio in the discharge of a narrow silo
Get PDFThe time evolution of silo discharge is investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, we confirm the widely known typical behavior with constant discharge rate (except for initial and final transients). For elongated particles with aspect ratios between 2 ⩽ L/d ⩽ 6.1, we find a peculiar flow rate increase for larger orifices before the end of the discharge process. While the flow field is practically homogeneous for spherical grains, it has strong gradients for elongated particles with a fast-flowing region in the middle of the silo surrounded by a stagnant zone. For large enough orifice sizes, the flow rate increase is connected with a suppression of the stagnant zone, resulting in an increase in both the packing fraction and flow velocity near the silo outlet within a certain parameter range
AdaSwarm: Augmenting Gradient-Based Optimizers in Deep Learning with Swarm Intelligence
Get PDFThis paper introduces AdaSwarm, a novel gradient-free optimizer which has similar or even better performance than the Adam optimizer adopted in neural networks. In order to support our proposed AdaSwarm, a novel Exponentially weighted Momentum Particle Swarm Optimizer (EMPSO), is proposed. The ability of AdaSwarm to tackle optimization problems is attributed to its capability to perform good gradient approximations. We show that, the gradient of any function, differentiable or not, can be approximated by using the parameters of EMPSO. This is a novel technique to simulate GD which lies at the boundary between numerical methods and swarm intelligence. Mathematical proofs of the gradient approximation produced are also provided. AdaSwarm competes closely with several state-of-the-art (SOTA) optimizers. We also show that AdaSwarm is able to handle a variety of loss functions during backpropagation, including the maximum absolute error (MAE)
Multiple source transfer learning for dynamic multiobjective optimization
Get PDFRecently, dynamic multiobjective evolutionary algorithms (DMOEAs) with transfer learning have become popular for solving dynamic multiobjective optimization problems (DMOPs), as the used transfer learning methods in DMOEAs can effectively generate a good initial population for the new environment. However, most of them only transfer non-dominated solutions from the previous one or two environments, which cannot fully exploit all historical information and may easily induce negative transfer as only limited knowledge is available. To address this problem, this paper presents a multiple source transfer learning method for DMOEA, called MSTL-DMOEA, which runs two transfer learning procedures to fully exploit the historical information from all previous environments. First, to select some representative solutions for knowledge transfer, one clustering-based manifold transfer learning is run to cluster non-dominated solutions of the last environment to obtain their centroids, which are then fed into the manifold transfer learning model to predict the corresponding centroids for the new environment. After that, multiple source transfer learning is further run by using multisource TrAdaboost, which can fully exploit information from the above centroids in new environment and old centroids from all previous environments, aiming to construct a more accurate prediction model. This way, MSTL-DMOEA can predict an initial population with better quality for the new environment. The experimental results also validate the superiority of MSTL-DMOEA over several competitive state-of-the-art DMOEAs in solving various kinds of DMOPs
The tempered space-fractional Cattaneo equation
Get PDFWe consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. There is an increasing interest in the recent literature for the applications of the fractional-type Cattaneo equations to heat transfer models. Our main aim is to discuss the role played by a fractional tempered operator in this framework. We show that the fundamental solution coincides with the probability law of a time-changed Brownian motion, obtained by means of a tempered stable subordinator. We find the characteristic function of this process and we explain the main differences with previous stochastic treatments of the time-fractional Cattaneo equation. We also provide the solution of a Dirichlet problem for the tempered fractional Cattaneo equation by means of the H-Fox function.BERC 2018–2021
PID2019- 107685RB-I0
A painless multi-level automatic goal-oriented hp-adaptive coarsening strategy for elliptic and non-elliptic problems
Get PDFThis work extends an automatic energy-norm -adaptive strategy based on performing quasi-optimal unrefinements to the case of non-elliptic problems and goal-oriented adaptivity. The proposed approach employs a multi-level hierarchical data structure and alternates global - and -refinements with a coarsening step. Thus, at each unrefinement step, we eliminate the basis functions with the lowest contributions to the solution. When solving elliptic problems using energy-norm adaptivity, the removed basis functions are those with the lowest contributions to the energy of the solution. For non-elliptic problems or goal-oriented adaptivity, we propose an upper bound of the error representation expressed in terms of an inner product of the specific equation, leading to error indicators that deliver quasi-optimal -unrefinements. This unrefinement strategy removes unneeded unknowns possibly introduced during the pre-asymptotical regime. In addition, the grids over which we perform the unrefinements are arbitrary, and thus, we can limit their size and associated computational costs. We numerically analyze our algorithm for energy-norm and goal-oriented adaptivity. In particular, we solve two-dimensional (D) Poisson, Helmholtz, convection-dominated equations, and a three-dimensional (D) Helmholtz-like problem. In all cases, we observe \revb{exponential} convergence rates. Our algorithm is robust and straightforward to implement; therefore, it can be easily adapted for industrial applications.BERC.2022-202
Exploring the link between coffee matrix microstructure and flow properties using combined X‐ray microtomography and smoothed particle hydrodynamics simulations
Get PDFCoffee extraction involves many complex physical and transport processes extremely difficult to model. Among the many factors that will affect the final quality of coffee, the microstructure of the coffee matrix is one of the most critical ones. In this article, we use X-ray micro-computed (microCT) technique to capture the microscopic details of coffee matrices at particle-level and perform fluid dynamics simulation based on the smoothed particle hydrodynamics method (SPH) with the 3D reconstructured data. Information like flow permeability and tortuosity of the matrices can be therefore obtained from our simulation. We found that inertial effects can be quite significant at the normal pressure gradient conditions typical for espresso brewing, and can provide an explanation for the inconsistency of permeability measurements seen in the literature. Several types of coffee powder are further examined, revealing their distinct microscopic details and resulting flow features. By comparing the microCT images of pre- and post-extraction coffee matrices, it is found that a decreasing porosity profile (from the bottom-outlet to the top-inlet) always develops after extraction. This counterintuitive phenomenon can be explained using a pressure-dependent erosion model proposed in our prior work. Our results reveal not only some important hydrodynamic mechanisms of coffee extraction, but also show that microCT scan can provide useful microscopic details for coffee extraction modelling. MicroCT scan establishes the basis for a data-driven numerical framework to explore the link between coffee powder microstructure and extraction dynamics, which is the prerequisite to study the time evolution of both volatile and non-volatile organic compounds and then the flavour profile of coffee brews.ILLYcaff
Some remarks on oscillation inequalities
Get PDFIn this paper, we establish uniform oscillation estimates on Lp(X) with p ∈ (1, ∞) for the polynomial ergodic averages. This result contributes to a certain problem about uniform oscillation bounds for ergodic averages formulated by Rosenblatt and Wierdl in the early 1990s [Pointwise ergodic theorems via harmonic analysis. Proceedings of Conference on Ergodic Theory (Alexandria, Egypt, 1993) (London Mathematical Society Lecture Notes, 205). Eds. K. Petersen and I. Salama. Cambridge University Press, Cambridge, 1995, pp. 3–151]. We also give a slightly different proof of the uniform oscillation inequality of Jones, Kaufman, Rosenblatt, and Wierdl for bounded martingales [Oscillation in ergodic theory. Ergod. Th. & Dynam. Sys. 18(4) (1998), 889–935]. Finally, we show that oscillations, in contrast to jump inequalities, cannot be seen as an endpoint for r-variation inequalities
On numerical solution of Fredholm and Hammerstein integral equations via Nystr\"{o}m method and Gaussian quadrature rules for splines
Get PDFNystr\"{o}m method is a standard numerical technique to solve Fredholm integral equations of the second kind where the integration of the kernel is approximated using a quadrature formula. Traditionally, the quadrature rule used is the classical polynomial Gauss quadrature. Motivated by the observation that a given function can be better approximated by a spline function of a lower degree than a single polynomial piece of a higher degree, in this work, we investigate the use of Gaussian rules for splines in the Nystr\"{o}m method. We show that, for continuous kernels, the approximate solution of linear Fredholm integral equations computed using spline Gaussian quadrature rules converges to the exact solution for , being the number of quadrature points. Our numerical results also show that, when fixing the same number of quadrature points, the approximation is more accurate using spline Gaussian rules than using the classical polynomial Gauss rules. We also investigate the non-linear case, considering Hammerstein integral equations, and present some numerical tests.RYC-2017-2264
Effect of General Cross-Immunity Protection and Antibody- Dependent Enhancement in Dengue Dynamics
Get PDFA mathematical model to describe the dynamic of a multiserotype infectious disease at the population level is studied. Applied to
dengue fever epidemiology, we analyse a mathematical model with time delay to describe the cross-immunity protection period,
including a key parameter for the antibody-dependent enhancement (ADE) effect, the well-known features of dengue fever
infection. Numerical experiments are performed to show the stability of the coexistence equilibrium, which is completely
determined by the basic reproduction number and by the invasion reproduction number, as well as the bifurcation structures
for different scenarios of dengue fever transmission in a population. The model shows a rich dynamical behavior, from fixed
points and periodic oscillations up to chaotic behaviour with complex attractors.Laboratory for
Industrial and Applied Mathematics (LIAM), Department
of Mathematics and Statistics, York University, CA
Almost Sure Pointwise Convergence of the Cubic Nonlinear Schrödinger Equation on {T}^2
No full textAbstract. We revisit a result from “Pointwise convergence of the Schr¨odinger
flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research
Notices, 2021 (1), 596-647” regarding the pointwise convergence of solutions
to the periodic cubic nonlinear Schr¨odinger equation in dimension d = 2